Question bank

test nlgraph-connectivity-test-341

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,8,1],[0,1,1],[0,6,1],[0,2,1],[0,3,1],[0,7,1],[0,5,1],[1,8,1],[1,6,1],[1,2,1],[1,3,1],[1,7,1],[1,5,1],[2,8,1],[2,6,1],[2,3,1],[2,7,1],[2,5,1],[3,8,1],[3,6,1],[3,7,1],[3,5,1],[5,8,1],[5,6,1],[5,7,1],[6,8,1],[6,7,1],[7,8,1]],"nodes":[0,1,2,3,4,5,6,7,8],"source":4,"target":8}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-293

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[2,3,1],[2,5,1],[3,5,1],[4,6,1]],"nodes":[0,2,3,4,5,6],"source":3,"target":2}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-278

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,7,1],[0,9,1],[0,8,1],[0,19,1],[0,13,1],[0,11,1],[1,15,1],[1,6,1],[1,3,1],[1,12,1],[1,4,1],[1,2,1],[1,23,1],[1,5,1],[1,16,1],[1,22,1],[1,17,1],[1,18,1],[1,21,1],[1,24,1],[1,25,1],[2,15,1],[2,3,1],[2,4,1],[2,20,1],[2,23,1],[2,22,1],[2,27,1],[2,18,1],[2,21,1],[2,24,1],[3,15,1],[3,4,1],[3,26,1],[3,20,1],[3,23,1],[3,5,1],[3,16,1],[3,14,1],[3,22,1],[3,27,1],[3,18,1],[3,21,1],[3,24,1],[3,25,1],[4,15,1],[4,6,1],[4,12,1],[4,26,1],[4,20,1],[4,5,1],[4,22,1],[4,27,1],[4,17,1],[4,21,1],[4,25,1],[5,15,1],[5,6,1],[5,12,1],[5,20,1],[5,16,1],[5,14,1],[5,22,1],[5,27,1],[5,18,1],[5,21,1],[5,25,1],[6,15,1],[6,12,1],[6,27,1],[6,17,1],[6,21,1],[6,24,1],[6,25,1],[7,19,1],[7,13,1],[8,9,1],[8,19,1],[8,13,1],[9,19,1],[9,10,1],[10,19,1],[10,13,1],[10,11,1],[11,13,1],[12,15,1],[12,26,1],[12,20,1],[12,14,1],[12,22,1],[12,21,1],[12,24,1],[13,19,1],[14,15,1],[14,26,1],[14,20,1],[14,16,1],[14,22,1],[14,17,1],[14,21,1],[14,24,1],[14,25,1],[15,26,1],[15,20,1],[15,23,1],[15,16,1],[15,22,1],[15,17,1],[15,18,1],[15,24,1],[16,26,1],[16,27,1],[16,18,1],[16,25,1],[17,26,1],[17,23,1],[17,18,1],[17,21,1],[17,24,1],[17,25,1],[18,26,1],[18,20,1],[18,22,1],[18,27,1],[18,24,1],[18,25,1],[20,26,1],[20,23,1],[20,22,1],[20,27,1],[20,24,1],[20,25,1],[21,22,1],[21,27,1],[21,24,1],[21,25,1],[22,23,1],[22,27,1],[22,24,1],[22,25,1],[23,27,1],[23,25,1],[24,26,1],[24,27,1],[25,26,1],[25,27,1],[26,27,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],"source":15,"target":18}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-6

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,26,1],[0,10,1],[0,15,1],[0,21,1],[0,1,1],[0,7,1],[0,29,1],[0,24,1],[0,16,1],[0,23,1],[0,17,1],[1,26,1],[1,10,1],[1,15,1],[1,7,1],[1,28,1],[1,29,1],[1,12,1],[1,24,1],[1,16,1],[1,3,1],[1,23,1],[2,14,1],[2,27,1],[2,34,1],[3,26,1],[3,32,1],[3,15,1],[3,21,1],[3,7,1],[3,28,1],[3,29,1],[3,12,1],[3,24,1],[3,23,1],[3,17,1],[4,9,1],[4,14,1],[4,27,1],[4,31,1],[5,19,1],[5,22,1],[5,13,1],[5,20,1],[5,25,1],[5,30,1],[5,8,1],[5,33,1],[6,9,1],[6,27,1],[6,34,1],[6,31,1],[7,26,1],[7,32,1],[7,10,1],[7,15,1],[7,21,1],[7,29,1],[7,12,1],[7,24,1],[7,16,1],[7,23,1],[7,17,1],[8,19,1],[8,22,1],[8,13,1],[8,20,1],[8,25,1],[8,18,1],[8,30,1],[8,33,1],[9,14,1],[9,34,1],[10,32,1],[10,15,1],[10,21,1],[10,29,1],[10,24,1],[10,23,1],[10,17,1],[11,19,1],[11,22,1],[11,13,1],[11,25,1],[11,18,1],[11,30,1],[12,26,1],[12,32,1],[12,15,1],[12,21,1],[12,24,1],[12,16,1],[12,23,1],[13,19,1],[13,20,1],[13,25,1],[13,18,1],[13,33,1],[14,27,1],[14,31,1],[15,26,1],[15,21,1],[15,28,1],[15,24,1],[15,16,1],[15,23,1],[15,17,1],[16,26,1],[16,32,1],[16,23,1],[16,17,1],[17,26,1],[17,32,1],[17,21,1],[17,28,1],[17,24,1],[18,19,1],[18,22,1],[18,20,1],[18,30,1],[19,22,1],[19,20,1],[19,25,1],[19,30,1],[20,25,1],[20,30,1],[20,33,1],[21,26,1],[21,32,1],[21,28,1],[21,29,1],[22,25,1],[22,30,1],[22,33,1],[23,32,1],[23,28,1],[23,29,1],[23,24,1],[24,32,1],[24,28,1],[25,30,1],[25,33,1],[26,32,1],[26,28,1],[27,31,1],[28,29,1],[30,33,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],"source":17,"target":28}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-170

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,9,1],[1,8,1],[1,4,1],[2,8,1],[2,4,1],[2,3,1],[3,7,1],[3,6,1],[3,10,1],[3,12,1],[3,11,1],[4,10,1],[4,12,1],[6,14,1],[6,8,1],[6,10,1],[7,14,1],[7,11,1],[8,14,1],[8,12,1],[10,14,1],[11,14,1],[12,14,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,14],"source":9,"target":10}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-85

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,29,1],[1,27,1],[1,24,1],[1,21,1],[1,3,1],[2,10,1],[2,22,1],[2,6,1],[2,18,1],[2,25,1],[2,12,1],[3,19,1],[3,27,1],[3,24,1],[4,10,1],[4,6,1],[4,18,1],[4,25,1],[5,28,1],[5,16,1],[6,10,1],[6,13,1],[6,25,1],[6,12,1],[6,9,1],[7,28,1],[8,10,1],[8,14,1],[8,18,1],[8,29,1],[8,25,1],[8,23,1],[9,13,1],[9,14,1],[10,29,1],[10,25,1],[12,22,1],[12,18,1],[12,17,1],[13,29,1],[13,26,1],[14,20,1],[14,17,1],[15,19,1],[17,25,1],[18,20,1],[18,25,1],[20,29,1],[20,26,1],[20,23,1],[21,27,1],[21,24,1],[23,26,1],[23,25,1],[24,27,1],[26,29,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],"source":23,"target":22}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-351

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,13,1],[0,2,1],[0,15,1],[0,6,1],[0,17,1],[0,8,1],[0,16,1],[0,18,1],[0,9,1],[0,12,1],[0,11,1],[1,10,1],[1,14,1],[1,7,1],[1,5,1],[1,4,1],[2,3,1],[2,13,1],[2,15,1],[2,6,1],[2,17,1],[2,8,1],[2,16,1],[2,18,1],[2,9,1],[2,12,1],[2,11,1],[3,13,1],[3,15,1],[3,6,1],[3,17,1],[3,8,1],[3,16,1],[3,18,1],[3,9,1],[3,12,1],[3,11,1],[4,10,1],[4,14,1],[4,7,1],[4,5,1],[5,10,1],[5,14,1],[5,7,1],[6,13,1],[6,15,1],[6,17,1],[6,8,1],[6,16,1],[6,18,1],[6,9,1],[6,12,1],[6,11,1],[7,10,1],[7,14,1],[8,13,1],[8,15,1],[8,17,1],[8,16,1],[8,18,1],[8,9,1],[8,12,1],[8,11,1],[9,13,1],[9,15,1],[9,17,1],[9,16,1],[9,18,1],[9,12,1],[9,11,1],[10,14,1],[11,13,1],[11,15,1],[11,17,1],[11,16,1],[11,18,1],[11,12,1],[12,13,1],[12,15,1],[12,17,1],[12,16,1],[12,18,1],[13,15,1],[13,17,1],[13,16,1],[13,18,1],[15,17,1],[15,16,1],[15,18,1],[16,17,1],[16,18,1],[17,18,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"source":1,"target":6}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✗ wrong
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-261

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,10,1],[0,15,1],[0,22,1],[0,18,1],[1,5,1],[1,14,1],[1,21,1],[1,16,1],[1,19,1],[1,3,1],[1,17,1],[1,13,1],[1,11,1],[1,2,1],[1,20,1],[1,8,1],[1,6,1],[1,12,1],[1,9,1],[1,7,1],[2,5,1],[2,14,1],[2,21,1],[2,16,1],[2,19,1],[2,3,1],[2,17,1],[2,13,1],[2,11,1],[2,20,1],[2,8,1],[2,6,1],[2,12,1],[2,9,1],[2,7,1],[3,5,1],[3,14,1],[3,21,1],[3,16,1],[3,19,1],[3,17,1],[3,13,1],[3,11,1],[3,20,1],[3,8,1],[3,6,1],[3,12,1],[3,9,1],[3,7,1],[5,14,1],[5,21,1],[5,16,1],[5,19,1],[5,17,1],[5,13,1],[5,11,1],[5,20,1],[5,8,1],[5,6,1],[5,12,1],[5,9,1],[5,7,1],[6,14,1],[6,21,1],[6,16,1],[6,19,1],[6,17,1],[6,13,1],[6,11,1],[6,20,1],[6,8,1],[6,12,1],[6,9,1],[6,7,1],[7,14,1],[7,21,1],[7,16,1],[7,19,1],[7,17,1],[7,13,1],[7,11,1],[7,20,1],[7,8,1],[7,12,1],[7,9,1],[8,14,1],[8,21,1],[8,16,1],[8,19,1],[8,17,1],[8,13,1],[8,11,1],[8,20,1],[8,12,1],[8,9,1],[9,14,1],[9,21,1],[9,16,1],[9,19,1],[9,17,1],[9,13,1],[9,11,1],[9,20,1],[9,12,1],[10,15,1],[10,22,1],[10,18,1],[11,14,1],[11,21,1],[11,16,1],[11,19,1],[11,17,1],[11,13,1],[11,20,1],[11,12,1],[12,14,1],[12,21,1],[12,16,1],[12,19,1],[12,17,1],[12,13,1],[12,20,1],[13,14,1],[13,21,1],[13,16,1],[13,19,1],[13,17,1],[13,20,1],[14,21,1],[14,16,1],[14,19,1],[14,17,1],[14,20,1],[15,22,1],[15,18,1],[16,21,1],[16,19,1],[16,17,1],[16,20,1],[17,21,1],[17,19,1],[17,20,1],[18,22,1],[19,21,1],[19,20,1],[20,21,1]],"nodes":[0,1,2,3,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],"source":2,"target":15}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-196

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,31,1],[0,11,1],[0,27,1],[0,18,1],[1,4,1],[1,12,1],[1,31,1],[1,7,1],[1,25,1],[1,8,1],[1,18,1],[2,17,1],[2,14,1],[2,6,1],[2,10,1],[2,19,1],[3,17,1],[3,22,1],[3,9,1],[4,12,1],[4,30,1],[4,31,1],[4,13,1],[4,27,1],[4,18,1],[5,29,1],[5,16,1],[5,22,1],[5,21,1],[5,20,1],[5,28,1],[5,19,1],[6,29,1],[6,9,1],[6,10,1],[6,28,1],[7,11,1],[7,27,1],[7,15,1],[7,18,1],[8,30,1],[8,23,1],[8,11,1],[9,14,1],[9,21,1],[9,10,1],[11,23,1],[11,18,1],[12,30,1],[12,31,1],[12,27,1],[12,25,1],[12,15,1],[12,18,1],[13,23,1],[13,25,1],[13,15,1],[14,29,1],[14,17,1],[16,24,1],[16,17,1],[16,20,1],[17,29,1],[18,30,1],[18,26,1],[20,29,1],[21,24,1],[22,24,1],[23,27,1],[23,25,1],[25,26,1],[25,27,1],[26,31,1],[27,31,1],[28,29,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],"source":26,"target":13}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-183

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,12,1],[0,4,1],[0,9,1],[0,1,1],[0,11,1],[0,2,1],[1,10,1],[1,6,1],[1,9,1],[1,15,1],[1,13,1],[2,12,1],[2,9,1],[2,17,1],[2,15,1],[3,4,1],[3,6,1],[3,11,1],[4,12,1],[4,9,1],[4,11,1],[6,10,1],[6,12,1],[6,9,1],[6,15,1],[6,13,1],[8,12,1],[8,9,1],[8,15,1],[8,13,1],[9,10,1],[9,11,1],[10,13,1],[10,11,1],[11,13,1],[12,13,1],[14,16,1]],"nodes":[0,1,2,3,4,6,7,8,9,10,11,12,13,14,15,16,17],"source":16,"target":7}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-223

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,16,1],[0,13,1],[0,1,1],[0,9,1],[0,5,1],[0,7,1],[0,3,1],[0,10,1],[0,23,1],[0,26,1],[0,27,1],[0,8,1],[0,14,1],[0,22,1],[0,20,1],[0,15,1],[0,4,1],[0,2,1],[1,25,1],[1,11,1],[1,21,1],[1,13,1],[1,9,1],[1,3,1],[1,10,1],[1,23,1],[1,26,1],[1,27,1],[1,14,1],[1,20,1],[1,15,1],[1,2,1],[1,28,1],[2,25,1],[2,11,1],[2,16,1],[2,21,1],[2,6,1],[2,13,1],[2,9,1],[2,7,1],[2,23,1],[2,26,1],[2,8,1],[2,20,1],[2,15,1],[3,25,1],[3,6,1],[3,13,1],[3,9,1],[3,10,1],[3,27,1],[3,20,1],[3,15,1],[3,4,1],[3,28,1],[4,11,1],[4,16,1],[4,6,1],[4,13,1],[4,10,1],[4,23,1],[4,26,1],[4,27,1],[4,8,1],[4,14,1],[4,22,1],[4,15,1],[4,28,1],[5,25,1],[5,16,1],[5,21,1],[5,6,1],[5,13,1],[5,9,1],[5,7,1],[5,26,1],[5,8,1],[5,22,1],[5,15,1],[5,28,1],[6,11,1],[6,16,1],[6,21,1],[6,13,1],[6,9,1],[6,7,1],[6,10,1],[6,27,1],[6,22,1],[6,20,1],[6,15,1],[7,25,1],[7,16,1],[7,21,1],[7,9,1],[7,10,1],[7,27,1],[7,8,1],[7,14,1],[7,22,1],[7,20,1],[7,15,1],[7,28,1],[8,25,1],[8,13,1],[8,23,1],[8,26,1],[8,27,1],[8,14,1],[8,20,1],[8,28,1],[9,25,1],[9,11,1],[9,16,1],[9,21,1],[9,10,1],[9,23,1],[9,26,1],[9,27,1],[9,22,1],[9,20,1],[9,28,1],[10,11,1],[10,16,1],[10,21,1],[10,13,1],[10,23,1],[10,26,1],[10,27,1],[10,14,1],[10,22,1],[10,20,1],[10,15,1],[10,28,1],[11,25,1],[11,16,1],[11,21,1],[11,13,1],[11,23,1],[11,26,1],[11,27,1],[11,14,1],[11,22,1],[11,20,1],[12,24,1],[12,19,1],[13,25,1],[13,16,1],[13,14,1],[13,22,1],[13,15,1],[13,28,1],[14,25,1],[14,21,1],[14,23,1],[14,26,1],[14,20,1],[14,15,1],[15,16,1],[15,21,1],[15,26,1],[15,27,1],[15,22,1],[15,28,1],[16,21,1],[16,23,1],[16,26,1],[16,27,1],[16,28,1],[17,18,1],[20,25,1],[20,23,1],[20,26,1],[20,27,1],[20,22,1],[20,28,1],[21,25,1],[21,23,1],[21,26,1],[21,22,1],[22,25,1],[22,23,1],[22,27,1],[23,25,1],[23,26,1],[23,27,1],[23,28,1],[25,26,1],[25,27,1],[26,27,1],[27,28,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],"source":28,"target":11}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-334

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,4,1],[0,11,1],[0,13,1],[1,8,1],[1,21,1],[1,10,1],[1,7,1],[1,2,1],[2,24,1],[2,8,1],[2,9,1],[2,10,1],[2,22,1],[3,5,1],[3,11,1],[3,13,1],[4,15,1],[4,6,1],[4,16,1],[4,11,1],[5,12,1],[5,15,1],[5,19,1],[5,18,1],[5,27,1],[6,19,1],[6,11,1],[7,26,1],[7,23,1],[7,9,1],[8,23,1],[8,9,1],[8,10,1],[8,22,1],[9,25,1],[9,14,1],[10,25,1],[10,17,1],[10,23,1],[11,20,1],[11,27,1],[12,15,1],[12,16,1],[12,18,1],[14,22,1],[15,19,1],[15,27,1],[16,19,1],[17,26,1],[17,24,1],[17,28,1],[17,23,1],[17,22,1],[19,20,1],[19,27,1],[21,26,1],[21,25,1],[21,29,1],[21,22,1],[22,29,1],[23,24,1],[23,29,1],[26,28,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],"source":3,"target":9}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✗ wrong
Qwen · on	false	✓ correct

test nlgraph-connectivity-test-51

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,5,1],[0,7,1],[0,6,1],[0,2,1],[0,4,1],[0,8,1],[0,9,1],[1,10,1],[2,3,1],[2,5,1],[2,7,1],[2,6,1],[2,4,1],[2,8,1],[2,9,1],[2,11,1],[3,5,1],[3,4,1],[3,8,1],[3,11,1],[4,5,1],[4,6,1],[4,9,1],[4,11,1],[5,6,1],[5,8,1],[5,9,1],[6,7,1],[6,8,1],[6,9,1],[6,11,1],[7,8,1],[7,11,1],[8,9,1],[9,11,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11],"source":9,"target":10}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-314

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,15,1],[1,14,1],[1,3,1],[1,9,1],[1,10,1],[1,4,1],[1,7,1],[1,6,1],[1,13,1],[1,12,1],[1,11,1],[2,15,1],[3,14,1],[3,8,1],[3,9,1],[3,10,1],[3,4,1],[3,12,1],[3,11,1],[4,8,1],[4,9,1],[4,10,1],[4,7,1],[4,5,1],[4,11,1],[5,9,1],[5,7,1],[5,13,1],[5,12,1],[5,11,1],[6,14,1],[6,8,1],[6,7,1],[6,13,1],[6,11,1],[7,8,1],[7,9,1],[7,10,1],[7,11,1],[8,14,1],[8,10,1],[8,12,1],[8,11,1],[9,14,1],[9,10,1],[9,13,1],[9,12,1],[10,14,1],[10,13,1],[10,12,1],[11,14,1],[11,13,1],[11,12,1],[12,14,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"source":0,"target":9}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-100

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,7,1],[0,2,1],[0,8,1],[1,6,1],[2,3,1],[3,6,1],[3,7,1],[4,6,1],[4,5,1],[5,8,1],[7,8,1]],"nodes":[0,1,2,3,4,5,6,7,8],"source":3,"target":7}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-322

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,21,1],[0,7,1],[0,6,1],[0,3,1],[0,17,1],[0,20,1],[0,22,1],[0,16,1],[0,23,1],[0,25,1],[0,27,1],[1,5,1],[1,21,1],[1,4,1],[1,7,1],[1,15,1],[1,18,1],[1,2,1],[1,24,1],[1,20,1],[1,11,1],[1,16,1],[1,25,1],[1,27,1],[2,14,1],[2,5,1],[2,21,1],[2,4,1],[2,15,1],[2,24,1],[2,22,1],[2,11,1],[2,23,1],[2,25,1],[2,27,1],[3,14,1],[3,13,1],[3,21,1],[3,7,1],[3,15,1],[3,6,1],[3,17,1],[3,24,1],[3,22,1],[3,11,1],[3,16,1],[3,23,1],[4,14,1],[4,13,1],[4,5,1],[4,19,1],[4,7,1],[4,18,1],[4,17,1],[4,22,1],[4,11,1],[4,23,1],[4,25,1],[4,27,1],[5,13,1],[5,19,1],[5,15,1],[5,18,1],[5,24,1],[5,20,1],[5,22,1],[5,11,1],[5,23,1],[5,27,1],[6,14,1],[6,21,1],[6,19,1],[6,7,1],[6,15,1],[6,18,1],[6,17,1],[6,24,1],[6,20,1],[6,11,1],[6,16,1],[6,25,1],[6,27,1],[7,14,1],[7,13,1],[7,21,1],[7,19,1],[7,15,1],[7,18,1],[7,17,1],[7,20,1],[7,22,1],[7,11,1],[7,23,1],[7,27,1],[8,30,1],[8,28,1],[9,31,1],[9,10,1],[9,26,1],[9,29,1],[10,31,1],[10,26,1],[10,29,1],[11,13,1],[11,21,1],[11,19,1],[11,15,1],[11,24,1],[11,22,1],[11,25,1],[11,27,1],[12,28,1],[13,14,1],[13,21,1],[13,15,1],[13,18,1],[13,17,1],[13,24,1],[13,20,1],[13,16,1],[13,23,1],[13,25,1],[13,27,1],[14,21,1],[14,19,1],[14,24,1],[14,20,1],[14,22,1],[14,16,1],[14,23,1],[14,25,1],[15,21,1],[15,18,1],[15,17,1],[15,24,1],[15,20,1],[15,22,1],[15,16,1],[15,25,1],[15,27,1],[16,21,1],[16,18,1],[16,17,1],[16,24,1],[16,20,1],[16,22,1],[16,25,1],[17,21,1],[17,19,1],[17,18,1],[17,24,1],[17,20,1],[17,22,1],[17,23,1],[17,25,1],[17,27,1],[18,21,1],[18,24,1],[18,20,1],[18,25,1],[18,27,1],[19,21,1],[19,20,1],[19,22,1],[19,27,1],[20,21,1],[20,24,1],[20,22,1],[20,23,1],[20,27,1],[21,24,1],[21,22,1],[21,25,1],[21,27,1],[22,25,1],[23,25,1],[23,27,1],[25,27,1],[26,31,1],[26,29,1],[29,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],"source":11,"target":28}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-86

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,12,1],[0,7,1],[0,13,1],[0,24,1],[0,19,1],[0,5,1],[0,10,1],[0,4,1],[0,2,1],[0,21,1],[0,17,1],[0,23,1],[0,9,1],[0,20,1],[0,15,1],[0,22,1],[1,3,1],[1,18,1],[1,6,1],[1,14,1],[1,8,1],[1,11,1],[2,12,1],[2,7,1],[2,13,1],[2,24,1],[2,19,1],[2,5,1],[2,10,1],[2,4,1],[2,21,1],[2,17,1],[2,23,1],[2,9,1],[2,20,1],[2,15,1],[2,22,1],[3,18,1],[3,6,1],[3,14,1],[3,8,1],[3,11,1],[4,12,1],[4,7,1],[4,13,1],[4,24,1],[4,19,1],[4,5,1],[4,10,1],[4,21,1],[4,17,1],[4,23,1],[4,9,1],[4,20,1],[4,15,1],[4,22,1],[5,12,1],[5,7,1],[5,13,1],[5,24,1],[5,19,1],[5,10,1],[5,21,1],[5,17,1],[5,23,1],[5,9,1],[5,20,1],[5,15,1],[5,22,1],[6,18,1],[6,14,1],[6,8,1],[6,11,1],[7,12,1],[7,13,1],[7,24,1],[7,19,1],[7,10,1],[7,21,1],[7,17,1],[7,23,1],[7,9,1],[7,20,1],[7,15,1],[7,22,1],[8,18,1],[8,14,1],[8,11,1],[9,12,1],[9,13,1],[9,24,1],[9,19,1],[9,10,1],[9,21,1],[9,17,1],[9,23,1],[9,20,1],[9,15,1],[9,22,1],[10,12,1],[10,13,1],[10,24,1],[10,19,1],[10,21,1],[10,17,1],[10,23,1],[10,20,1],[10,15,1],[10,22,1],[11,18,1],[11,14,1],[12,13,1],[12,24,1],[12,19,1],[12,21,1],[12,17,1],[12,23,1],[12,20,1],[12,15,1],[12,22,1],[13,24,1],[13,19,1],[13,21,1],[13,17,1],[13,23,1],[13,20,1],[13,15,1],[13,22,1],[14,18,1],[15,24,1],[15,19,1],[15,21,1],[15,17,1],[15,23,1],[15,20,1],[15,22,1],[17,24,1],[17,19,1],[17,21,1],[17,23,1],[17,20,1],[17,22,1],[19,24,1],[19,21,1],[19,23,1],[19,20,1],[19,22,1],[20,24,1],[20,21,1],[20,23,1],[20,22,1],[21,24,1],[21,23,1],[21,22,1],[22,24,1],[22,23,1],[23,24,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24],"source":15,"target":2}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-311

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[1,4,1],[1,13,1],[2,11,1],[3,4,1],[3,6,1],[3,19,1],[4,20,1],[4,12,1],[4,16,1],[5,14,1],[5,9,1],[6,18,1],[6,8,1],[7,13,1],[7,8,1],[7,19,1],[7,15,1],[8,18,1],[8,20,1],[8,15,1],[11,14,1],[12,20,1],[12,13,1],[12,19,1],[12,16,1],[13,18,1],[13,15,1],[15,18,1],[15,19,1],[18,20,1],[18,19,1]],"nodes":[1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20],"source":1,"target":4}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	true	✓ correct

test nlgraph-connectivity-test-97

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[1,2,1],[3,5,1]],"nodes":[0,1,2,3,4,5],"source":2,"target":4}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-160

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,8,1],[0,11,1],[0,17,1],[0,1,1],[0,2,1],[0,12,1],[0,6,1],[0,18,1],[0,7,1],[0,15,1],[1,19,1],[1,8,1],[1,9,1],[1,11,1],[1,2,1],[1,12,1],[1,6,1],[1,7,1],[1,15,1],[2,19,1],[2,4,1],[2,9,1],[2,11,1],[2,17,1],[2,12,1],[2,6,1],[2,18,1],[2,15,1],[3,5,1],[3,13,1],[3,10,1],[4,19,1],[4,8,1],[4,9,1],[4,11,1],[4,17,1],[4,12,1],[4,6,1],[4,7,1],[4,15,1],[5,13,1],[5,10,1],[6,9,1],[6,11,1],[6,12,1],[6,18,1],[7,19,1],[7,8,1],[7,9,1],[7,11,1],[7,17,1],[7,15,1],[8,19,1],[8,11,1],[8,17,1],[8,12,1],[9,17,1],[9,12,1],[9,18,1],[10,13,1],[11,17,1],[11,15,1],[12,19,1],[12,17,1],[12,18,1],[12,15,1],[14,20,1],[14,21,1],[15,17,1],[15,18,1],[17,19,1],[17,18,1],[18,19,1],[20,21,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21],"source":10,"target":6}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-104

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,18,1],[0,10,1],[0,23,1],[0,3,1],[0,9,1],[0,26,1],[1,8,1],[1,20,1],[1,6,1],[1,4,1],[1,19,1],[1,16,1],[1,13,1],[1,24,1],[2,8,1],[2,20,1],[2,4,1],[2,19,1],[2,16,1],[2,13,1],[2,24,1],[2,12,1],[3,10,1],[3,9,1],[3,21,1],[3,22,1],[4,6,1],[4,19,1],[4,13,1],[4,24,1],[4,12,1],[5,15,1],[5,25,1],[5,11,1],[5,7,1],[6,8,1],[6,20,1],[6,19,1],[6,16,1],[6,13,1],[6,24,1],[7,15,1],[7,25,1],[7,14,1],[8,19,1],[8,13,1],[8,24,1],[8,12,1],[9,18,1],[9,23,1],[10,18,1],[10,23,1],[10,21,1],[10,26,1],[11,15,1],[11,17,1],[11,25,1],[12,20,1],[12,19,1],[12,16,1],[12,24,1],[13,20,1],[13,19,1],[13,16,1],[13,24,1],[14,17,1],[14,25,1],[15,17,1],[15,25,1],[16,20,1],[16,24,1],[17,25,1],[18,21,1],[18,22,1],[19,20,1],[19,24,1],[20,24,1],[21,23,1],[22,23,1],[22,26,1],[23,26,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],"source":21,"target":24}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✗ wrong
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-25

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,7,1],[0,15,1],[0,6,1],[0,17,1],[0,4,1],[0,12,1],[0,16,1],[0,9,1],[1,14,1],[1,23,1],[1,18,1],[1,19,1],[1,3,1],[1,21,1],[2,14,1],[2,5,1],[2,11,1],[2,23,1],[2,22,1],[2,8,1],[2,18,1],[2,19,1],[2,3,1],[2,20,1],[3,14,1],[3,5,1],[3,23,1],[3,22,1],[3,8,1],[3,18,1],[3,19,1],[3,20,1],[3,21,1],[4,7,1],[4,15,1],[4,6,1],[4,17,1],[4,13,1],[4,10,1],[4,16,1],[5,14,1],[5,8,1],[5,18,1],[5,19,1],[5,21,1],[6,13,1],[6,10,1],[6,16,1],[6,9,1],[7,15,1],[7,13,1],[7,9,1],[8,14,1],[8,11,1],[8,23,1],[8,22,1],[8,18,1],[8,19,1],[8,20,1],[8,21,1],[9,15,1],[9,13,1],[9,12,1],[9,16,1],[10,15,1],[10,17,1],[10,13,1],[10,12,1],[11,14,1],[11,23,1],[11,22,1],[11,18,1],[11,19,1],[12,17,1],[12,16,1],[13,17,1],[13,16,1],[14,23,1],[14,19,1],[15,17,1],[16,17,1],[18,23,1],[18,22,1],[18,19,1],[18,21,1],[19,23,1],[19,22,1],[19,20,1],[20,23,1],[20,21,1],[21,23,1],[22,23,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"source":14,"target":2}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-340

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,19,1],[0,4,1],[1,23,1],[1,7,1],[1,18,1],[1,24,1],[1,32,1],[1,31,1],[1,21,1],[1,27,1],[1,11,1],[1,6,1],[1,29,1],[1,17,1],[1,20,1],[2,23,1],[2,7,1],[2,18,1],[2,33,1],[2,24,1],[2,31,1],[2,21,1],[2,8,1],[2,27,1],[2,11,1],[2,29,1],[2,17,1],[2,26,1],[3,9,1],[3,22,1],[3,13,1],[3,5,1],[3,30,1],[3,28,1],[3,16,1],[3,14,1],[3,15,1],[4,19,1],[4,10,1],[5,9,1],[5,22,1],[5,13,1],[5,28,1],[5,16,1],[5,14,1],[6,18,1],[6,32,1],[6,25,1],[6,21,1],[6,8,1],[6,11,1],[6,17,1],[6,20,1],[6,26,1],[7,18,1],[7,33,1],[7,24,1],[7,32,1],[7,25,1],[7,31,1],[7,21,1],[7,17,1],[7,20,1],[7,26,1],[8,18,1],[8,33,1],[8,32,1],[8,25,1],[8,31,1],[8,27,1],[8,11,1],[8,29,1],[8,20,1],[8,26,1],[9,22,1],[9,13,1],[9,30,1],[9,28,1],[9,14,1],[9,15,1],[10,19,1],[10,12,1],[11,18,1],[11,33,1],[11,24,1],[11,25,1],[11,31,1],[11,27,1],[11,29,1],[11,26,1],[12,19,1],[13,28,1],[13,15,1],[14,30,1],[14,28,1],[14,16,1],[14,15,1],[15,22,1],[15,30,1],[15,16,1],[16,22,1],[17,23,1],[17,18,1],[17,33,1],[17,25,1],[17,31,1],[17,21,1],[17,27,1],[17,29,1],[17,20,1],[17,26,1],[18,23,1],[18,32,1],[18,25,1],[18,21,1],[18,29,1],[18,20,1],[18,26,1],[20,23,1],[20,33,1],[20,32,1],[20,25,1],[20,31,1],[20,21,1],[20,27,1],[20,29,1],[20,26,1],[21,23,1],[21,33,1],[21,24,1],[21,25,1],[21,29,1],[23,33,1],[23,24,1],[23,25,1],[23,31,1],[23,27,1],[23,29,1],[23,26,1],[24,33,1],[24,32,1],[24,25,1],[24,27,1],[24,29,1],[24,26,1],[25,32,1],[25,31,1],[25,27,1],[25,29,1],[25,26,1],[26,33,1],[26,31,1],[26,27,1],[27,31,1],[27,29,1],[28,30,1],[31,32,1],[32,33,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],"source":0,"target":11}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-343

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[0,5,1],[0,12,1],[0,11,1],[0,8,1],[0,1,1],[0,13,1],[0,10,1],[0,3,1],[1,2,1],[1,5,1],[1,12,1],[1,11,1],[1,8,1],[1,13,1],[1,10,1],[1,3,1],[2,5,1],[2,12,1],[2,11,1],[2,8,1],[2,13,1],[2,10,1],[2,3,1],[3,5,1],[3,12,1],[3,11,1],[3,8,1],[3,13,1],[3,10,1],[4,9,1],[4,6,1],[4,7,1],[4,14,1],[5,12,1],[5,11,1],[5,8,1],[5,13,1],[5,10,1],[6,9,1],[6,7,1],[6,14,1],[7,9,1],[7,14,1],[8,12,1],[8,11,1],[8,13,1],[8,10,1],[9,14,1],[10,12,1],[10,11,1],[10,13,1],[11,12,1],[11,13,1],[12,13,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"source":6,"target":11}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	false	✓ correct
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-266

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,11,1],[0,2,1],[0,14,1],[0,7,1],[0,13,1],[1,17,1],[1,3,1],[1,10,1],[1,6,1],[2,11,1],[2,12,1],[2,14,1],[2,13,1],[3,17,1],[3,10,1],[3,6,1],[4,9,1],[4,5,1],[5,9,1],[5,16,1],[6,17,1],[6,8,1],[6,10,1],[7,11,1],[7,12,1],[7,14,1],[7,13,1],[8,17,1],[8,15,1],[9,18,1],[9,16,1],[10,17,1],[12,14,1],[12,13,1],[13,14,1],[15,17,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"source":6,"target":15}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-137

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[0,5,1],[0,6,1],[0,3,1],[0,4,1],[0,1,1],[1,2,1],[1,5,1],[1,6,1],[1,3,1],[1,4,1],[2,5,1],[2,6,1],[2,3,1],[2,4,1],[3,5,1],[3,6,1],[3,4,1],[4,5,1],[4,6,1],[5,6,1]],"nodes":[0,1,2,3,4,5,6],"source":2,"target":1}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-24

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,34,1],[0,4,1],[0,7,1],[0,28,1],[0,8,1],[0,15,1],[0,23,1],[0,13,1],[0,22,1],[0,32,1],[0,11,1],[0,18,1],[1,7,1],[1,2,1],[1,13,1],[1,27,1],[1,26,1],[1,9,1],[2,14,1],[2,31,1],[2,15,1],[2,23,1],[2,13,1],[2,9,1],[2,22,1],[2,17,1],[2,32,1],[2,18,1],[3,24,1],[4,7,1],[4,27,1],[4,17,1],[5,16,1],[5,12,1],[5,29,1],[5,20,1],[6,34,1],[6,7,1],[6,14,1],[6,31,1],[6,10,1],[6,23,1],[6,26,1],[6,21,1],[6,17,1],[6,18,1],[7,33,1],[7,14,1],[7,28,1],[7,15,1],[7,26,1],[7,19,1],[8,14,1],[8,28,1],[8,31,1],[8,10,1],[8,13,1],[8,25,1],[8,30,1],[8,18,1],[9,14,1],[9,21,1],[9,25,1],[9,22,1],[9,11,1],[10,31,1],[10,15,1],[10,27,1],[10,25,1],[10,17,1],[10,32,1],[11,28,1],[11,31,1],[11,15,1],[11,13,1],[11,27,1],[11,21,1],[11,25,1],[11,22,1],[12,16,1],[13,33,1],[13,14,1],[13,28,1],[13,26,1],[13,21,1],[13,17,1],[13,32,1],[13,18,1],[14,33,1],[14,31,1],[14,23,1],[14,27,1],[14,25,1],[15,34,1],[15,30,1],[15,17,1],[15,19,1],[16,24,1],[17,23,1],[17,26,1],[17,19,1],[18,34,1],[18,21,1],[18,30,1],[19,33,1],[19,21,1],[19,25,1],[19,30,1],[21,33,1],[21,28,1],[21,25,1],[21,30,1],[22,33,1],[22,23,1],[22,26,1],[22,25,1],[23,34,1],[23,25,1],[25,33,1],[25,32,1],[26,33,1],[26,28,1],[26,31,1],[26,32,1],[27,33,1],[27,32,1],[32,33,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],"source":9,"target":19}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-284

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,12,1],[0,13,1],[0,2,1],[0,14,1],[0,23,1],[0,8,1],[0,1,1],[0,25,1],[0,27,1],[0,10,1],[1,29,1],[1,13,1],[1,19,1],[1,28,1],[1,23,1],[1,30,1],[1,25,1],[1,24,1],[2,12,1],[2,5,1],[2,14,1],[2,17,1],[2,23,1],[3,7,1],[3,12,1],[3,19,1],[3,23,1],[3,8,1],[3,30,1],[3,25,1],[3,24,1],[4,33,1],[5,20,1],[5,23,1],[5,30,1],[6,15,1],[6,11,1],[7,32,1],[7,17,1],[7,23,1],[7,8,1],[7,10,1],[8,29,1],[8,12,1],[8,32,1],[8,20,1],[8,19,1],[8,17,1],[8,30,1],[9,29,1],[9,28,1],[9,30,1],[9,24,1],[10,13,1],[10,20,1],[10,14,1],[10,22,1],[11,31,1],[12,13,1],[12,23,1],[12,27,1],[12,26,1],[13,29,1],[13,32,1],[13,14,1],[13,28,1],[13,30,1],[13,24,1],[14,17,1],[14,30,1],[14,22,1],[14,27,1],[15,16,1],[15,31,1],[15,33,1],[17,32,1],[17,20,1],[17,19,1],[17,27,1],[17,24,1],[17,26,1],[18,21,1],[20,28,1],[20,30,1],[20,25,1],[21,31,1],[22,32,1],[22,28,1],[22,30,1],[23,28,1],[23,25,1],[23,27,1],[24,29,1],[24,28,1],[24,26,1],[25,32,1],[26,29,1],[26,27,1],[27,32,1],[27,30,1],[28,32,1],[28,30,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],"source":15,"target":32}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-368

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,14,1],[0,20,1],[0,13,1],[0,24,1],[0,4,1],[1,21,1],[1,3,1],[1,11,1],[1,10,1],[1,23,1],[1,8,1],[1,2,1],[1,22,1],[1,19,1],[1,18,1],[2,21,1],[2,3,1],[2,11,1],[2,10,1],[2,23,1],[2,8,1],[2,22,1],[2,19,1],[2,18,1],[3,21,1],[3,11,1],[3,10,1],[3,23,1],[3,8,1],[3,22,1],[3,19,1],[3,18,1],[4,14,1],[4,20,1],[4,13,1],[4,24,1],[5,7,1],[5,9,1],[5,12,1],[5,16,1],[5,15,1],[5,17,1],[5,6,1],[6,7,1],[6,9,1],[6,12,1],[6,16,1],[6,15,1],[6,17,1],[7,9,1],[7,12,1],[7,16,1],[7,15,1],[7,17,1],[8,21,1],[8,11,1],[8,10,1],[8,23,1],[8,22,1],[8,19,1],[8,18,1],[9,12,1],[9,16,1],[9,15,1],[9,17,1],[10,21,1],[10,11,1],[10,23,1],[10,22,1],[10,19,1],[10,18,1],[11,21,1],[11,23,1],[11,22,1],[11,19,1],[11,18,1],[12,16,1],[12,15,1],[12,17,1],[13,14,1],[13,20,1],[13,24,1],[14,20,1],[14,24,1],[15,16,1],[15,17,1],[16,17,1],[18,21,1],[18,23,1],[18,22,1],[18,19,1],[19,21,1],[19,23,1],[19,22,1],[20,24,1],[21,23,1],[21,22,1],[22,23,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"source":23,"target":18}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-17

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,3,1],[0,2,1],[1,5,1],[1,3,1],[2,5,1],[2,3,1],[3,5,1]],"nodes":[0,1,2,3,4,5],"source":1,"target":4}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-270

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,16,1],[0,28,1],[0,26,1],[0,7,1],[0,22,1],[0,6,1],[0,1,1],[0,30,1],[0,3,1],[1,16,1],[1,28,1],[1,26,1],[1,22,1],[1,10,1],[1,30,1],[2,4,1],[2,29,1],[2,24,1],[2,14,1],[2,21,1],[2,25,1],[2,13,1],[2,12,1],[2,31,1],[2,19,1],[2,33,1],[2,27,1],[2,23,1],[2,8,1],[2,18,1],[3,16,1],[3,28,1],[3,26,1],[3,9,1],[3,7,1],[3,10,1],[4,29,1],[4,32,1],[4,24,1],[4,21,1],[4,25,1],[4,15,1],[4,12,1],[4,31,1],[4,19,1],[4,33,1],[4,27,1],[4,17,1],[4,23,1],[4,18,1],[5,32,1],[5,14,1],[5,21,1],[5,15,1],[5,12,1],[5,19,1],[5,33,1],[5,27,1],[5,23,1],[5,8,1],[6,28,1],[6,26,1],[6,7,1],[6,22,1],[6,10,1],[7,16,1],[7,9,1],[7,22,1],[7,10,1],[8,29,1],[8,32,1],[8,24,1],[8,21,1],[8,15,1],[8,13,1],[8,33,1],[8,27,1],[8,23,1],[8,18,1],[9,16,1],[9,28,1],[9,26,1],[9,22,1],[9,10,1],[10,28,1],[10,22,1],[10,30,1],[12,29,1],[12,14,1],[12,21,1],[12,25,1],[12,15,1],[12,13,1],[12,31,1],[12,19,1],[12,33,1],[12,17,1],[12,23,1],[12,18,1],[13,20,1],[13,29,1],[13,24,1],[13,21,1],[13,25,1],[13,15,1],[13,31,1],[13,19,1],[13,33,1],[13,27,1],[13,17,1],[13,23,1],[13,18,1],[14,20,1],[14,29,1],[14,32,1],[14,24,1],[14,21,1],[14,15,1],[14,31,1],[14,19,1],[14,33,1],[14,17,1],[14,18,1],[15,20,1],[15,29,1],[15,32,1],[15,24,1],[15,21,1],[15,25,1],[15,31,1],[15,19,1],[15,33,1],[15,27,1],[15,17,1],[15,23,1],[15,18,1],[16,28,1],[16,26,1],[16,22,1],[16,30,1],[17,20,1],[17,29,1],[17,32,1],[17,24,1],[17,21,1],[17,25,1],[17,31,1],[17,19,1],[17,18,1],[18,20,1],[18,29,1],[18,32,1],[18,24,1],[18,21,1],[18,25,1],[18,31,1],[18,19,1],[18,27,1],[18,23,1],[19,32,1],[19,24,1],[19,33,1],[19,27,1],[19,23,1],[20,29,1],[20,32,1],[20,24,1],[20,21,1],[20,25,1],[20,31,1],[20,33,1],[20,27,1],[20,23,1],[21,32,1],[21,24,1],[21,25,1],[21,31,1],[21,33,1],[21,27,1],[21,23,1],[22,26,1],[22,30,1],[23,29,1],[23,32,1],[23,24,1],[23,25,1],[23,31,1],[23,33,1],[23,27,1],[24,32,1],[24,25,1],[24,31,1],[24,27,1],[25,29,1],[25,33,1],[25,27,1],[26,28,1],[26,30,1],[27,29,1],[27,31,1],[27,33,1],[28,30,1],[29,32,1],[29,31,1],[29,33,1],[31,32,1],[31,33,1],[32,33,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],"source":33,"target":27}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-216

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,18,1],[0,25,1],[0,19,1],[0,16,1],[0,22,1],[0,8,1],[0,10,1],[0,31,1],[0,13,1],[0,5,1],[0,14,1],[0,24,1],[0,27,1],[0,1,1],[0,15,1],[0,23,1],[1,9,1],[1,30,1],[1,25,1],[1,19,1],[1,16,1],[1,17,1],[1,22,1],[1,8,1],[1,21,1],[1,4,1],[1,31,1],[1,13,1],[1,14,1],[1,24,1],[1,12,1],[1,27,1],[1,15,1],[2,11,1],[2,28,1],[2,29,1],[2,7,1],[3,9,1],[3,18,1],[3,25,1],[3,19,1],[3,16,1],[3,22,1],[3,10,1],[3,4,1],[3,31,1],[3,13,1],[3,5,1],[3,14,1],[3,24,1],[3,12,1],[3,20,1],[3,27,1],[3,15,1],[3,23,1],[4,18,1],[4,30,1],[4,19,1],[4,22,1],[4,8,1],[4,21,1],[4,31,1],[4,5,1],[4,24,1],[4,12,1],[4,27,1],[4,23,1],[5,18,1],[5,30,1],[5,25,1],[5,19,1],[5,17,1],[5,10,1],[5,21,1],[5,31,1],[5,12,1],[5,20,1],[5,15,1],[5,23,1],[6,28,1],[6,29,1],[6,7,1],[6,26,1],[7,28,1],[8,9,1],[8,25,1],[8,19,1],[8,16,1],[8,22,1],[8,10,1],[8,13,1],[8,14,1],[8,24,1],[8,12,1],[8,27,1],[8,15,1],[8,23,1],[9,18,1],[9,30,1],[9,19,1],[9,16,1],[9,17,1],[9,22,1],[9,10,1],[9,31,1],[9,13,1],[9,27,1],[9,15,1],[9,23,1],[10,18,1],[10,30,1],[10,25,1],[10,16,1],[10,22,1],[10,21,1],[10,31,1],[10,14,1],[10,24,1],[10,12,1],[10,20,1],[10,15,1],[11,28,1],[11,26,1],[12,19,1],[12,22,1],[12,21,1],[12,13,1],[12,24,1],[12,15,1],[12,23,1],[13,25,1],[13,19,1],[13,16,1],[13,17,1],[13,22,1],[13,31,1],[13,14,1],[13,27,1],[14,30,1],[14,25,1],[14,16,1],[14,17,1],[14,22,1],[14,31,1],[14,24,1],[14,20,1],[14,15,1],[14,23,1],[15,18,1],[15,30,1],[15,25,1],[15,19,1],[15,16,1],[15,22,1],[15,31,1],[15,24,1],[16,18,1],[16,30,1],[16,22,1],[16,21,1],[16,31,1],[16,20,1],[16,27,1],[17,18,1],[17,30,1],[17,25,1],[17,19,1],[17,22,1],[17,21,1],[17,31,1],[17,24,1],[17,27,1],[17,23,1],[18,30,1],[18,25,1],[18,19,1],[18,22,1],[18,21,1],[18,31,1],[18,24,1],[18,27,1],[18,23,1],[19,30,1],[19,25,1],[19,21,1],[19,24,1],[19,20,1],[19,27,1],[19,23,1],[20,21,1],[20,31,1],[20,24,1],[20,27,1],[20,23,1],[21,25,1],[21,22,1],[21,31,1],[21,24,1],[21,27,1],[21,23,1],[22,30,1],[22,31,1],[22,24,1],[22,23,1],[23,30,1],[23,25,1],[23,24,1],[23,27,1],[24,30,1],[24,25,1],[24,31,1],[24,27,1],[25,30,1],[25,27,1],[26,28,1],[27,30,1],[27,31,1],[28,29,1],[30,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],"source":28,"target":24}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-333

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,11,1],[0,15,1],[0,25,1],[0,31,1],[0,23,1],[0,14,1],[1,28,1],[1,20,1],[1,12,1],[1,21,1],[1,19,1],[1,24,1],[1,27,1],[1,13,1],[1,6,1],[2,20,1],[2,22,1],[2,21,1],[2,19,1],[2,13,1],[2,6,1],[3,15,1],[3,4,1],[3,25,1],[3,23,1],[4,9,1],[4,15,1],[4,14,1],[5,8,1],[5,17,1],[5,10,1],[5,26,1],[5,7,1],[5,16,1],[6,20,1],[6,21,1],[6,19,1],[6,27,1],[6,13,1],[7,17,1],[7,16,1],[7,29,1],[8,17,1],[9,11,1],[9,15,1],[9,31,1],[9,23,1],[9,14,1],[10,17,1],[11,15,1],[11,30,1],[11,23,1],[11,14,1],[12,20,1],[12,22,1],[12,19,1],[12,27,1],[12,13,1],[12,18,1],[13,28,1],[13,22,1],[13,21,1],[13,24,1],[13,27,1],[13,18,1],[14,15,1],[14,25,1],[14,31,1],[14,23,1],[15,25,1],[15,30,1],[15,23,1],[16,26,1],[17,26,1],[17,29,1],[18,28,1],[18,20,1],[18,22,1],[18,21,1],[18,19,1],[18,24,1],[18,27,1],[19,22,1],[19,21,1],[19,24,1],[19,27,1],[20,28,1],[20,22,1],[20,21,1],[20,24,1],[20,27,1],[21,28,1],[21,22,1],[21,24,1],[22,24,1],[22,27,1],[23,30,1],[23,31,1],[24,28,1],[25,31,1],[27,28,1],[30,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],"source":19,"target":9}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✗ wrong
Qwen · on	false	✓ correct

test nlgraph-connectivity-test-234

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[0,5,1],[0,6,1],[0,3,1],[0,4,1],[0,1,1],[1,2,1],[1,5,1],[1,6,1],[1,3,1],[1,4,1],[2,5,1],[2,6,1],[2,3,1],[2,4,1],[3,5,1],[3,6,1],[3,4,1],[4,5,1],[4,6,1],[5,6,1]],"nodes":[0,1,2,3,4,5,6],"source":5,"target":4}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-325

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,34,1],[0,4,1],[0,7,1],[0,28,1],[0,8,1],[0,15,1],[0,23,1],[0,13,1],[0,22,1],[0,32,1],[0,11,1],[0,18,1],[1,7,1],[1,2,1],[1,13,1],[1,27,1],[1,26,1],[1,9,1],[2,14,1],[2,31,1],[2,15,1],[2,23,1],[2,13,1],[2,9,1],[2,22,1],[2,17,1],[2,32,1],[2,18,1],[3,24,1],[4,7,1],[4,27,1],[4,17,1],[5,16,1],[5,12,1],[5,29,1],[5,20,1],[6,34,1],[6,7,1],[6,14,1],[6,31,1],[6,10,1],[6,23,1],[6,26,1],[6,21,1],[6,17,1],[6,18,1],[7,33,1],[7,14,1],[7,28,1],[7,15,1],[7,26,1],[7,19,1],[8,14,1],[8,28,1],[8,31,1],[8,10,1],[8,13,1],[8,25,1],[8,30,1],[8,18,1],[9,14,1],[9,21,1],[9,25,1],[9,22,1],[9,11,1],[10,31,1],[10,15,1],[10,27,1],[10,25,1],[10,17,1],[10,32,1],[11,28,1],[11,31,1],[11,15,1],[11,13,1],[11,27,1],[11,21,1],[11,25,1],[11,22,1],[12,16,1],[13,33,1],[13,14,1],[13,28,1],[13,26,1],[13,21,1],[13,17,1],[13,32,1],[13,18,1],[14,33,1],[14,31,1],[14,23,1],[14,27,1],[14,25,1],[15,34,1],[15,30,1],[15,17,1],[15,19,1],[16,24,1],[17,23,1],[17,26,1],[17,19,1],[18,34,1],[18,21,1],[18,30,1],[19,33,1],[19,21,1],[19,25,1],[19,30,1],[21,33,1],[21,28,1],[21,25,1],[21,30,1],[22,33,1],[22,23,1],[22,26,1],[22,25,1],[23,34,1],[23,25,1],[25,33,1],[25,32,1],[26,33,1],[26,28,1],[26,31,1],[26,32,1],[27,33,1],[27,32,1],[32,33,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],"source":24,"target":6}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-264

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,17,1],[0,24,1],[1,11,1],[1,9,1],[1,3,1],[2,19,1],[2,29,1],[2,27,1],[3,7,1],[3,20,1],[4,23,1],[4,25,1],[5,17,1],[6,22,1],[7,29,1],[7,27,1],[7,9,1],[8,16,1],[8,30,1],[8,26,1],[8,18,1],[8,31,1],[9,11,1],[9,27,1],[10,13,1],[10,12,1],[11,19,1],[11,27,1],[12,26,1],[12,18,1],[14,28,1],[15,27,1],[16,30,1],[17,23,1],[18,26,1],[19,28,1],[20,29,1],[21,22,1],[23,24,1],[24,25,1],[27,28,1],[30,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],"source":28,"target":27}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-130

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,2,1],[0,8,1],[0,4,1],[0,7,1],[0,3,1],[0,1,1],[1,5,1],[1,2,1],[1,8,1],[1,4,1],[1,7,1],[1,3,1],[2,5,1],[2,8,1],[2,4,1],[2,7,1],[2,3,1],[3,5,1],[3,8,1],[3,4,1],[3,7,1],[4,5,1],[4,8,1],[4,7,1],[5,8,1],[5,7,1],[6,9,1],[7,8,1]],"nodes":[0,1,2,3,4,5,6,7,8,9],"source":5,"target":8}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-362

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[1,26,1],[2,26,1],[2,30,1],[2,6,1],[3,19,1],[4,29,1],[4,8,1],[4,11,1],[4,9,1],[5,25,1],[6,30,1],[6,19,1],[6,13,1],[6,25,1],[7,23,1],[7,29,1],[7,10,1],[7,28,1],[7,14,1],[8,23,1],[8,15,1],[8,27,1],[8,18,1],[8,11,1],[8,28,1],[8,9,1],[9,23,1],[9,29,1],[9,15,1],[9,18,1],[9,12,1],[10,15,1],[11,29,1],[11,27,1],[11,28,1],[11,14,1],[12,27,1],[13,16,1],[13,26,1],[14,17,1],[15,29,1],[15,21,1],[15,28,1],[16,25,1],[17,23,1],[17,29,1],[17,18,1],[19,20,1],[19,22,1],[20,22,1],[21,27,1],[21,28,1],[22,26,1],[23,29,1],[23,28,1],[24,26,1],[24,30,1],[25,26,1],[25,30,1],[27,28,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],"source":28,"target":14}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-250

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,10,1],[1,11,1],[1,9,1],[1,14,1],[2,5,1],[2,6,1],[3,11,1],[3,13,1],[4,11,1],[4,13,1],[4,15,1],[5,7,1],[5,6,1],[7,10,1],[8,11,1],[8,9,1],[9,14,1],[9,12,1],[11,13,1],[13,14,1],[13,15,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"source":15,"target":1}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	{"true": true}	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-217

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,18,1],[0,24,1],[0,5,1],[0,12,1],[0,26,1],[0,14,1],[0,16,1],[0,21,1],[0,9,1],[0,1,1],[0,28,1],[0,25,1],[1,3,1],[1,18,1],[1,24,1],[1,5,1],[1,12,1],[1,26,1],[1,14,1],[1,16,1],[1,21,1],[1,2,1],[1,23,1],[1,20,1],[1,28,1],[1,25,1],[2,3,1],[2,18,1],[2,10,1],[2,24,1],[2,5,1],[2,12,1],[2,26,1],[2,14,1],[2,16,1],[2,9,1],[2,23,1],[2,20,1],[2,28,1],[2,7,1],[2,25,1],[2,22,1],[2,13,1],[3,18,1],[3,24,1],[3,12,1],[3,26,1],[3,16,1],[3,9,1],[3,19,1],[3,7,1],[3,25,1],[3,22,1],[4,11,1],[4,27,1],[4,17,1],[4,15,1],[4,8,1],[5,18,1],[5,24,1],[5,12,1],[5,26,1],[5,14,1],[5,16,1],[5,21,1],[5,9,1],[5,23,1],[5,19,1],[5,20,1],[5,7,1],[5,13,1],[6,11,1],[6,27,1],[6,29,1],[6,15,1],[6,8,1],[7,18,1],[7,10,1],[7,12,1],[7,26,1],[7,14,1],[7,16,1],[7,21,1],[7,9,1],[7,20,1],[7,25,1],[7,22,1],[7,13,1],[8,11,1],[8,27,1],[8,29,1],[8,17,1],[8,15,1],[9,18,1],[9,10,1],[9,24,1],[9,16,1],[9,21,1],[9,19,1],[9,20,1],[9,28,1],[9,25,1],[9,13,1],[10,18,1],[10,24,1],[10,12,1],[10,26,1],[10,14,1],[10,16,1],[10,23,1],[10,20,1],[10,28,1],[10,25,1],[10,22,1],[10,13,1],[11,27,1],[11,29,1],[12,18,1],[12,24,1],[12,16,1],[12,21,1],[12,23,1],[12,20,1],[12,28,1],[12,22,1],[12,13,1],[13,18,1],[13,24,1],[13,26,1],[13,14,1],[13,16,1],[13,21,1],[13,23,1],[13,20,1],[13,28,1],[13,25,1],[13,22,1],[14,26,1],[14,16,1],[14,21,1],[14,23,1],[14,19,1],[14,20,1],[14,28,1],[14,25,1],[15,27,1],[15,17,1],[16,18,1],[16,24,1],[16,26,1],[16,20,1],[16,25,1],[16,22,1],[17,29,1],[18,24,1],[18,26,1],[18,23,1],[18,19,1],[18,20,1],[18,25,1],[18,22,1],[19,21,1],[19,23,1],[19,28,1],[19,25,1],[20,26,1],[20,23,1],[20,28,1],[20,25,1],[20,22,1],[21,26,1],[21,23,1],[21,28,1],[21,22,1],[22,26,1],[22,23,1],[22,25,1],[23,24,1],[23,26,1],[24,26,1],[24,28,1],[25,26,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],"source":10,"target":11}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	false	✓ correct
Qwen · off	true	✗ wrong
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-355

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,19,1],[0,21,1],[0,17,1],[0,7,1],[0,29,1],[1,20,1],[2,32,1],[2,6,1],[2,13,1],[3,22,1],[3,23,1],[3,8,1],[4,30,1],[4,31,1],[6,23,1],[6,16,1],[6,32,1],[7,19,1],[8,14,1],[8,23,1],[8,16,1],[8,32,1],[8,13,1],[9,24,1],[9,17,1],[9,29,1],[13,14,1],[13,32,1],[14,16,1],[14,32,1],[16,20,1],[16,28,1],[17,24,1],[20,28,1],[21,29,1],[24,29,1],[27,30,1],[30,31,1]],"nodes":[0,1,2,3,4,6,7,8,9,13,14,16,17,19,20,21,22,23,24,27,28,29,30,31,32],"source":20,"target":28}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-115

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,1,1],[0,12,1],[0,4,1],[1,13,1],[1,3,1],[1,6,1],[1,9,1],[2,15,1],[2,14,1],[2,11,1],[4,7,1],[5,16,1],[5,6,1],[5,9,1],[6,13,1],[6,8,1],[10,13,1],[10,12,1],[11,15,1],[11,14,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"source":3,"target":7}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-36

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,18,1],[1,4,1],[1,11,1],[2,21,1],[2,20,1],[2,24,1],[3,24,1],[4,13,1],[4,15,1],[4,8,1],[5,19,1],[5,24,1],[6,20,1],[6,24,1],[7,25,1],[7,21,1],[8,17,1],[8,15,1],[8,12,1],[9,13,1],[9,12,1],[10,16,1],[11,13,1],[11,18,1],[11,23,1],[11,14,1],[11,12,1],[13,17,1],[14,23,1],[15,18,1],[15,23,1],[18,23,1],[19,25,1],[19,24,1],[20,21,1],[21,25,1],[24,25,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],"source":22,"target":1}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-68

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,7,1],[0,15,1],[0,6,1],[0,17,1],[0,4,1],[0,12,1],[0,16,1],[0,9,1],[1,14,1],[1,23,1],[1,18,1],[1,19,1],[1,3,1],[1,21,1],[2,14,1],[2,5,1],[2,11,1],[2,23,1],[2,22,1],[2,8,1],[2,18,1],[2,19,1],[2,3,1],[2,20,1],[3,14,1],[3,5,1],[3,23,1],[3,22,1],[3,8,1],[3,18,1],[3,19,1],[3,20,1],[3,21,1],[4,7,1],[4,15,1],[4,6,1],[4,17,1],[4,13,1],[4,10,1],[4,16,1],[5,14,1],[5,8,1],[5,18,1],[5,19,1],[5,21,1],[6,13,1],[6,10,1],[6,16,1],[6,9,1],[7,15,1],[7,13,1],[7,9,1],[8,14,1],[8,11,1],[8,23,1],[8,22,1],[8,18,1],[8,19,1],[8,20,1],[8,21,1],[9,15,1],[9,13,1],[9,12,1],[9,16,1],[10,15,1],[10,17,1],[10,13,1],[10,12,1],[11,14,1],[11,23,1],[11,22,1],[11,18,1],[11,19,1],[12,17,1],[12,16,1],[13,17,1],[13,16,1],[14,23,1],[14,19,1],[15,17,1],[16,17,1],[18,23,1],[18,22,1],[18,19,1],[18,21,1],[19,23,1],[19,22,1],[19,20,1],[20,23,1],[20,21,1],[21,23,1],[22,23,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"source":3,"target":18}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-253

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[0,4,1],[0,9,1],[0,5,1],[0,13,1],[1,14,1],[1,15,1],[1,12,1],[1,5,1],[1,7,1],[2,4,1],[2,6,1],[2,9,1],[2,12,1],[2,13,1],[4,11,1],[4,6,1],[4,15,1],[4,7,1],[4,8,1],[4,13,1],[5,11,1],[5,10,1],[5,14,1],[5,6,1],[5,9,1],[5,15,1],[5,12,1],[5,7,1],[5,13,1],[6,14,1],[7,14,1],[7,8,1],[9,13,1],[10,14,1],[12,15,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"source":3,"target":9}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-173

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,8,1],[0,19,1],[0,17,1],[0,7,1],[0,16,1],[0,21,1],[1,22,1],[1,19,1],[1,20,1],[1,21,1],[2,23,1],[2,6,1],[3,13,1],[3,18,1],[3,4,1],[3,10,1],[3,21,1],[4,19,1],[4,10,1],[4,16,1],[5,14,1],[5,12,1],[5,9,1],[5,11,1],[6,14,1],[6,23,1],[7,15,1],[7,22,1],[7,18,1],[7,8,1],[7,17,1],[7,20,1],[8,13,1],[8,21,1],[9,12,1],[9,11,1],[10,17,1],[13,19,1],[13,17,1],[13,21,1],[15,20,1],[16,18,1],[16,20,1],[19,20,1],[19,21,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"source":20,"target":7}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-304

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,6,1],[0,4,1],[0,1,1],[0,5,1],[0,24,1],[0,3,1],[0,21,1],[0,19,1],[0,9,1],[0,15,1],[0,20,1],[0,27,1],[0,13,1],[1,24,1],[1,21,1],[1,31,1],[1,10,1],[1,7,1],[1,20,1],[1,27,1],[1,13,1],[2,6,1],[2,5,1],[2,24,1],[2,3,1],[2,21,1],[2,19,1],[2,9,1],[2,31,1],[2,15,1],[2,7,1],[2,27,1],[2,13,1],[3,6,1],[3,4,1],[3,5,1],[3,22,1],[3,24,1],[3,21,1],[3,19,1],[3,9,1],[3,31,1],[3,18,1],[3,7,1],[3,20,1],[4,5,1],[4,21,1],[4,19,1],[4,9,1],[4,31,1],[4,7,1],[4,20,1],[4,27,1],[4,13,1],[5,6,1],[5,22,1],[5,24,1],[5,21,1],[5,9,1],[5,31,1],[5,10,1],[5,15,1],[5,18,1],[5,20,1],[5,27,1],[5,13,1],[6,22,1],[6,21,1],[6,19,1],[6,9,1],[6,31,1],[6,10,1],[6,15,1],[6,18,1],[6,7,1],[6,27,1],[6,13,1],[7,22,1],[7,9,1],[7,10,1],[7,15,1],[7,18,1],[7,20,1],[7,27,1],[7,13,1],[8,16,1],[8,11,1],[8,28,1],[8,12,1],[8,25,1],[8,30,1],[8,14,1],[8,32,1],[8,29,1],[9,22,1],[9,24,1],[9,21,1],[9,19,1],[9,31,1],[9,10,1],[9,15,1],[9,18,1],[9,20,1],[10,22,1],[10,19,1],[10,31,1],[10,15,1],[10,20,1],[10,27,1],[10,13,1],[11,16,1],[11,28,1],[11,26,1],[11,23,1],[11,30,1],[11,14,1],[11,32,1],[11,17,1],[12,16,1],[12,28,1],[12,23,1],[12,30,1],[12,14,1],[12,33,1],[12,32,1],[12,17,1],[12,29,1],[13,22,1],[13,24,1],[13,21,1],[13,19,1],[13,15,1],[13,18,1],[13,20,1],[14,28,1],[14,26,1],[14,23,1],[14,25,1],[14,33,1],[14,32,1],[14,29,1],[15,22,1],[15,24,1],[15,21,1],[15,19,1],[15,20,1],[15,27,1],[16,26,1],[16,25,1],[16,30,1],[16,33,1],[16,32,1],[16,17,1],[16,29,1],[17,28,1],[17,26,1],[17,25,1],[17,30,1],[17,33,1],[17,32,1],[17,29,1],[18,24,1],[18,19,1],[18,31,1],[19,22,1],[19,24,1],[19,31,1],[19,20,1],[19,27,1],[20,21,1],[20,31,1],[20,27,1],[21,31,1],[23,28,1],[23,26,1],[23,25,1],[23,30,1],[24,31,1],[24,27,1],[25,26,1],[25,30,1],[25,33,1],[25,32,1],[25,29,1],[26,28,1],[26,33,1],[26,32,1],[28,30,1],[28,29,1],[29,30,1],[29,33,1],[29,32,1],[30,32,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],"source":24,"target":5}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-18

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,26,1],[0,10,1],[0,15,1],[0,21,1],[0,1,1],[0,7,1],[0,29,1],[0,24,1],[0,16,1],[0,23,1],[0,17,1],[1,26,1],[1,10,1],[1,15,1],[1,7,1],[1,28,1],[1,29,1],[1,12,1],[1,24,1],[1,16,1],[1,3,1],[1,23,1],[2,14,1],[2,27,1],[2,34,1],[3,26,1],[3,32,1],[3,15,1],[3,21,1],[3,7,1],[3,28,1],[3,29,1],[3,12,1],[3,24,1],[3,23,1],[3,17,1],[4,9,1],[4,14,1],[4,27,1],[4,31,1],[5,19,1],[5,22,1],[5,13,1],[5,20,1],[5,25,1],[5,30,1],[5,8,1],[5,33,1],[6,9,1],[6,27,1],[6,34,1],[6,31,1],[7,26,1],[7,32,1],[7,10,1],[7,15,1],[7,21,1],[7,29,1],[7,12,1],[7,24,1],[7,16,1],[7,23,1],[7,17,1],[8,19,1],[8,22,1],[8,13,1],[8,20,1],[8,25,1],[8,18,1],[8,30,1],[8,33,1],[9,14,1],[9,34,1],[10,32,1],[10,15,1],[10,21,1],[10,29,1],[10,24,1],[10,23,1],[10,17,1],[11,19,1],[11,22,1],[11,13,1],[11,25,1],[11,18,1],[11,30,1],[12,26,1],[12,32,1],[12,15,1],[12,21,1],[12,24,1],[12,16,1],[12,23,1],[13,19,1],[13,20,1],[13,25,1],[13,18,1],[13,33,1],[14,27,1],[14,31,1],[15,26,1],[15,21,1],[15,28,1],[15,24,1],[15,16,1],[15,23,1],[15,17,1],[16,26,1],[16,32,1],[16,23,1],[16,17,1],[17,26,1],[17,32,1],[17,21,1],[17,28,1],[17,24,1],[18,19,1],[18,22,1],[18,20,1],[18,30,1],[19,22,1],[19,20,1],[19,25,1],[19,30,1],[20,25,1],[20,30,1],[20,33,1],[21,26,1],[21,32,1],[21,28,1],[21,29,1],[22,25,1],[22,30,1],[22,33,1],[23,32,1],[23,28,1],[23,29,1],[23,24,1],[24,32,1],[24,28,1],[25,30,1],[25,33,1],[26,32,1],[26,28,1],[27,31,1],[28,29,1],[30,33,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],"source":5,"target":30}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-121

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[1,3,1],[1,2,1],[1,6,1],[2,5,1],[2,6,1],[3,5,1],[5,6,1]],"nodes":[0,1,2,3,4,5,6],"source":4,"target":5}

Model	Answer given
Gemma 4	{"reachable": false}	✓ correct
Llama 3.3	true	✗ wrong
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-224

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[0,5,1],[0,6,1],[1,3,1],[1,4,1],[2,5,1],[2,6,1],[3,4,1],[5,6,1]],"nodes":[0,1,2,3,4,5,6],"source":5,"target":3}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-140

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,11,1],[0,18,1],[0,19,1],[0,20,1],[0,23,1],[0,9,1],[0,10,1],[0,22,1],[0,13,1],[0,1,1],[0,12,1],[0,5,1],[0,7,1],[0,15,1],[0,4,1],[1,11,1],[1,18,1],[1,19,1],[1,20,1],[1,23,1],[1,9,1],[1,10,1],[1,22,1],[1,13,1],[1,12,1],[1,5,1],[1,7,1],[1,15,1],[1,4,1],[2,8,1],[2,6,1],[2,3,1],[2,24,1],[2,16,1],[2,21,1],[2,17,1],[2,14,1],[3,8,1],[3,6,1],[3,24,1],[3,16,1],[3,21,1],[3,17,1],[3,14,1],[4,11,1],[4,18,1],[4,19,1],[4,20,1],[4,23,1],[4,9,1],[4,10,1],[4,22,1],[4,13,1],[4,12,1],[4,5,1],[4,7,1],[4,15,1],[5,11,1],[5,18,1],[5,19,1],[5,20,1],[5,23,1],[5,9,1],[5,10,1],[5,22,1],[5,13,1],[5,12,1],[5,7,1],[5,15,1],[6,8,1],[6,24,1],[6,16,1],[6,21,1],[6,17,1],[6,14,1],[7,11,1],[7,18,1],[7,19,1],[7,20,1],[7,23,1],[7,9,1],[7,10,1],[7,22,1],[7,13,1],[7,12,1],[7,15,1],[8,24,1],[8,16,1],[8,21,1],[8,17,1],[8,14,1],[9,11,1],[9,18,1],[9,19,1],[9,20,1],[9,23,1],[9,10,1],[9,22,1],[9,13,1],[9,12,1],[9,15,1],[10,11,1],[10,18,1],[10,19,1],[10,20,1],[10,23,1],[10,22,1],[10,13,1],[10,12,1],[10,15,1],[11,18,1],[11,19,1],[11,20,1],[11,23,1],[11,22,1],[11,13,1],[11,12,1],[11,15,1],[12,18,1],[12,19,1],[12,20,1],[12,23,1],[12,22,1],[12,13,1],[12,15,1],[13,18,1],[13,19,1],[13,20,1],[13,23,1],[13,22,1],[13,15,1],[14,24,1],[14,16,1],[14,21,1],[14,17,1],[15,18,1],[15,19,1],[15,20,1],[15,23,1],[15,22,1],[16,24,1],[16,21,1],[16,17,1],[17,24,1],[17,21,1],[18,19,1],[18,20,1],[18,23,1],[18,22,1],[19,20,1],[19,23,1],[19,22,1],[20,23,1],[20,22,1],[21,24,1],[22,23,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"source":17,"target":11}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	false	✓ correct
Qwen · off	true	✗ wrong
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-120

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,2,1],[0,1,1],[1,5,1],[1,6,1],[2,6,1],[3,7,1],[4,7,1],[5,6,1]],"nodes":[0,1,2,3,4,5,6,7],"source":6,"target":5}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	true	✓ correct

test nlgraph-connectivity-test-242

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,12,1],[0,13,1],[0,2,1],[0,14,1],[0,23,1],[0,8,1],[0,1,1],[0,25,1],[0,27,1],[0,10,1],[1,29,1],[1,13,1],[1,19,1],[1,28,1],[1,23,1],[1,30,1],[1,25,1],[1,24,1],[2,12,1],[2,5,1],[2,14,1],[2,17,1],[2,23,1],[3,7,1],[3,12,1],[3,19,1],[3,23,1],[3,8,1],[3,30,1],[3,25,1],[3,24,1],[4,33,1],[5,20,1],[5,23,1],[5,30,1],[6,15,1],[6,11,1],[7,32,1],[7,17,1],[7,23,1],[7,8,1],[7,10,1],[8,29,1],[8,12,1],[8,32,1],[8,20,1],[8,19,1],[8,17,1],[8,30,1],[9,29,1],[9,28,1],[9,30,1],[9,24,1],[10,13,1],[10,20,1],[10,14,1],[10,22,1],[11,31,1],[12,13,1],[12,23,1],[12,27,1],[12,26,1],[13,29,1],[13,32,1],[13,14,1],[13,28,1],[13,30,1],[13,24,1],[14,17,1],[14,30,1],[14,22,1],[14,27,1],[15,16,1],[15,31,1],[15,33,1],[17,32,1],[17,20,1],[17,19,1],[17,27,1],[17,24,1],[17,26,1],[18,21,1],[20,28,1],[20,30,1],[20,25,1],[21,31,1],[22,32,1],[22,28,1],[22,30,1],[23,28,1],[23,25,1],[23,27,1],[24,29,1],[24,28,1],[24,26,1],[25,32,1],[26,29,1],[26,27,1],[27,32,1],[27,30,1],[28,32,1],[28,30,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],"source":17,"target":18}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	false	✓ correct

test nlgraph-connectivity-test-185

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,11,1],[0,7,1],[0,4,1],[0,10,1],[0,5,1],[0,13,1],[0,12,1],[0,1,1],[0,2,1],[0,3,1],[0,15,1],[0,6,1],[0,8,1],[0,14,1],[1,11,1],[1,7,1],[1,4,1],[1,10,1],[1,5,1],[1,13,1],[1,12,1],[1,2,1],[1,3,1],[1,15,1],[1,6,1],[1,8,1],[1,14,1],[2,11,1],[2,7,1],[2,4,1],[2,10,1],[2,5,1],[2,13,1],[2,12,1],[2,3,1],[2,15,1],[2,6,1],[2,8,1],[2,14,1],[3,11,1],[3,7,1],[3,4,1],[3,10,1],[3,5,1],[3,13,1],[3,12,1],[3,15,1],[3,6,1],[3,8,1],[3,14,1],[4,11,1],[4,7,1],[4,10,1],[4,5,1],[4,13,1],[4,12,1],[4,15,1],[4,6,1],[4,8,1],[4,14,1],[5,11,1],[5,7,1],[5,10,1],[5,13,1],[5,12,1],[5,15,1],[5,6,1],[5,8,1],[5,14,1],[6,11,1],[6,7,1],[6,10,1],[6,13,1],[6,12,1],[6,15,1],[6,8,1],[6,14,1],[7,11,1],[7,10,1],[7,13,1],[7,12,1],[7,15,1],[7,8,1],[7,14,1],[8,11,1],[8,10,1],[8,13,1],[8,12,1],[8,15,1],[8,14,1],[10,11,1],[10,13,1],[10,12,1],[10,15,1],[10,14,1],[11,13,1],[11,12,1],[11,15,1],[11,14,1],[12,13,1],[12,15,1],[12,14,1],[13,15,1],[13,14,1],[14,15,1]],"nodes":[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15],"source":14,"target":1}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-275

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,21,1],[0,14,1],[0,1,1],[0,22,1],[0,16,1],[0,19,1],[0,5,1],[0,10,1],[0,20,1],[0,11,1],[0,24,1],[0,13,1],[1,21,1],[1,9,1],[1,3,1],[1,14,1],[1,22,1],[1,10,1],[1,20,1],[1,12,1],[1,11,1],[1,24,1],[1,13,1],[1,23,1],[2,8,1],[2,4,1],[2,18,1],[2,15,1],[3,9,1],[3,14,1],[3,16,1],[3,19,1],[3,7,1],[3,6,1],[3,5,1],[3,10,1],[3,11,1],[4,8,1],[4,17,1],[4,18,1],[4,15,1],[5,9,1],[5,14,1],[5,22,1],[5,7,1],[5,6,1],[5,10,1],[5,20,1],[5,12,1],[5,11,1],[5,13,1],[5,23,1],[6,21,1],[6,9,1],[6,22,1],[6,19,1],[6,7,1],[6,20,1],[6,12,1],[6,11,1],[6,13,1],[6,23,1],[7,21,1],[7,9,1],[7,14,1],[7,16,1],[7,19,1],[7,10,1],[7,20,1],[7,12,1],[7,11,1],[7,24,1],[7,13,1],[7,23,1],[8,17,1],[8,18,1],[8,15,1],[9,21,1],[9,16,1],[9,10,1],[9,20,1],[9,12,1],[9,11,1],[9,24,1],[9,13,1],[9,23,1],[10,22,1],[10,19,1],[10,12,1],[10,11,1],[10,13,1],[10,23,1],[11,21,1],[11,22,1],[11,19,1],[11,20,1],[11,12,1],[11,24,1],[11,13,1],[11,23,1],[12,21,1],[12,14,1],[12,22,1],[12,20,1],[12,24,1],[12,13,1],[12,23,1],[13,21,1],[13,14,1],[13,22,1],[13,16,1],[13,20,1],[13,23,1],[14,21,1],[14,16,1],[14,20,1],[14,24,1],[14,23,1],[15,18,1],[16,21,1],[16,22,1],[16,19,1],[16,20,1],[16,24,1],[16,23,1],[17,18,1],[19,21,1],[19,20,1],[19,24,1],[19,23,1],[20,21,1],[20,24,1],[20,23,1],[21,24,1],[21,23,1],[22,23,1],[23,24,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"source":22,"target":20}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-342

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,11,1],[0,25,1],[0,13,1],[0,3,1],[0,1,1],[1,11,1],[1,25,1],[1,13,1],[1,2,1],[1,3,1],[1,8,1],[2,21,1],[2,22,1],[2,25,1],[2,13,1],[2,3,1],[3,18,1],[3,22,1],[3,11,1],[3,13,1],[4,23,1],[4,14,1],[4,6,1],[4,12,1],[4,27,1],[4,15,1],[4,5,1],[4,16,1],[4,26,1],[4,20,1],[4,7,1],[4,19,1],[5,14,1],[5,6,1],[5,12,1],[5,27,1],[5,15,1],[5,16,1],[5,9,1],[5,20,1],[5,7,1],[6,23,1],[6,14,1],[6,12,1],[6,24,1],[6,15,1],[6,16,1],[6,9,1],[6,17,1],[6,26,1],[6,20,1],[6,7,1],[6,19,1],[7,23,1],[7,14,1],[7,12,1],[7,24,1],[7,10,1],[7,16,1],[7,9,1],[7,17,1],[7,26,1],[7,20,1],[7,19,1],[8,21,1],[8,18,1],[8,22,1],[8,11,1],[8,25,1],[8,13,1],[9,23,1],[9,12,1],[9,10,1],[9,16,1],[9,17,1],[9,26,1],[9,20,1],[10,23,1],[10,14,1],[10,12,1],[10,24,1],[10,27,1],[10,16,1],[10,17,1],[10,26,1],[10,19,1],[11,21,1],[11,22,1],[11,25,1],[11,13,1],[12,23,1],[12,14,1],[12,24,1],[12,27,1],[12,16,1],[12,26,1],[12,20,1],[12,19,1],[13,22,1],[13,25,1],[14,23,1],[14,24,1],[14,16,1],[14,26,1],[14,19,1],[15,24,1],[15,27,1],[15,16,1],[15,26,1],[16,23,1],[16,27,1],[16,17,1],[16,26,1],[16,20,1],[17,27,1],[17,26,1],[17,20,1],[17,19,1],[18,22,1],[19,23,1],[19,24,1],[19,27,1],[19,26,1],[19,20,1],[20,23,1],[20,26,1],[21,22,1],[21,25,1],[22,25,1],[23,24,1],[23,27,1],[24,27,1],[24,26,1],[26,27,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],"source":25,"target":20}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-169

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,11,1],[0,25,1],[0,13,1],[0,3,1],[0,1,1],[1,11,1],[1,25,1],[1,13,1],[1,2,1],[1,3,1],[1,8,1],[2,21,1],[2,22,1],[2,25,1],[2,13,1],[2,3,1],[3,18,1],[3,22,1],[3,11,1],[3,13,1],[4,23,1],[4,14,1],[4,6,1],[4,12,1],[4,27,1],[4,15,1],[4,5,1],[4,16,1],[4,26,1],[4,20,1],[4,7,1],[4,19,1],[5,14,1],[5,6,1],[5,12,1],[5,27,1],[5,15,1],[5,16,1],[5,9,1],[5,20,1],[5,7,1],[6,23,1],[6,14,1],[6,12,1],[6,24,1],[6,15,1],[6,16,1],[6,9,1],[6,17,1],[6,26,1],[6,20,1],[6,7,1],[6,19,1],[7,23,1],[7,14,1],[7,12,1],[7,24,1],[7,10,1],[7,16,1],[7,9,1],[7,17,1],[7,26,1],[7,20,1],[7,19,1],[8,21,1],[8,18,1],[8,22,1],[8,11,1],[8,25,1],[8,13,1],[9,23,1],[9,12,1],[9,10,1],[9,16,1],[9,17,1],[9,26,1],[9,20,1],[10,23,1],[10,14,1],[10,12,1],[10,24,1],[10,27,1],[10,16,1],[10,17,1],[10,26,1],[10,19,1],[11,21,1],[11,22,1],[11,25,1],[11,13,1],[12,23,1],[12,14,1],[12,24,1],[12,27,1],[12,16,1],[12,26,1],[12,20,1],[12,19,1],[13,22,1],[13,25,1],[14,23,1],[14,24,1],[14,16,1],[14,26,1],[14,19,1],[15,24,1],[15,27,1],[15,16,1],[15,26,1],[16,23,1],[16,27,1],[16,17,1],[16,26,1],[16,20,1],[17,27,1],[17,26,1],[17,20,1],[17,19,1],[18,22,1],[19,23,1],[19,24,1],[19,27,1],[19,26,1],[19,20,1],[20,23,1],[20,26,1],[21,22,1],[21,25,1],[22,25,1],[23,24,1],[23,27,1],[24,27,1],[24,26,1],[26,27,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],"source":16,"target":27}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-309

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,4,1],[1,5,1]],"nodes":[0,1,3,4,5],"source":0,"target":5}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	true	✗ wrong
Qwen · off	false	✓ correct
Qwen · on	false	✓ correct

test nlgraph-connectivity-test-157

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,6,1],[0,5,1],[0,1,1],[0,9,1],[0,3,1],[0,4,1],[1,6,1],[1,5,1],[1,9,1],[1,3,1],[1,4,1],[2,7,1],[2,8,1],[2,10,1],[3,6,1],[3,5,1],[3,9,1],[3,4,1],[4,6,1],[4,5,1],[4,9,1],[5,6,1],[5,9,1],[6,9,1],[7,8,1],[7,10,1],[8,10,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10],"source":8,"target":0}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	false	✓ correct

test nlgraph-connectivity-test-329

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,18,1],[0,24,1],[0,5,1],[0,12,1],[0,26,1],[0,14,1],[0,16,1],[0,21,1],[0,9,1],[0,1,1],[0,28,1],[0,25,1],[1,3,1],[1,18,1],[1,24,1],[1,5,1],[1,12,1],[1,26,1],[1,14,1],[1,16,1],[1,21,1],[1,2,1],[1,23,1],[1,20,1],[1,28,1],[1,25,1],[2,3,1],[2,18,1],[2,10,1],[2,24,1],[2,5,1],[2,12,1],[2,26,1],[2,14,1],[2,16,1],[2,9,1],[2,23,1],[2,20,1],[2,28,1],[2,7,1],[2,25,1],[2,22,1],[2,13,1],[3,18,1],[3,24,1],[3,12,1],[3,26,1],[3,16,1],[3,9,1],[3,19,1],[3,7,1],[3,25,1],[3,22,1],[4,11,1],[4,27,1],[4,17,1],[4,15,1],[4,8,1],[5,18,1],[5,24,1],[5,12,1],[5,26,1],[5,14,1],[5,16,1],[5,21,1],[5,9,1],[5,23,1],[5,19,1],[5,20,1],[5,7,1],[5,13,1],[6,11,1],[6,27,1],[6,29,1],[6,15,1],[6,8,1],[7,18,1],[7,10,1],[7,12,1],[7,26,1],[7,14,1],[7,16,1],[7,21,1],[7,9,1],[7,20,1],[7,25,1],[7,22,1],[7,13,1],[8,11,1],[8,27,1],[8,29,1],[8,17,1],[8,15,1],[9,18,1],[9,10,1],[9,24,1],[9,16,1],[9,21,1],[9,19,1],[9,20,1],[9,28,1],[9,25,1],[9,13,1],[10,18,1],[10,24,1],[10,12,1],[10,26,1],[10,14,1],[10,16,1],[10,23,1],[10,20,1],[10,28,1],[10,25,1],[10,22,1],[10,13,1],[11,27,1],[11,29,1],[12,18,1],[12,24,1],[12,16,1],[12,21,1],[12,23,1],[12,20,1],[12,28,1],[12,22,1],[12,13,1],[13,18,1],[13,24,1],[13,26,1],[13,14,1],[13,16,1],[13,21,1],[13,23,1],[13,20,1],[13,28,1],[13,25,1],[13,22,1],[14,26,1],[14,16,1],[14,21,1],[14,23,1],[14,19,1],[14,20,1],[14,28,1],[14,25,1],[15,27,1],[15,17,1],[16,18,1],[16,24,1],[16,26,1],[16,20,1],[16,25,1],[16,22,1],[17,29,1],[18,24,1],[18,26,1],[18,23,1],[18,19,1],[18,20,1],[18,25,1],[18,22,1],[19,21,1],[19,23,1],[19,28,1],[19,25,1],[20,26,1],[20,23,1],[20,28,1],[20,25,1],[20,22,1],[21,26,1],[21,23,1],[21,28,1],[21,22,1],[22,26,1],[22,23,1],[22,25,1],[23,24,1],[23,26,1],[24,26,1],[24,28,1],[25,26,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],"source":7,"target":26}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-61

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[1,2,1],[2,3,1]],"nodes":[0,1,2,3],"source":2,"target":0}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-289

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,11,1],[0,7,1],[0,4,1],[0,10,1],[0,5,1],[0,13,1],[0,12,1],[0,1,1],[0,2,1],[0,3,1],[0,15,1],[0,6,1],[0,8,1],[0,14,1],[1,11,1],[1,7,1],[1,4,1],[1,10,1],[1,5,1],[1,13,1],[1,12,1],[1,2,1],[1,3,1],[1,15,1],[1,6,1],[1,8,1],[1,14,1],[2,11,1],[2,7,1],[2,4,1],[2,10,1],[2,5,1],[2,13,1],[2,12,1],[2,3,1],[2,15,1],[2,6,1],[2,8,1],[2,14,1],[3,11,1],[3,7,1],[3,4,1],[3,10,1],[3,5,1],[3,13,1],[3,12,1],[3,15,1],[3,6,1],[3,8,1],[3,14,1],[4,11,1],[4,7,1],[4,10,1],[4,5,1],[4,13,1],[4,12,1],[4,15,1],[4,6,1],[4,8,1],[4,14,1],[5,11,1],[5,7,1],[5,10,1],[5,13,1],[5,12,1],[5,15,1],[5,6,1],[5,8,1],[5,14,1],[6,11,1],[6,7,1],[6,10,1],[6,13,1],[6,12,1],[6,15,1],[6,8,1],[6,14,1],[7,11,1],[7,10,1],[7,13,1],[7,12,1],[7,15,1],[7,8,1],[7,14,1],[8,11,1],[8,10,1],[8,13,1],[8,12,1],[8,15,1],[8,14,1],[10,11,1],[10,13,1],[10,12,1],[10,15,1],[10,14,1],[11,13,1],[11,12,1],[11,15,1],[11,14,1],[12,13,1],[12,15,1],[12,14,1],[13,15,1],[13,14,1],[14,15,1]],"nodes":[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15],"source":14,"target":12}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-321

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,26,1],[0,15,1],[0,25,1],[0,14,1],[0,7,1],[0,2,1],[0,9,1],[0,5,1],[1,26,1],[1,15,1],[1,25,1],[1,7,1],[1,6,1],[1,2,1],[1,20,1],[1,22,1],[2,25,1],[2,19,1],[2,14,1],[2,4,1],[3,12,1],[3,16,1],[4,15,1],[4,7,1],[4,6,1],[4,8,1],[5,26,1],[5,20,1],[5,8,1],[5,9,1],[5,22,1],[5,13,1],[6,19,1],[6,17,1],[6,7,1],[6,20,1],[6,22,1],[7,19,1],[7,17,1],[7,9,1],[8,19,1],[9,26,1],[9,14,1],[9,24,1],[11,12,1],[12,21,1],[12,18,1],[12,16,1],[13,17,1],[13,22,1],[14,26,1],[14,22,1],[15,19,1],[15,20,1],[16,21,1],[18,23,1],[19,20,1],[19,22,1],[25,26,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],"source":12,"target":25}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-44

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,4,1],[1,5,1]],"nodes":[0,1,3,4,5],"source":4,"target":0}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-103

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[1,10,1],[2,9,1],[2,5,1],[3,12,1],[3,14,1],[3,4,1],[3,8,1],[3,18,1],[4,19,1],[4,16,1],[4,11,1],[5,20,1],[5,12,1],[5,14,1],[5,11,1],[6,18,1],[6,16,1],[7,15,1],[8,20,1],[8,12,1],[8,18,1],[8,16,1],[9,20,1],[9,14,1],[9,19,1],[9,11,1],[11,13,1],[11,12,1],[11,18,1],[11,16,1],[12,18,1],[13,19,1],[13,18,1],[14,19,1],[16,20,1],[18,19,1]],"nodes":[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20],"source":5,"target":20}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-154

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,11,1],[0,32,1],[0,29,1],[0,7,1],[0,15,1],[1,30,1],[1,10,1],[1,8,1],[2,27,1],[2,18,1],[2,20,1],[2,7,1],[2,26,1],[3,14,1],[3,9,1],[4,18,1],[4,11,1],[4,13,1],[4,15,1],[5,30,1],[5,21,1],[6,14,1],[6,21,1],[6,17,1],[7,18,1],[7,22,1],[7,31,1],[7,29,1],[7,26,1],[8,14,1],[8,10,1],[9,21,1],[10,12,1],[10,21,1],[10,17,1],[11,19,1],[11,22,1],[11,28,1],[11,32,1],[11,29,1],[11,15,1],[11,26,1],[12,30,1],[12,21,1],[13,27,1],[13,20,1],[13,28,1],[13,31,1],[14,17,1],[15,20,1],[15,31,1],[15,26,1],[16,27,1],[16,32,1],[17,30,1],[18,27,1],[18,28,1],[18,32,1],[18,26,1],[18,24,1],[18,23,1],[19,27,1],[19,20,1],[19,31,1],[19,29,1],[19,26,1],[19,24,1],[20,25,1],[20,28,1],[20,32,1],[20,26,1],[22,31,1],[22,23,1],[23,27,1],[23,28,1],[23,26,1],[25,26,1],[26,27,1],[26,28,1],[26,29,1],[28,32,1],[28,31,1],[29,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],"source":1,"target":22}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-268

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,20,1],[0,1,1],[0,15,1],[0,6,1],[0,9,1],[0,4,1],[0,16,1],[0,19,1],[1,20,1],[1,15,1],[1,6,1],[1,9,1],[1,4,1],[1,16,1],[1,19,1],[2,14,1],[2,10,1],[2,3,1],[2,11,1],[2,7,1],[2,18,1],[2,5,1],[2,12,1],[2,17,1],[2,8,1],[3,14,1],[3,10,1],[3,11,1],[3,7,1],[3,18,1],[3,5,1],[3,12,1],[3,17,1],[3,8,1],[4,20,1],[4,15,1],[4,6,1],[4,9,1],[4,16,1],[4,19,1],[5,14,1],[5,10,1],[5,11,1],[5,7,1],[5,18,1],[5,12,1],[5,17,1],[5,8,1],[6,20,1],[6,15,1],[6,9,1],[6,16,1],[6,19,1],[7,14,1],[7,10,1],[7,11,1],[7,18,1],[7,12,1],[7,17,1],[7,8,1],[8,14,1],[8,10,1],[8,11,1],[8,18,1],[8,12,1],[8,17,1],[9,20,1],[9,15,1],[9,16,1],[9,19,1],[10,14,1],[10,11,1],[10,18,1],[10,12,1],[10,17,1],[11,14,1],[11,18,1],[11,12,1],[11,17,1],[12,14,1],[12,18,1],[12,17,1],[14,18,1],[14,17,1],[15,20,1],[15,16,1],[15,19,1],[16,20,1],[16,19,1],[17,18,1],[19,20,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20],"source":4,"target":9}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-257

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,6,1],[0,3,1],[0,2,1],[0,1,1],[1,6,1],[1,3,1],[1,2,1],[2,6,1],[2,3,1],[3,6,1],[4,5,1]],"nodes":[0,1,2,3,4,5,6],"source":6,"target":0}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-295

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,29,1],[0,10,1],[0,18,1],[0,21,1],[0,30,1],[0,28,1],[0,15,1],[1,27,1],[1,24,1],[1,22,1],[1,32,1],[1,14,1],[1,5,1],[2,29,1],[2,10,1],[2,18,1],[2,21,1],[2,19,1],[2,30,1],[2,16,1],[2,28,1],[2,15,1],[3,24,1],[3,13,1],[3,22,1],[3,20,1],[3,5,1],[4,17,1],[4,11,1],[4,6,1],[4,26,1],[4,23,1],[4,31,1],[4,25,1],[5,27,1],[5,13,1],[5,22,1],[5,20,1],[5,32,1],[5,14,1],[6,17,1],[6,9,1],[6,23,1],[6,31,1],[6,25,1],[7,29,1],[7,10,1],[7,18,1],[7,19,1],[7,30,1],[7,16,1],[7,15,1],[8,17,1],[8,11,1],[8,26,1],[8,23,1],[8,31,1],[9,17,1],[9,26,1],[9,23,1],[9,31,1],[9,25,1],[10,29,1],[10,18,1],[10,21,1],[10,30,1],[10,28,1],[10,15,1],[11,17,1],[11,26,1],[11,23,1],[12,27,1],[12,24,1],[12,13,1],[12,22,1],[12,32,1],[13,27,1],[13,24,1],[13,22,1],[13,20,1],[13,32,1],[13,14,1],[14,27,1],[14,22,1],[14,32,1],[15,29,1],[15,18,1],[15,21,1],[15,19,1],[15,28,1],[16,29,1],[16,21,1],[16,19,1],[16,28,1],[17,23,1],[18,29,1],[18,21,1],[18,30,1],[18,28,1],[19,29,1],[19,21,1],[19,30,1],[19,28,1],[20,24,1],[20,22,1],[20,32,1],[21,29,1],[21,30,1],[21,28,1],[22,27,1],[22,24,1],[22,32,1],[23,31,1],[24,27,1],[25,26,1],[26,31,1],[28,30,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],"source":30,"target":23}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	TokenLimit	✗ no usable answer
Qwen · off	true	✗ wrong
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-318

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,27,1],[0,13,1],[0,10,1],[0,15,1],[0,2,1],[0,17,1],[1,5,1],[1,22,1],[1,8,1],[1,19,1],[1,26,1],[1,24,1],[1,18,1],[1,16,1],[1,14,1],[1,12,1],[1,4,1],[1,9,1],[2,7,1],[2,27,1],[2,13,1],[2,3,1],[2,6,1],[2,10,1],[2,11,1],[2,17,1],[3,7,1],[3,27,1],[3,20,1],[3,6,1],[3,10,1],[3,15,1],[3,21,1],[3,17,1],[4,5,1],[4,8,1],[4,19,1],[4,26,1],[4,25,1],[4,18,1],[4,14,1],[4,12,1],[5,8,1],[5,26,1],[5,18,1],[5,16,1],[5,14,1],[5,12,1],[6,7,1],[6,13,1],[6,10,1],[6,21,1],[7,20,1],[7,13,1],[7,10,1],[7,15,1],[7,11,1],[8,19,1],[8,26,1],[8,18,1],[8,16,1],[8,14,1],[8,9,1],[9,22,1],[9,19,1],[9,26,1],[9,25,1],[9,16,1],[9,14,1],[9,12,1],[10,13,1],[10,21,1],[10,17,1],[11,27,1],[11,13,1],[11,15,1],[11,21,1],[11,17,1],[12,22,1],[12,19,1],[12,26,1],[12,24,1],[12,25,1],[12,16,1],[12,14,1],[13,27,1],[13,15,1],[14,22,1],[14,19,1],[14,26,1],[15,27,1],[15,20,1],[15,21,1],[15,17,1],[16,22,1],[16,19,1],[16,24,1],[16,25,1],[16,18,1],[17,27,1],[17,20,1],[17,21,1],[18,22,1],[18,19,1],[18,26,1],[18,24,1],[19,26,1],[19,25,1],[20,27,1],[20,21,1],[21,27,1],[22,26,1],[22,24,1],[24,26,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,24,25,26,27],"source":24,"target":25}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-265

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,13,1],[0,5,1],[0,11,1],[0,15,1],[0,10,1],[0,16,1],[0,14,1],[0,8,1],[0,9,1],[1,18,1],[1,12,1],[1,7,1],[1,6,1],[2,13,1],[2,11,1],[2,15,1],[2,17,1],[2,16,1],[2,14,1],[2,3,1],[2,8,1],[2,9,1],[3,5,1],[3,11,1],[3,4,1],[3,15,1],[3,10,1],[3,14,1],[3,8,1],[3,9,1],[4,13,1],[4,5,1],[4,17,1],[4,16,1],[4,14,1],[4,8,1],[5,17,1],[5,16,1],[5,14,1],[6,12,1],[6,19,1],[6,20,1],[6,7,1],[7,18,1],[8,15,1],[8,17,1],[8,16,1],[8,14,1],[8,9,1],[9,13,1],[9,11,1],[9,17,1],[9,16,1],[9,14,1],[10,11,1],[10,15,1],[10,17,1],[10,16,1],[10,14,1],[11,13,1],[11,15,1],[11,16,1],[12,18,1],[12,19,1],[12,20,1],[13,17,1],[13,14,1],[14,15,1],[14,17,1],[14,16,1],[15,17,1],[16,17,1],[18,19,1],[18,20,1],[19,20,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"source":10,"target":15}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-156

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,7,1],[0,6,1],[0,3,1],[0,18,1],[0,1,1],[0,15,1],[0,12,1],[0,14,1],[0,9,1],[0,16,1],[0,8,1],[0,2,1],[0,11,1],[0,19,1],[1,7,1],[1,6,1],[1,3,1],[1,18,1],[1,15,1],[1,9,1],[1,8,1],[1,2,1],[1,20,1],[2,7,1],[2,3,1],[2,18,1],[2,15,1],[2,12,1],[2,14,1],[2,9,1],[2,16,1],[2,8,1],[2,11,1],[2,19,1],[2,20,1],[3,18,1],[3,15,1],[3,12,1],[3,9,1],[3,16,1],[3,8,1],[3,19,1],[3,20,1],[4,13,1],[4,17,1],[5,17,1],[6,7,1],[6,18,1],[6,15,1],[6,14,1],[6,9,1],[6,16,1],[6,11,1],[6,19,1],[6,20,1],[7,15,1],[7,12,1],[7,14,1],[7,9,1],[7,16,1],[8,18,1],[8,12,1],[8,14,1],[8,9,1],[8,16,1],[8,11,1],[8,19,1],[8,20,1],[9,18,1],[9,15,1],[9,12,1],[9,11,1],[9,19,1],[9,20,1],[10,13,1],[11,18,1],[11,12,1],[11,14,1],[11,16,1],[11,19,1],[11,20,1],[12,18,1],[12,15,1],[12,14,1],[12,19,1],[12,20,1],[13,17,1],[14,19,1],[16,18,1],[16,19,1],[18,20,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"source":20,"target":1}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-344

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,22,1],[0,12,1],[0,24,1],[0,18,1],[0,19,1],[0,30,1],[0,1,1],[0,21,1],[0,9,1],[0,5,1],[0,6,1],[0,7,1],[0,2,1],[1,22,1],[1,24,1],[1,18,1],[1,19,1],[1,30,1],[1,21,1],[1,9,1],[1,5,1],[1,6,1],[1,11,1],[1,7,1],[1,31,1],[1,2,1],[2,12,1],[2,24,1],[2,18,1],[2,19,1],[2,21,1],[2,5,1],[2,6,1],[2,11,1],[2,7,1],[2,31,1],[3,26,1],[3,16,1],[3,4,1],[3,28,1],[3,13,1],[3,20,1],[4,26,1],[4,16,1],[4,8,1],[4,28,1],[5,12,1],[5,24,1],[5,30,1],[5,21,1],[5,9,1],[5,11,1],[5,7,1],[5,31,1],[6,22,1],[6,12,1],[6,24,1],[6,30,1],[6,21,1],[6,9,1],[6,11,1],[6,7,1],[7,12,1],[7,18,1],[7,30,1],[7,9,1],[7,11,1],[7,31,1],[8,26,1],[8,16,1],[8,28,1],[9,22,1],[9,12,1],[9,24,1],[9,18,1],[9,19,1],[9,30,1],[9,11,1],[9,31,1],[10,25,1],[10,14,1],[10,29,1],[10,32,1],[10,15,1],[10,23,1],[11,22,1],[11,12,1],[11,24,1],[11,18,1],[11,30,1],[11,21,1],[12,24,1],[12,30,1],[12,21,1],[12,31,1],[13,26,1],[13,28,1],[14,27,1],[14,17,1],[14,29,1],[14,32,1],[14,15,1],[15,25,1],[15,27,1],[15,17,1],[15,29,1],[15,32,1],[15,23,1],[16,26,1],[17,29,1],[18,22,1],[18,24,1],[18,19,1],[18,21,1],[19,22,1],[19,30,1],[19,21,1],[20,26,1],[21,22,1],[21,24,1],[21,31,1],[22,24,1],[23,25,1],[23,27,1],[23,32,1],[24,30,1],[24,31,1],[25,27,1],[25,29,1],[25,32,1],[26,28,1],[27,29,1],[27,32,1],[30,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],"source":10,"target":1}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	true	✗ wrong
Qwen · off	false	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-243

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,13,1],[0,12,1],[0,14,1],[0,8,1],[0,3,1],[0,6,1],[0,2,1],[0,9,1],[0,5,1],[1,10,1],[1,7,1],[1,11,1],[2,4,1],[2,13,1],[2,12,1],[2,14,1],[2,8,1],[2,3,1],[2,6,1],[2,9,1],[2,5,1],[3,4,1],[3,13,1],[3,12,1],[3,14,1],[3,8,1],[3,6,1],[3,9,1],[3,5,1],[4,13,1],[4,12,1],[4,14,1],[4,8,1],[4,6,1],[4,9,1],[4,5,1],[5,13,1],[5,12,1],[5,14,1],[5,8,1],[5,6,1],[5,9,1],[6,13,1],[6,12,1],[6,14,1],[6,8,1],[6,9,1],[7,10,1],[7,11,1],[8,13,1],[8,12,1],[8,14,1],[8,9,1],[9,13,1],[9,12,1],[9,14,1],[10,11,1],[12,13,1],[12,14,1],[13,14,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"source":3,"target":9}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-252

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,7,1],[0,15,1],[0,18,1],[0,27,1],[0,9,1],[0,13,1],[0,25,1],[0,3,1],[1,8,1],[1,5,1],[1,26,1],[1,12,1],[1,2,1],[1,16,1],[1,14,1],[2,8,1],[2,26,1],[2,12,1],[2,16,1],[2,14,1],[3,7,1],[3,4,1],[3,15,1],[3,18,1],[3,27,1],[3,13,1],[4,7,1],[4,15,1],[4,18,1],[4,27,1],[4,13,1],[5,8,1],[5,12,1],[5,11,1],[5,16,1],[5,14,1],[5,20,1],[6,17,1],[6,21,1],[6,29,1],[6,28,1],[7,15,1],[7,18,1],[7,27,1],[7,9,1],[7,13,1],[8,26,1],[8,23,1],[8,16,1],[8,14,1],[9,15,1],[10,29,1],[10,24,1],[11,12,1],[11,16,1],[11,14,1],[11,20,1],[12,22,1],[12,23,1],[12,14,1],[12,20,1],[13,18,1],[13,27,1],[14,26,1],[14,22,1],[14,23,1],[14,20,1],[15,18,1],[15,27,1],[15,25,1],[16,26,1],[16,22,1],[16,23,1],[16,20,1],[17,21,1],[17,19,1],[17,24,1],[17,28,1],[19,21,1],[19,29,1],[19,24,1],[19,28,1],[20,26,1],[20,22,1],[20,23,1],[21,29,1],[21,24,1],[22,26,1],[22,23,1],[24,29,1],[24,28,1],[25,27,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],"source":13,"target":19}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-30

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,1,1],[3,7,1],[4,6,1],[5,6,1]],"nodes":[0,1,3,4,5,6,7],"source":6,"target":5}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	true	✓ correct

test nlgraph-connectivity-test-249

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,3,1],[0,11,1],[0,8,1],[0,2,1],[0,12,1],[0,9,1],[0,1,1],[1,4,1],[1,3,1],[1,6,1],[1,11,1],[1,8,1],[1,7,1],[1,10,1],[1,2,1],[1,12,1],[2,3,1],[2,6,1],[2,11,1],[2,8,1],[2,9,1],[3,6,1],[3,11,1],[3,8,1],[3,7,1],[3,10,1],[3,9,1],[4,6,1],[4,11,1],[4,8,1],[4,7,1],[4,10,1],[4,12,1],[4,9,1],[6,8,1],[6,10,1],[7,10,1],[7,12,1],[7,9,1],[8,11,1],[8,10,1],[8,12,1],[9,10,1],[10,12,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12],"source":2,"target":5}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-29

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,8,1],[0,2,1],[0,20,1],[0,16,1],[0,14,1],[0,15,1],[0,7,1],[1,18,1],[1,24,1],[1,22,1],[1,5,1],[1,19,1],[1,11,1],[1,17,1],[2,6,1],[2,4,1],[2,23,1],[2,8,1],[2,20,1],[2,16,1],[2,21,1],[2,14,1],[2,15,1],[2,10,1],[3,6,1],[3,4,1],[3,23,1],[3,8,1],[3,16,1],[3,14,1],[3,25,1],[3,15,1],[3,7,1],[4,6,1],[4,23,1],[4,8,1],[4,20,1],[4,16,1],[4,21,1],[4,14,1],[4,15,1],[4,10,1],[4,7,1],[5,18,1],[5,24,1],[5,22,1],[5,13,1],[5,9,1],[5,11,1],[5,12,1],[6,23,1],[6,8,1],[6,20,1],[6,16,1],[6,14,1],[6,25,1],[6,15,1],[7,23,1],[7,20,1],[7,16,1],[7,21,1],[7,14,1],[7,25,1],[7,15,1],[7,10,1],[8,20,1],[8,16,1],[8,14,1],[8,25,1],[8,15,1],[9,18,1],[9,24,1],[9,22,1],[9,19,1],[9,11,1],[9,17,1],[9,12,1],[10,23,1],[10,20,1],[10,16,1],[10,21,1],[10,14,1],[10,25,1],[11,22,1],[11,19,1],[11,17,1],[11,12,1],[12,18,1],[12,13,1],[12,19,1],[13,18,1],[13,24,1],[13,22,1],[13,17,1],[14,23,1],[14,20,1],[14,16,1],[14,25,1],[15,20,1],[15,16,1],[15,21,1],[15,25,1],[16,23,1],[16,20,1],[16,25,1],[17,18,1],[17,22,1],[17,19,1],[18,24,1],[18,22,1],[18,19,1],[19,24,1],[19,22,1],[20,21,1],[20,25,1],[21,23,1],[21,25,1],[22,24,1],[23,25,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],"source":5,"target":11}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-134

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[1,4,1],[1,13,1],[2,11,1],[3,4,1],[3,6,1],[3,19,1],[4,20,1],[4,12,1],[4,16,1],[5,14,1],[5,9,1],[6,18,1],[6,8,1],[7,13,1],[7,8,1],[7,19,1],[7,15,1],[8,18,1],[8,20,1],[8,15,1],[11,14,1],[12,20,1],[12,13,1],[12,19,1],[12,16,1],[13,18,1],[13,15,1],[15,18,1],[15,19,1],[18,20,1],[18,19,1]],"nodes":[1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20],"source":16,"target":7}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-269

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,11,1],[0,22,1],[0,30,1],[0,25,1],[0,19,1],[0,12,1],[0,13,1],[0,10,1],[0,29,1],[1,17,1],[1,4,1],[1,18,1],[1,7,1],[1,27,1],[1,2,1],[1,3,1],[1,9,1],[1,23,1],[1,28,1],[2,4,1],[2,21,1],[2,26,1],[2,7,1],[2,27,1],[2,9,1],[2,23,1],[2,28,1],[3,17,1],[3,4,1],[3,21,1],[3,26,1],[3,18,1],[3,7,1],[3,27,1],[3,14,1],[3,9,1],[3,23,1],[3,28,1],[3,24,1],[4,17,1],[4,21,1],[4,26,1],[4,18,1],[4,14,1],[4,9,1],[4,28,1],[4,24,1],[5,11,1],[5,22,1],[5,20,1],[5,25,1],[5,29,1],[6,8,1],[7,21,1],[7,26,1],[7,18,1],[7,27,1],[7,23,1],[7,28,1],[7,24,1],[9,21,1],[9,26,1],[9,18,1],[9,27,1],[9,14,1],[9,23,1],[9,28,1],[9,24,1],[10,11,1],[10,22,1],[10,20,1],[10,30,1],[10,25,1],[10,16,1],[10,19,1],[10,15,1],[10,13,1],[10,29,1],[11,22,1],[11,20,1],[11,30,1],[11,25,1],[11,16,1],[11,19,1],[11,12,1],[11,15,1],[11,13,1],[11,29,1],[12,22,1],[12,20,1],[12,30,1],[12,16,1],[12,15,1],[12,13,1],[13,22,1],[13,20,1],[13,30,1],[13,25,1],[13,16,1],[13,19,1],[13,15,1],[13,29,1],[14,26,1],[14,18,1],[14,23,1],[14,28,1],[14,24,1],[15,22,1],[15,30,1],[15,16,1],[15,19,1],[15,29,1],[16,22,1],[16,30,1],[16,25,1],[16,19,1],[16,29,1],[17,26,1],[17,18,1],[17,27,1],[17,23,1],[17,28,1],[18,21,1],[18,26,1],[18,27,1],[18,24,1],[19,20,1],[19,30,1],[19,25,1],[19,29,1],[20,22,1],[20,25,1],[20,29,1],[21,26,1],[21,27,1],[21,28,1],[21,24,1],[22,30,1],[22,29,1],[23,26,1],[23,27,1],[23,28,1],[23,24,1],[24,27,1],[24,28,1],[25,29,1],[26,27,1],[27,28,1],[29,30,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],"source":28,"target":1}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-354

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,8,1],[0,11,1],[0,17,1],[0,1,1],[0,2,1],[0,12,1],[0,6,1],[0,18,1],[0,7,1],[0,15,1],[1,19,1],[1,8,1],[1,9,1],[1,11,1],[1,2,1],[1,12,1],[1,6,1],[1,7,1],[1,15,1],[2,19,1],[2,4,1],[2,9,1],[2,11,1],[2,17,1],[2,12,1],[2,6,1],[2,18,1],[2,15,1],[3,5,1],[3,13,1],[3,10,1],[4,19,1],[4,8,1],[4,9,1],[4,11,1],[4,17,1],[4,12,1],[4,6,1],[4,7,1],[4,15,1],[5,13,1],[5,10,1],[6,9,1],[6,11,1],[6,12,1],[6,18,1],[7,19,1],[7,8,1],[7,9,1],[7,11,1],[7,17,1],[7,15,1],[8,19,1],[8,11,1],[8,17,1],[8,12,1],[9,17,1],[9,12,1],[9,18,1],[10,13,1],[11,17,1],[11,15,1],[12,19,1],[12,17,1],[12,18,1],[12,15,1],[14,20,1],[14,21,1],[15,17,1],[15,18,1],[17,19,1],[17,18,1],[18,19,1],[20,21,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21],"source":4,"target":0}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-151

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,14,1],[0,10,1],[0,2,1],[2,15,1],[2,20,1],[2,23,1],[2,14,1],[2,17,1],[2,24,1],[2,18,1],[3,21,1],[4,27,1],[5,9,1],[5,22,1],[6,29,1],[6,8,1],[7,29,1],[7,25,1],[7,20,1],[7,17,1],[7,18,1],[7,8,1],[8,23,1],[8,24,1],[10,23,1],[10,18,1],[11,27,1],[12,13,1],[13,21,1],[14,25,1],[14,23,1],[14,17,1],[14,24,1],[15,29,1],[15,25,1],[15,23,1],[15,16,1],[16,29,1],[16,17,1],[17,25,1],[17,23,1],[17,24,1],[17,18,1],[18,29,1],[20,25,1],[22,26,1],[23,25,1],[24,29,1],[26,27,1]],"nodes":[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25,26,27,29],"source":6,"target":7}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-34

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,11,1],[0,15,1],[0,25,1],[0,31,1],[0,23,1],[0,14,1],[1,28,1],[1,20,1],[1,12,1],[1,21,1],[1,19,1],[1,24,1],[1,27,1],[1,13,1],[1,6,1],[2,20,1],[2,22,1],[2,21,1],[2,19,1],[2,13,1],[2,6,1],[3,15,1],[3,4,1],[3,25,1],[3,23,1],[4,9,1],[4,15,1],[4,14,1],[5,8,1],[5,17,1],[5,10,1],[5,26,1],[5,7,1],[5,16,1],[6,20,1],[6,21,1],[6,19,1],[6,27,1],[6,13,1],[7,17,1],[7,16,1],[7,29,1],[8,17,1],[9,11,1],[9,15,1],[9,31,1],[9,23,1],[9,14,1],[10,17,1],[11,15,1],[11,30,1],[11,23,1],[11,14,1],[12,20,1],[12,22,1],[12,19,1],[12,27,1],[12,13,1],[12,18,1],[13,28,1],[13,22,1],[13,21,1],[13,24,1],[13,27,1],[13,18,1],[14,15,1],[14,25,1],[14,31,1],[14,23,1],[15,25,1],[15,30,1],[15,23,1],[16,26,1],[17,26,1],[17,29,1],[18,28,1],[18,20,1],[18,22,1],[18,21,1],[18,19,1],[18,24,1],[18,27,1],[19,22,1],[19,21,1],[19,24,1],[19,27,1],[20,28,1],[20,22,1],[20,21,1],[20,24,1],[20,27,1],[21,28,1],[21,22,1],[21,24,1],[22,24,1],[22,27,1],[23,30,1],[23,31,1],[24,28,1],[25,31,1],[27,28,1],[30,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],"source":10,"target":26}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-361

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,10,1],[0,5,1],[0,7,1],[0,2,1],[0,8,1],[0,4,1],[0,9,1],[0,1,1],[0,12,1],[0,3,1],[0,11,1],[0,13,1],[1,10,1],[1,5,1],[1,7,1],[1,2,1],[1,8,1],[1,4,1],[1,9,1],[1,12,1],[1,3,1],[1,11,1],[1,13,1],[2,10,1],[2,5,1],[2,7,1],[2,8,1],[2,4,1],[2,9,1],[2,12,1],[2,3,1],[2,11,1],[2,13,1],[3,10,1],[3,5,1],[3,7,1],[3,8,1],[3,4,1],[3,9,1],[3,12,1],[3,11,1],[3,13,1],[4,10,1],[4,5,1],[4,7,1],[4,8,1],[4,9,1],[4,12,1],[4,11,1],[4,13,1],[5,10,1],[5,7,1],[5,8,1],[5,9,1],[5,12,1],[5,11,1],[5,13,1],[7,10,1],[7,8,1],[7,9,1],[7,12,1],[7,11,1],[7,13,1],[8,10,1],[8,9,1],[8,12,1],[8,11,1],[8,13,1],[9,10,1],[9,12,1],[9,11,1],[9,13,1],[10,12,1],[10,11,1],[10,13,1],[11,12,1],[11,13,1],[12,13,1]],"nodes":[0,1,2,3,4,5,7,8,9,10,11,12,13],"source":8,"target":5}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-174

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,10,1],[1,11,1],[1,9,1],[1,14,1],[2,5,1],[2,6,1],[3,11,1],[3,13,1],[4,11,1],[4,13,1],[4,15,1],[5,7,1],[5,6,1],[7,10,1],[8,11,1],[8,9,1],[9,14,1],[9,12,1],[11,13,1],[13,14,1],[13,15,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"source":8,"target":9}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	true	✓ correct

test nlgraph-connectivity-test-180

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,4,1],[1,2,1],[3,4,1]],"nodes":[0,1,2,3,4],"source":4,"target":0}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	true	✓ correct

test nlgraph-connectivity-test-246

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,11,1],[0,2,1],[0,7,1],[0,8,1],[0,16,1],[0,15,1],[1,11,1],[1,2,1],[1,7,1],[1,8,1],[1,16,1],[1,15,1],[1,14,1],[2,4,1],[2,11,1],[2,5,1],[2,7,1],[2,12,1],[2,16,1],[2,15,1],[3,13,1],[3,10,1],[4,6,1],[4,5,1],[4,7,1],[4,8,1],[4,12,1],[4,16,1],[4,15,1],[4,14,1],[5,6,1],[5,7,1],[5,8,1],[5,12,1],[5,16,1],[5,14,1],[6,11,1],[6,7,1],[6,8,1],[6,12,1],[6,16,1],[6,15,1],[6,14,1],[7,11,1],[7,8,1],[7,16,1],[7,14,1],[8,11,1],[8,12,1],[8,16,1],[11,12,1],[11,16,1],[11,15,1],[11,14,1],[12,14,1],[14,16,1],[14,15,1]],"nodes":[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16],"source":15,"target":1}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-117

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,10,1],[1,11,1],[1,9,1],[1,14,1],[2,5,1],[2,6,1],[3,11,1],[3,13,1],[4,11,1],[4,13,1],[4,15,1],[5,7,1],[5,6,1],[7,10,1],[8,11,1],[8,9,1],[9,14,1],[9,12,1],[11,13,1],[13,14,1],[13,15,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"source":15,"target":7}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-73

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,10,1],[0,26,1],[0,13,1],[0,23,1],[0,14,1],[0,27,1],[0,30,1],[0,31,1],[0,28,1],[0,2,1],[0,8,1],[0,12,1],[0,9,1],[0,24,1],[0,5,1],[1,19,1],[1,15,1],[1,6,1],[1,11,1],[1,29,1],[1,17,1],[1,21,1],[1,4,1],[1,25,1],[1,7,1],[2,3,1],[2,14,1],[2,31,1],[2,28,1],[2,18,1],[2,8,1],[2,12,1],[2,9,1],[2,24,1],[2,5,1],[3,10,1],[3,13,1],[3,23,1],[3,27,1],[3,30,1],[3,31,1],[3,28,1],[3,18,1],[3,8,1],[3,12,1],[3,9,1],[3,24,1],[3,5,1],[4,20,1],[4,19,1],[4,15,1],[4,11,1],[4,29,1],[4,16,1],[4,22,1],[4,7,1],[5,10,1],[5,13,1],[5,23,1],[5,14,1],[5,27,1],[5,31,1],[5,18,1],[5,8,1],[5,12,1],[5,9,1],[6,20,1],[6,15,1],[6,11,1],[6,29,1],[6,17,1],[6,21,1],[6,16,1],[6,25,1],[6,7,1],[7,20,1],[7,15,1],[7,11,1],[7,29,1],[7,17,1],[7,21,1],[7,25,1],[8,10,1],[8,26,1],[8,13,1],[8,23,1],[8,14,1],[8,27,1],[8,30,1],[8,12,1],[8,24,1],[9,10,1],[9,26,1],[9,13,1],[9,14,1],[9,27,1],[9,30,1],[9,31,1],[9,18,1],[9,24,1],[10,26,1],[10,13,1],[10,23,1],[10,14,1],[10,27,1],[10,30,1],[10,31,1],[10,18,1],[11,20,1],[11,19,1],[11,15,1],[11,29,1],[11,17,1],[11,21,1],[11,16,1],[11,25,1],[11,22,1],[12,13,1],[12,23,1],[12,14,1],[12,27,1],[12,28,1],[13,26,1],[13,23,1],[13,14,1],[13,27,1],[13,31,1],[13,28,1],[14,23,1],[14,30,1],[14,28,1],[14,18,1],[14,24,1],[15,19,1],[15,29,1],[15,21,1],[15,16,1],[15,22,1],[16,20,1],[16,19,1],[16,29,1],[16,17,1],[16,21,1],[16,25,1],[17,20,1],[17,19,1],[17,29,1],[17,21,1],[17,25,1],[17,22,1],[18,26,1],[18,27,1],[18,30,1],[18,31,1],[18,28,1],[19,29,1],[19,21,1],[19,25,1],[19,22,1],[20,29,1],[20,22,1],[21,29,1],[21,25,1],[21,22,1],[22,25,1],[23,26,1],[23,27,1],[23,30,1],[23,31,1],[23,24,1],[24,27,1],[24,30,1],[24,31,1],[25,29,1],[26,27,1],[26,30,1],[26,28,1],[27,30,1],[27,31,1],[28,30,1],[28,31,1],[30,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],"source":8,"target":14}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-198

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,21,1],[0,11,1],[0,15,1],[0,4,1],[0,22,1],[0,5,1],[0,3,1],[0,6,1],[0,20,1],[0,13,1],[0,18,1],[0,9,1],[0,1,1],[0,12,1],[0,24,1],[0,16,1],[0,8,1],[0,23,1],[0,2,1],[1,21,1],[1,11,1],[1,15,1],[1,4,1],[1,22,1],[1,5,1],[1,3,1],[1,6,1],[1,20,1],[1,13,1],[1,18,1],[1,9,1],[1,12,1],[1,24,1],[1,16,1],[1,8,1],[1,23,1],[1,2,1],[2,21,1],[2,11,1],[2,15,1],[2,4,1],[2,22,1],[2,5,1],[2,3,1],[2,6,1],[2,20,1],[2,13,1],[2,18,1],[2,9,1],[2,12,1],[2,24,1],[2,16,1],[2,8,1],[2,23,1],[3,21,1],[3,11,1],[3,15,1],[3,4,1],[3,22,1],[3,5,1],[3,6,1],[3,20,1],[3,13,1],[3,18,1],[3,9,1],[3,12,1],[3,24,1],[3,16,1],[3,8,1],[3,23,1],[4,21,1],[4,11,1],[4,15,1],[4,22,1],[4,5,1],[4,6,1],[4,20,1],[4,13,1],[4,18,1],[4,9,1],[4,12,1],[4,24,1],[4,16,1],[4,8,1],[4,23,1],[5,21,1],[5,11,1],[5,15,1],[5,22,1],[5,6,1],[5,20,1],[5,13,1],[5,18,1],[5,9,1],[5,12,1],[5,24,1],[5,16,1],[5,8,1],[5,23,1],[6,21,1],[6,11,1],[6,15,1],[6,22,1],[6,20,1],[6,13,1],[6,18,1],[6,9,1],[6,12,1],[6,24,1],[6,16,1],[6,8,1],[6,23,1],[7,10,1],[7,14,1],[7,17,1],[7,19,1],[8,21,1],[8,11,1],[8,15,1],[8,22,1],[8,20,1],[8,13,1],[8,18,1],[8,9,1],[8,12,1],[8,24,1],[8,16,1],[8,23,1],[9,21,1],[9,11,1],[9,15,1],[9,22,1],[9,20,1],[9,13,1],[9,18,1],[9,12,1],[9,24,1],[9,16,1],[9,23,1],[10,14,1],[10,17,1],[10,19,1],[11,21,1],[11,15,1],[11,22,1],[11,20,1],[11,13,1],[11,18,1],[11,12,1],[11,24,1],[11,16,1],[11,23,1],[12,21,1],[12,15,1],[12,22,1],[12,20,1],[12,13,1],[12,18,1],[12,24,1],[12,16,1],[12,23,1],[13,21,1],[13,15,1],[13,22,1],[13,20,1],[13,18,1],[13,24,1],[13,16,1],[13,23,1],[14,17,1],[14,19,1],[15,21,1],[15,22,1],[15,20,1],[15,18,1],[15,24,1],[15,16,1],[15,23,1],[16,21,1],[16,22,1],[16,20,1],[16,18,1],[16,24,1],[16,23,1],[17,19,1],[18,21,1],[18,22,1],[18,20,1],[18,24,1],[18,23,1],[20,21,1],[20,22,1],[20,24,1],[20,23,1],[21,22,1],[21,24,1],[21,23,1],[22,24,1],[22,23,1],[23,24,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"source":6,"target":5}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-123

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[1,11,1],[1,9,1],[1,19,1],[1,31,1],[1,20,1],[2,15,1],[2,11,1],[2,27,1],[2,29,1],[2,16,1],[2,31,1],[3,8,1],[3,4,1],[3,12,1],[3,18,1],[3,17,1],[3,10,1],[3,25,1],[3,31,1],[3,20,1],[4,30,1],[4,24,1],[4,19,1],[5,26,1],[5,23,1],[6,13,1],[7,15,1],[7,9,1],[7,30,1],[7,12,1],[7,16,1],[7,19,1],[7,10,1],[7,25,1],[8,15,1],[8,11,1],[8,30,1],[8,24,1],[8,10,1],[8,31,1],[9,11,1],[9,30,1],[9,27,1],[9,29,1],[9,10,1],[10,15,1],[10,30,1],[10,12,1],[10,18,1],[10,19,1],[10,17,1],[10,14,1],[11,30,1],[11,29,1],[11,19,1],[12,15,1],[12,19,1],[12,14,1],[12,20,1],[13,28,1],[14,27,1],[14,24,1],[14,20,1],[15,27,1],[15,18,1],[15,25,1],[15,20,1],[16,29,1],[16,24,1],[16,19,1],[17,29,1],[17,19,1],[17,31,1],[18,30,1],[18,24,1],[18,19,1],[18,31,1],[19,30,1],[19,25,1],[21,28,1],[21,23,1],[22,23,1],[25,27,1],[25,31,1],[26,28,1],[29,31,1]],"nodes":[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],"source":2,"target":8}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-339

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,11,1],[0,7,1],[0,4,1],[0,10,1],[0,5,1],[0,13,1],[0,12,1],[0,1,1],[0,2,1],[0,3,1],[0,15,1],[0,6,1],[0,8,1],[0,14,1],[1,11,1],[1,7,1],[1,4,1],[1,10,1],[1,5,1],[1,13,1],[1,12,1],[1,2,1],[1,3,1],[1,15,1],[1,6,1],[1,8,1],[1,14,1],[2,11,1],[2,7,1],[2,4,1],[2,10,1],[2,5,1],[2,13,1],[2,12,1],[2,3,1],[2,15,1],[2,6,1],[2,8,1],[2,14,1],[3,11,1],[3,7,1],[3,4,1],[3,10,1],[3,5,1],[3,13,1],[3,12,1],[3,15,1],[3,6,1],[3,8,1],[3,14,1],[4,11,1],[4,7,1],[4,10,1],[4,5,1],[4,13,1],[4,12,1],[4,15,1],[4,6,1],[4,8,1],[4,14,1],[5,11,1],[5,7,1],[5,10,1],[5,13,1],[5,12,1],[5,15,1],[5,6,1],[5,8,1],[5,14,1],[6,11,1],[6,7,1],[6,10,1],[6,13,1],[6,12,1],[6,15,1],[6,8,1],[6,14,1],[7,11,1],[7,10,1],[7,13,1],[7,12,1],[7,15,1],[7,8,1],[7,14,1],[8,11,1],[8,10,1],[8,13,1],[8,12,1],[8,15,1],[8,14,1],[10,11,1],[10,13,1],[10,12,1],[10,15,1],[10,14,1],[11,13,1],[11,12,1],[11,15,1],[11,14,1],[12,13,1],[12,15,1],[12,14,1],[13,15,1],[13,14,1],[14,15,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"source":9,"target":8}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-107

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,18,1],[0,12,1],[0,2,1],[0,11,1],[0,8,1],[0,13,1],[1,4,1],[1,10,1],[1,17,1],[1,5,1],[1,14,1],[1,7,1],[1,6,1],[1,15,1],[2,3,1],[2,18,1],[2,12,1],[2,11,1],[2,8,1],[2,13,1],[3,18,1],[3,12,1],[3,11,1],[3,8,1],[3,13,1],[4,10,1],[4,17,1],[4,5,1],[4,14,1],[4,7,1],[4,6,1],[4,15,1],[5,10,1],[5,17,1],[5,14,1],[5,7,1],[5,6,1],[5,15,1],[6,10,1],[6,17,1],[6,14,1],[6,7,1],[6,15,1],[7,10,1],[7,17,1],[7,14,1],[7,15,1],[8,18,1],[8,12,1],[8,11,1],[8,13,1],[9,16,1],[10,17,1],[10,14,1],[10,15,1],[11,18,1],[11,12,1],[11,13,1],[12,18,1],[12,13,1],[13,18,1],[14,17,1],[14,15,1],[15,17,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"source":7,"target":13}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-75

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,8,1],[0,5,1],[0,2,1],[0,3,1],[0,10,1],[0,6,1],[0,1,1],[0,4,1],[0,9,1],[0,7,1],[0,12,1],[1,8,1],[1,5,1],[1,2,1],[1,3,1],[1,10,1],[1,6,1],[1,4,1],[1,9,1],[1,7,1],[1,12,1],[2,8,1],[2,5,1],[2,3,1],[2,10,1],[2,6,1],[2,4,1],[2,9,1],[2,7,1],[2,12,1],[3,8,1],[3,5,1],[3,10,1],[3,6,1],[3,4,1],[3,9,1],[3,7,1],[3,12,1],[4,8,1],[4,5,1],[4,10,1],[4,6,1],[4,9,1],[4,7,1],[4,12,1],[5,8,1],[5,10,1],[5,6,1],[5,9,1],[5,7,1],[5,12,1],[6,8,1],[6,10,1],[6,9,1],[6,7,1],[6,12,1],[7,8,1],[7,10,1],[7,9,1],[7,12,1],[8,10,1],[8,9,1],[8,12,1],[9,10,1],[9,12,1],[10,12,1],[11,13,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"source":2,"target":12}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-43

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,22,1],[0,15,1],[0,8,1],[0,12,1],[0,14,1],[0,2,1],[0,9,1],[0,1,1],[1,15,1],[1,20,1],[1,12,1],[2,20,1],[2,12,1],[2,7,1],[2,16,1],[3,15,1],[3,7,1],[3,16,1],[3,13,1],[3,14,1],[3,17,1],[3,21,1],[4,22,1],[4,8,1],[4,12,1],[4,17,1],[4,11,1],[6,23,1],[7,15,1],[7,17,1],[7,11,1],[7,21,1],[7,18,1],[8,22,1],[8,15,1],[8,20,1],[8,16,1],[8,9,1],[9,22,1],[9,13,1],[9,11,1],[9,21,1],[9,18,1],[10,22,1],[10,13,1],[10,21,1],[11,22,1],[11,15,1],[11,20,1],[11,12,1],[11,21,1],[11,18,1],[12,15,1],[12,13,1],[13,20,1],[13,18,1],[14,20,1],[17,22,1],[17,18,1],[18,20,1],[19,23,1],[20,22,1],[21,22,1]],"nodes":[0,1,2,3,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"source":13,"target":20}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-307

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,11,1],[0,5,1],[0,9,1],[0,6,1],[1,2,1],[1,7,1],[1,3,1],[1,10,1],[1,8,1],[2,7,1],[2,3,1],[2,10,1],[2,8,1],[3,7,1],[3,10,1],[3,8,1],[4,11,1],[4,5,1],[4,9,1],[4,6,1],[5,11,1],[5,9,1],[5,6,1],[6,11,1],[6,9,1],[7,10,1],[7,8,1],[8,10,1],[9,11,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11],"source":11,"target":4}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-226

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,14,1],[0,20,1],[0,13,1],[0,24,1],[0,4,1],[1,21,1],[1,3,1],[1,11,1],[1,10,1],[1,23,1],[1,8,1],[1,2,1],[1,22,1],[1,19,1],[1,18,1],[2,21,1],[2,3,1],[2,11,1],[2,10,1],[2,23,1],[2,8,1],[2,22,1],[2,19,1],[2,18,1],[3,21,1],[3,11,1],[3,10,1],[3,23,1],[3,8,1],[3,22,1],[3,19,1],[3,18,1],[4,14,1],[4,20,1],[4,13,1],[4,24,1],[5,7,1],[5,9,1],[5,12,1],[5,16,1],[5,15,1],[5,17,1],[5,6,1],[6,7,1],[6,9,1],[6,12,1],[6,16,1],[6,15,1],[6,17,1],[7,9,1],[7,12,1],[7,16,1],[7,15,1],[7,17,1],[8,21,1],[8,11,1],[8,10,1],[8,23,1],[8,22,1],[8,19,1],[8,18,1],[9,12,1],[9,16,1],[9,15,1],[9,17,1],[10,21,1],[10,11,1],[10,23,1],[10,22,1],[10,19,1],[10,18,1],[11,21,1],[11,23,1],[11,22,1],[11,19,1],[11,18,1],[12,16,1],[12,15,1],[12,17,1],[13,14,1],[13,20,1],[13,24,1],[14,20,1],[14,24,1],[15,16,1],[15,17,1],[16,17,1],[18,21,1],[18,23,1],[18,22,1],[18,19,1],[19,21,1],[19,23,1],[19,22,1],[20,24,1],[21,23,1],[21,22,1],[22,23,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"source":24,"target":0}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-122

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,29,1],[1,27,1],[1,24,1],[1,21,1],[1,3,1],[2,10,1],[2,22,1],[2,6,1],[2,18,1],[2,25,1],[2,12,1],[3,19,1],[3,27,1],[3,24,1],[4,10,1],[4,6,1],[4,18,1],[4,25,1],[5,28,1],[5,16,1],[6,10,1],[6,13,1],[6,25,1],[6,12,1],[6,9,1],[7,28,1],[8,10,1],[8,14,1],[8,18,1],[8,29,1],[8,25,1],[8,23,1],[9,13,1],[9,14,1],[10,29,1],[10,25,1],[12,22,1],[12,18,1],[12,17,1],[13,29,1],[13,26,1],[14,20,1],[14,17,1],[15,19,1],[17,25,1],[18,20,1],[18,25,1],[20,29,1],[20,26,1],[20,23,1],[21,27,1],[21,24,1],[23,26,1],[23,25,1],[24,27,1],[26,29,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],"source":6,"target":22}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-367

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,6,1],[0,3,1],[0,2,1],[0,1,1],[1,6,1],[1,3,1],[1,2,1],[2,6,1],[2,3,1],[3,6,1],[4,5,1]],"nodes":[0,1,2,3,4,5,6],"source":0,"target":5}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-142

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,10,1],[0,5,1],[0,20,1],[0,7,1],[0,19,1],[0,1,1],[0,14,1],[0,12,1],[0,15,1],[0,18,1],[0,4,1],[1,10,1],[1,5,1],[1,7,1],[1,2,1],[1,14,1],[1,12,1],[1,3,1],[1,15,1],[1,16,1],[1,4,1],[2,10,1],[2,5,1],[2,20,1],[2,7,1],[2,19,1],[2,14,1],[2,12,1],[2,15,1],[2,16,1],[2,17,1],[2,18,1],[2,4,1],[3,5,1],[3,20,1],[3,7,1],[3,19,1],[3,14,1],[3,16,1],[3,17,1],[3,18,1],[4,10,1],[4,5,1],[4,20,1],[4,7,1],[4,19,1],[4,14,1],[4,12,1],[4,15,1],[4,16,1],[4,17,1],[5,20,1],[5,7,1],[5,19,1],[5,14,1],[5,12,1],[5,16,1],[5,17,1],[5,18,1],[6,11,1],[6,8,1],[7,10,1],[7,19,1],[7,14,1],[7,12,1],[7,15,1],[7,16,1],[7,17,1],[7,18,1],[8,11,1],[9,21,1],[9,13,1],[10,19,1],[10,14,1],[10,12,1],[10,16,1],[10,18,1],[12,20,1],[12,19,1],[12,14,1],[12,15,1],[12,16,1],[12,17,1],[14,20,1],[14,19,1],[14,15,1],[14,16,1],[14,17,1],[15,20,1],[15,19,1],[15,16,1],[15,17,1],[15,18,1],[16,20,1],[16,19,1],[16,17,1],[16,18,1],[17,20,1],[17,19,1],[17,18,1],[18,19,1],[19,20,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],"source":17,"target":21}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-277

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[1,10,1],[2,9,1],[2,5,1],[3,12,1],[3,14,1],[3,4,1],[3,8,1],[3,18,1],[4,19,1],[4,16,1],[4,11,1],[5,20,1],[5,12,1],[5,14,1],[5,11,1],[6,18,1],[6,16,1],[7,15,1],[8,20,1],[8,12,1],[8,18,1],[8,16,1],[9,20,1],[9,14,1],[9,19,1],[9,11,1],[11,13,1],[11,12,1],[11,18,1],[11,16,1],[12,18,1],[13,19,1],[13,18,1],[14,19,1],[16,20,1],[18,19,1]],"nodes":[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20],"source":3,"target":9}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-280

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[0,23,1],[0,8,1],[1,6,1],[1,26,1],[1,11,1],[2,6,1],[2,11,1],[3,12,1],[3,19,1],[3,20,1],[4,13,1],[4,21,1],[4,17,1],[4,10,1],[4,6,1],[4,23,1],[4,8,1],[5,13,1],[5,7,1],[5,21,1],[5,17,1],[5,28,1],[5,6,1],[5,23,1],[5,8,1],[5,26,1],[5,24,1],[5,11,1],[6,13,1],[6,17,1],[6,10,1],[6,23,1],[6,24,1],[7,17,1],[7,28,1],[7,23,1],[8,21,1],[8,10,1],[9,15,1],[10,13,1],[10,21,1],[10,23,1],[10,11,1],[11,13,1],[11,17,1],[12,19,1],[12,14,1],[12,27,1],[12,15,1],[12,22,1],[13,17,1],[13,16,1],[14,22,1],[15,19,1],[16,17,1],[16,28,1],[16,24,1],[17,24,1],[18,19,1],[18,27,1],[19,27,1],[21,26,1],[21,24,1],[22,25,1],[23,28,1],[24,28,1],[25,27,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],"source":19,"target":28}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-197

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,23,1],[0,4,1],[1,32,1],[1,22,1],[1,34,1],[1,7,1],[1,5,1],[1,28,1],[1,11,1],[1,13,1],[1,30,1],[1,31,1],[1,26,1],[2,12,1],[2,3,1],[2,24,1],[2,15,1],[2,18,1],[2,8,1],[2,20,1],[2,25,1],[2,19,1],[2,17,1],[2,16,1],[3,10,1],[3,24,1],[3,15,1],[3,18,1],[3,8,1],[3,20,1],[3,14,1],[3,19,1],[3,21,1],[4,23,1],[4,6,1],[5,32,1],[5,22,1],[5,7,1],[5,33,1],[5,11,1],[5,13,1],[5,27,1],[5,31,1],[5,26,1],[6,23,1],[7,22,1],[7,34,1],[7,28,1],[7,13,1],[7,27,1],[7,30,1],[7,26,1],[7,29,1],[8,10,1],[8,24,1],[8,15,1],[8,18,1],[8,20,1],[8,14,1],[8,17,1],[8,21,1],[8,16,1],[9,32,1],[9,22,1],[9,34,1],[9,28,1],[9,13,1],[9,27,1],[9,31,1],[9,26,1],[9,29,1],[10,12,1],[10,24,1],[10,15,1],[10,18,1],[10,20,1],[10,25,1],[10,17,1],[11,32,1],[11,22,1],[11,34,1],[11,28,1],[11,13,1],[11,27,1],[11,30,1],[11,31,1],[11,26,1],[12,24,1],[12,25,1],[12,14,1],[12,17,1],[12,21,1],[12,16,1],[13,34,1],[13,33,1],[13,27,1],[13,30,1],[13,31,1],[13,29,1],[14,15,1],[14,18,1],[14,20,1],[14,25,1],[14,19,1],[14,17,1],[14,21,1],[14,16,1],[15,24,1],[15,18,1],[15,20,1],[15,17,1],[15,21,1],[16,24,1],[16,20,1],[16,19,1],[16,17,1],[17,24,1],[17,20,1],[17,21,1],[18,20,1],[18,25,1],[18,19,1],[20,24,1],[20,25,1],[20,21,1],[21,25,1],[22,32,1],[22,28,1],[22,27,1],[22,30,1],[22,31,1],[22,26,1],[24,25,1],[26,34,1],[26,33,1],[26,31,1],[27,34,1],[27,33,1],[27,28,1],[27,30,1],[27,31,1],[27,29,1],[28,32,1],[28,33,1],[28,30,1],[28,31,1],[28,29,1],[29,32,1],[29,33,1],[30,32,1],[31,32,1],[31,34,1],[32,34,1],[32,33,1],[33,34,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],"source":1,"target":26}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-262

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,18,1],[0,17,1],[0,10,1],[1,7,1],[1,24,1],[1,27,1],[2,4,1],[2,8,1],[2,13,1],[2,19,1],[2,27,1],[3,16,1],[3,28,1],[3,9,1],[4,18,1],[4,6,1],[4,10,1],[4,11,1],[4,27,1],[6,20,1],[6,8,1],[6,7,1],[6,27,1],[7,8,1],[7,18,1],[7,17,1],[7,23,1],[7,24,1],[7,10,1],[7,13,1],[7,19,1],[7,11,1],[7,14,1],[8,17,1],[8,22,1],[8,24,1],[8,10,1],[8,11,1],[10,18,1],[10,17,1],[10,12,1],[10,11,1],[10,27,1],[11,17,1],[11,12,1],[12,20,1],[12,18,1],[12,17,1],[12,14,1],[13,20,1],[13,18,1],[13,24,1],[13,27,1],[13,26,1],[14,18,1],[15,28,1],[15,25,1],[16,25,1],[17,20,1],[17,18,1],[17,26,1],[18,22,1],[18,23,1],[18,19,1],[18,27,1],[19,23,1],[19,27,1],[19,26,1],[20,24,1],[22,23,1],[22,24,1],[22,26,1],[26,27,1]],"nodes":[0,1,2,3,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,27,28],"source":2,"target":6}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-8

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,18,1],[0,17,1],[0,10,1],[1,7,1],[1,24,1],[1,27,1],[2,4,1],[2,8,1],[2,13,1],[2,19,1],[2,27,1],[3,16,1],[3,28,1],[3,9,1],[4,18,1],[4,6,1],[4,10,1],[4,11,1],[4,27,1],[6,20,1],[6,8,1],[6,7,1],[6,27,1],[7,8,1],[7,18,1],[7,17,1],[7,23,1],[7,24,1],[7,10,1],[7,13,1],[7,19,1],[7,11,1],[7,14,1],[8,17,1],[8,22,1],[8,24,1],[8,10,1],[8,11,1],[10,18,1],[10,17,1],[10,12,1],[10,11,1],[10,27,1],[11,17,1],[11,12,1],[12,20,1],[12,18,1],[12,17,1],[12,14,1],[13,20,1],[13,18,1],[13,24,1],[13,27,1],[13,26,1],[14,18,1],[15,28,1],[15,25,1],[16,25,1],[17,20,1],[17,18,1],[17,26,1],[18,22,1],[18,23,1],[18,19,1],[18,27,1],[19,23,1],[19,27,1],[19,26,1],[20,24,1],[22,23,1],[22,24,1],[22,26,1],[26,27,1]],"nodes":[0,1,2,3,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,27,28],"source":17,"target":0}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-161

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[0,19,1],[1,11,1],[2,4,1],[2,13,1],[3,17,1],[3,10,1],[3,11,1],[5,8,1],[5,13,1],[6,10,1],[6,12,1],[7,18,1],[7,9,1],[10,17,1],[10,12,1],[11,12,1],[12,17,1],[13,16,1],[13,15,1],[14,18,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"source":16,"target":4}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	false	✗ wrong
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-184

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,7,1],[0,20,1],[0,27,1],[0,29,1],[0,26,1],[0,17,1],[0,3,1],[0,1,1],[0,16,1],[1,6,1],[1,7,1],[1,20,1],[1,19,1],[1,3,1],[1,33,1],[1,4,1],[2,27,1],[2,34,1],[2,26,1],[2,19,1],[2,17,1],[2,3,1],[2,21,1],[2,4,1],[3,6,1],[3,7,1],[3,11,1],[3,28,1],[3,29,1],[4,6,1],[4,28,1],[4,27,1],[4,29,1],[4,26,1],[4,19,1],[4,33,1],[4,23,1],[5,7,1],[5,11,1],[5,28,1],[5,19,1],[5,33,1],[5,16,1],[6,7,1],[6,28,1],[6,27,1],[6,26,1],[6,21,1],[7,34,1],[8,13,1],[8,12,1],[8,22,1],[8,15,1],[9,24,1],[9,12,1],[9,10,1],[10,25,1],[11,16,1],[11,23,1],[12,32,1],[12,18,1],[12,22,1],[12,15,1],[13,14,1],[14,18,1],[14,15,1],[15,30,1],[15,18,1],[16,27,1],[16,17,1],[16,23,1],[17,29,1],[17,19,1],[17,33,1],[17,23,1],[18,31,1],[18,24,1],[19,28,1],[19,27,1],[19,34,1],[19,29,1],[19,33,1],[19,21,1],[20,21,1],[21,26,1],[21,33,1],[22,30,1],[22,25,1],[25,30,1],[25,31,1],[26,28,1],[26,34,1],[26,29,1],[27,28,1],[30,32,1],[31,32,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],"source":12,"target":31}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-119

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,8,1],[0,19,1],[0,17,1],[0,7,1],[0,16,1],[0,21,1],[1,22,1],[1,19,1],[1,20,1],[1,21,1],[2,23,1],[2,6,1],[3,13,1],[3,18,1],[3,4,1],[3,10,1],[3,21,1],[4,19,1],[4,10,1],[4,16,1],[5,14,1],[5,12,1],[5,9,1],[5,11,1],[6,14,1],[6,23,1],[7,15,1],[7,22,1],[7,18,1],[7,8,1],[7,17,1],[7,20,1],[8,13,1],[8,21,1],[9,12,1],[9,11,1],[10,17,1],[13,19,1],[13,17,1],[13,21,1],[15,20,1],[16,18,1],[16,20,1],[19,20,1],[19,21,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"source":0,"target":19}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-324

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,16,1],[0,3,1],[0,12,1],[0,6,1],[0,11,1],[1,16,1],[1,3,1],[1,12,1],[1,6,1],[1,11,1],[1,14,1],[1,10,1],[2,15,1],[2,7,1],[2,13,1],[2,5,1],[2,9,1],[2,4,1],[2,18,1],[3,17,1],[3,12,1],[3,11,1],[3,14,1],[4,15,1],[4,7,1],[4,5,1],[4,9,1],[4,8,1],[5,15,1],[5,13,1],[5,9,1],[5,8,1],[5,18,1],[6,16,1],[6,17,1],[6,12,1],[6,14,1],[6,10,1],[7,15,1],[7,13,1],[7,9,1],[7,18,1],[8,15,1],[8,9,1],[8,18,1],[9,13,1],[9,18,1],[10,16,1],[10,17,1],[10,12,1],[10,11,1],[11,16,1],[11,17,1],[11,12,1],[12,16,1],[12,17,1],[12,14,1],[13,15,1],[13,18,1],[14,16,1],[14,17,1],[15,18,1],[16,17,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"source":4,"target":12}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-356

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,31,1],[0,11,1],[0,27,1],[0,18,1],[1,4,1],[1,12,1],[1,31,1],[1,7,1],[1,25,1],[1,8,1],[1,18,1],[2,17,1],[2,14,1],[2,6,1],[2,10,1],[2,19,1],[3,17,1],[3,22,1],[3,9,1],[4,12,1],[4,30,1],[4,31,1],[4,13,1],[4,27,1],[4,18,1],[5,29,1],[5,16,1],[5,22,1],[5,21,1],[5,20,1],[5,28,1],[5,19,1],[6,29,1],[6,9,1],[6,10,1],[6,28,1],[7,11,1],[7,27,1],[7,15,1],[7,18,1],[8,30,1],[8,23,1],[8,11,1],[9,14,1],[9,21,1],[9,10,1],[11,23,1],[11,18,1],[12,30,1],[12,31,1],[12,27,1],[12,25,1],[12,15,1],[12,18,1],[13,23,1],[13,25,1],[13,15,1],[14,29,1],[14,17,1],[16,24,1],[16,17,1],[16,20,1],[17,29,1],[18,30,1],[18,26,1],[20,29,1],[21,24,1],[22,24,1],[23,27,1],[23,25,1],[25,26,1],[25,27,1],[26,31,1],[27,31,1],[28,29,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],"source":3,"target":8}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-221

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[0,7,1],[0,6,1],[0,8,1],[0,4,1],[0,1,1],[1,2,1],[1,7,1],[1,6,1],[1,8,1],[1,4,1],[2,7,1],[2,6,1],[2,8,1],[2,4,1],[3,5,1],[4,7,1],[4,6,1],[4,8,1],[6,7,1],[6,8,1],[7,8,1]],"nodes":[0,1,2,3,4,5,6,7,8],"source":2,"target":6}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-360

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,10,1],[0,26,1],[0,13,1],[0,23,1],[0,14,1],[0,27,1],[0,30,1],[0,31,1],[0,28,1],[0,2,1],[0,8,1],[0,12,1],[0,9,1],[0,24,1],[0,5,1],[1,19,1],[1,15,1],[1,6,1],[1,11,1],[1,29,1],[1,17,1],[1,21,1],[1,4,1],[1,25,1],[1,7,1],[2,3,1],[2,14,1],[2,31,1],[2,28,1],[2,18,1],[2,8,1],[2,12,1],[2,9,1],[2,24,1],[2,5,1],[3,10,1],[3,13,1],[3,23,1],[3,27,1],[3,30,1],[3,31,1],[3,28,1],[3,18,1],[3,8,1],[3,12,1],[3,9,1],[3,24,1],[3,5,1],[4,20,1],[4,19,1],[4,15,1],[4,11,1],[4,29,1],[4,16,1],[4,22,1],[4,7,1],[5,10,1],[5,13,1],[5,23,1],[5,14,1],[5,27,1],[5,31,1],[5,18,1],[5,8,1],[5,12,1],[5,9,1],[6,20,1],[6,15,1],[6,11,1],[6,29,1],[6,17,1],[6,21,1],[6,16,1],[6,25,1],[6,7,1],[7,20,1],[7,15,1],[7,11,1],[7,29,1],[7,17,1],[7,21,1],[7,25,1],[8,10,1],[8,26,1],[8,13,1],[8,23,1],[8,14,1],[8,27,1],[8,30,1],[8,12,1],[8,24,1],[9,10,1],[9,26,1],[9,13,1],[9,14,1],[9,27,1],[9,30,1],[9,31,1],[9,18,1],[9,24,1],[10,26,1],[10,13,1],[10,23,1],[10,14,1],[10,27,1],[10,30,1],[10,31,1],[10,18,1],[11,20,1],[11,19,1],[11,15,1],[11,29,1],[11,17,1],[11,21,1],[11,16,1],[11,25,1],[11,22,1],[12,13,1],[12,23,1],[12,14,1],[12,27,1],[12,28,1],[13,26,1],[13,23,1],[13,14,1],[13,27,1],[13,31,1],[13,28,1],[14,23,1],[14,30,1],[14,28,1],[14,18,1],[14,24,1],[15,19,1],[15,29,1],[15,21,1],[15,16,1],[15,22,1],[16,20,1],[16,19,1],[16,29,1],[16,17,1],[16,21,1],[16,25,1],[17,20,1],[17,19,1],[17,29,1],[17,21,1],[17,25,1],[17,22,1],[18,26,1],[18,27,1],[18,30,1],[18,31,1],[18,28,1],[19,29,1],[19,21,1],[19,25,1],[19,22,1],[20,29,1],[20,22,1],[21,29,1],[21,25,1],[21,22,1],[22,25,1],[23,26,1],[23,27,1],[23,30,1],[23,31,1],[23,24,1],[24,27,1],[24,30,1],[24,31,1],[25,29,1],[26,27,1],[26,30,1],[26,28,1],[27,30,1],[27,31,1],[28,30,1],[28,31,1],[30,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],"source":24,"target":28}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-288

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[0,4,1],[0,9,1],[0,5,1],[0,13,1],[1,14,1],[1,15,1],[1,12,1],[1,5,1],[1,7,1],[2,4,1],[2,6,1],[2,9,1],[2,12,1],[2,13,1],[4,11,1],[4,6,1],[4,15,1],[4,7,1],[4,8,1],[4,13,1],[5,11,1],[5,10,1],[5,14,1],[5,6,1],[5,9,1],[5,15,1],[5,12,1],[5,7,1],[5,13,1],[6,14,1],[7,14,1],[7,8,1],[9,13,1],[10,14,1],[12,15,1]],"nodes":[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15],"source":1,"target":6}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-199

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,23,1],[1,6,1],[1,19,1],[1,7,1],[2,17,1],[2,24,1],[2,10,1],[2,20,1],[3,22,1],[3,27,1],[4,17,1],[4,15,1],[5,19,1],[5,12,1],[5,25,1],[6,19,1],[6,7,1],[7,18,1],[7,23,1],[8,16,1],[8,13,1],[9,27,1],[9,13,1],[10,21,1],[10,15,1],[10,11,1],[11,17,1],[11,26,1],[11,24,1],[11,14,1],[12,25,1],[12,23,1],[14,17,1],[14,26,1],[15,21,1],[17,26,1],[17,21,1],[17,24,1],[20,21,1],[20,24,1],[21,26,1],[21,24,1],[23,25,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],"source":9,"target":26}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✗ wrong
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-292

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,16,1],[0,3,1],[0,12,1],[0,6,1],[0,11,1],[1,16,1],[1,3,1],[1,12,1],[1,6,1],[1,11,1],[1,14,1],[1,10,1],[2,15,1],[2,7,1],[2,13,1],[2,5,1],[2,9,1],[2,4,1],[2,18,1],[3,17,1],[3,12,1],[3,11,1],[3,14,1],[4,15,1],[4,7,1],[4,5,1],[4,9,1],[4,8,1],[5,15,1],[5,13,1],[5,9,1],[5,8,1],[5,18,1],[6,16,1],[6,17,1],[6,12,1],[6,14,1],[6,10,1],[7,15,1],[7,13,1],[7,9,1],[7,18,1],[8,15,1],[8,9,1],[8,18,1],[9,13,1],[9,18,1],[10,16,1],[10,17,1],[10,12,1],[10,11,1],[11,16,1],[11,17,1],[11,12,1],[12,16,1],[12,17,1],[12,14,1],[13,15,1],[13,18,1],[14,16,1],[14,17,1],[15,18,1],[16,17,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"source":18,"target":6}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-251

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,4,1],[1,5,1]],"nodes":[0,1,3,4,5],"source":0,"target":4}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	true	✓ correct

test nlgraph-connectivity-test-88

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,2,1],[0,1,1],[1,5,1],[1,6,1],[2,6,1],[3,7,1],[4,7,1],[5,6,1]],"nodes":[0,1,2,3,4,5,6,7],"source":7,"target":3}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-194

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,1,1],[0,6,1],[0,21,1],[0,18,1],[1,24,1],[1,3,1],[3,24,1],[3,14,1],[4,6,1],[4,5,1],[4,23,1],[6,14,1],[6,21,1],[6,23,1],[7,11,1],[8,19,1],[8,13,1],[9,15,1],[9,19,1],[10,11,1],[10,12,1],[10,16,1],[10,17,1],[11,12,1],[11,16,1],[12,17,1],[13,15,1],[13,22,1],[14,23,1],[15,22,1],[16,17,1],[18,24,1],[18,21,1]],"nodes":[0,1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24],"source":19,"target":8}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-306

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,9,1],[0,10,1],[0,1,1],[1,8,1],[1,3,1],[1,14,1],[3,5,1],[3,6,1],[3,9,1],[3,12,1],[4,9,1],[4,16,1],[6,7,1],[6,12,1],[7,14,1],[8,16,1],[8,14,1],[10,11,1],[10,14,1],[10,12,1],[11,14,1],[12,14,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,14,16],"source":1,"target":2}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	{"directed": false, "edges": [[0, 9, 1], [0, 10, 1], [0, 1, 1], [1, 8, 1], [1, 3, 1], [1, 14, 1], [3, 5, 1], [3, 6, 1], [3, 9, 1], [3, 12, 1…	✗ wrong
Qwen · off	false	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-370

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[1,4,1],[1,13,1],[2,11,1],[3,4,1],[3,6,1],[3,19,1],[4,20,1],[4,12,1],[4,16,1],[5,14,1],[5,9,1],[6,18,1],[6,8,1],[7,13,1],[7,8,1],[7,19,1],[7,15,1],[8,18,1],[8,20,1],[8,15,1],[11,14,1],[12,20,1],[12,13,1],[12,19,1],[12,16,1],[13,18,1],[13,15,1],[15,18,1],[15,19,1],[18,20,1],[18,19,1]],"nodes":[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20],"source":10,"target":3}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-240

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,9,1],[0,2,1],[0,5,1],[0,10,1],[0,1,1],[1,4,1],[1,9,1],[1,2,1],[1,5,1],[1,10,1],[2,4,1],[2,9,1],[2,5,1],[2,10,1],[3,11,1],[3,8,1],[3,12,1],[3,7,1],[3,6,1],[4,9,1],[4,5,1],[4,10,1],[5,9,1],[5,10,1],[6,11,1],[6,8,1],[6,12,1],[6,7,1],[7,11,1],[7,8,1],[7,12,1],[8,11,1],[8,12,1],[9,10,1],[11,12,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12],"source":12,"target":8}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-188

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[1,8,1],[1,4,1],[1,5,1],[1,7,1],[1,2,1],[1,9,1],[1,6,1],[2,8,1],[2,4,1],[2,5,1],[2,7,1],[2,9,1],[2,6,1],[4,8,1],[4,5,1],[4,7,1],[4,9,1],[4,6,1],[5,8,1],[5,7,1],[5,9,1],[5,6,1],[6,8,1],[6,7,1],[6,9,1],[7,8,1],[7,9,1],[8,9,1]],"nodes":[0,1,2,3,4,5,6,7,8,9],"source":5,"target":4}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-167

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[1,4,1],[1,13,1],[2,11,1],[3,4,1],[3,6,1],[3,19,1],[4,20,1],[4,12,1],[4,16,1],[5,14,1],[5,9,1],[6,18,1],[6,8,1],[7,13,1],[7,8,1],[7,19,1],[7,15,1],[8,18,1],[8,20,1],[8,15,1],[11,14,1],[12,20,1],[12,13,1],[12,19,1],[12,16,1],[13,18,1],[13,15,1],[15,18,1],[15,19,1],[18,20,1],[18,19,1]],"nodes":[1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20],"source":7,"target":18}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-200

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,12,1],[0,3,1],[0,11,1],[0,18,1],[0,7,1],[0,8,1],[0,9,1],[0,1,1],[0,10,1],[0,15,1],[0,17,1],[0,13,1],[0,16,1],[0,19,1],[0,2,1],[0,6,1],[0,5,1],[0,14,1],[1,12,1],[1,3,1],[1,11,1],[1,18,1],[1,7,1],[1,8,1],[1,9,1],[1,10,1],[1,15,1],[1,17,1],[1,13,1],[1,16,1],[1,19,1],[1,2,1],[1,6,1],[1,5,1],[1,14,1],[2,12,1],[2,3,1],[2,11,1],[2,18,1],[2,7,1],[2,8,1],[2,9,1],[2,10,1],[2,15,1],[2,17,1],[2,13,1],[2,16,1],[2,19,1],[2,6,1],[2,5,1],[2,14,1],[3,12,1],[3,11,1],[3,18,1],[3,7,1],[3,8,1],[3,9,1],[3,10,1],[3,15,1],[3,17,1],[3,13,1],[3,16,1],[3,19,1],[3,6,1],[3,5,1],[3,14,1],[4,20,1],[4,21,1],[5,12,1],[5,11,1],[5,18,1],[5,7,1],[5,8,1],[5,9,1],[5,10,1],[5,15,1],[5,17,1],[5,13,1],[5,16,1],[5,19,1],[5,6,1],[5,14,1],[6,12,1],[6,11,1],[6,18,1],[6,7,1],[6,8,1],[6,9,1],[6,10,1],[6,15,1],[6,17,1],[6,13,1],[6,16,1],[6,19,1],[6,14,1],[7,12,1],[7,11,1],[7,18,1],[7,8,1],[7,9,1],[7,10,1],[7,15,1],[7,17,1],[7,13,1],[7,16,1],[7,19,1],[7,14,1],[8,12,1],[8,11,1],[8,18,1],[8,9,1],[8,10,1],[8,15,1],[8,17,1],[8,13,1],[8,16,1],[8,19,1],[8,14,1],[9,12,1],[9,11,1],[9,18,1],[9,10,1],[9,15,1],[9,17,1],[9,13,1],[9,16,1],[9,19,1],[9,14,1],[10,12,1],[10,11,1],[10,18,1],[10,15,1],[10,17,1],[10,13,1],[10,16,1],[10,19,1],[10,14,1],[11,12,1],[11,18,1],[11,15,1],[11,17,1],[11,13,1],[11,16,1],[11,19,1],[11,14,1],[12,18,1],[12,15,1],[12,17,1],[12,13,1],[12,16,1],[12,19,1],[12,14,1],[13,18,1],[13,15,1],[13,17,1],[13,16,1],[13,19,1],[13,14,1],[14,18,1],[14,15,1],[14,17,1],[14,16,1],[14,19,1],[15,18,1],[15,17,1],[15,16,1],[15,19,1],[16,18,1],[16,17,1],[16,19,1],[17,18,1],[17,19,1],[18,19,1],[20,21,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],"source":7,"target":21}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	true	✗ wrong
Qwen · off	false	✓ correct
Qwen · on	false	✓ correct

test nlgraph-connectivity-test-299

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,11,1],[0,2,1],[0,14,1],[0,7,1],[0,13,1],[1,17,1],[1,3,1],[1,10,1],[1,6,1],[2,11,1],[2,12,1],[2,14,1],[2,13,1],[3,17,1],[3,10,1],[3,6,1],[4,9,1],[4,5,1],[5,9,1],[5,16,1],[6,17,1],[6,8,1],[6,10,1],[7,11,1],[7,12,1],[7,14,1],[7,13,1],[8,17,1],[8,15,1],[9,18,1],[9,16,1],[10,17,1],[12,14,1],[12,13,1],[13,14,1],[15,17,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"source":12,"target":16}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-49

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,7,1],[0,3,1],[0,2,1],[0,9,1],[0,8,1],[1,6,1],[1,4,1],[2,7,1],[2,10,1],[2,3,1],[2,8,1],[2,5,1],[3,10,1],[3,9,1],[3,8,1],[4,6,1],[5,7,1],[5,10,1],[5,9,1],[7,8,1],[8,9,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10],"source":0,"target":2}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	true	✓ correct

test nlgraph-connectivity-test-271

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,17,1],[0,10,1],[0,19,1],[0,16,1],[0,7,1],[0,8,1],[0,4,1],[0,3,1],[0,11,1],[0,1,1],[0,18,1],[0,9,1],[0,5,1],[0,2,1],[0,13,1],[1,17,1],[1,10,1],[1,19,1],[1,16,1],[1,7,1],[1,8,1],[1,4,1],[1,3,1],[1,11,1],[1,18,1],[1,9,1],[1,5,1],[1,2,1],[1,13,1],[2,17,1],[2,10,1],[2,19,1],[2,16,1],[2,7,1],[2,8,1],[2,4,1],[2,3,1],[2,11,1],[2,18,1],[2,9,1],[2,5,1],[2,13,1],[3,17,1],[3,10,1],[3,19,1],[3,16,1],[3,7,1],[3,8,1],[3,4,1],[3,11,1],[3,18,1],[3,9,1],[3,5,1],[3,13,1],[4,17,1],[4,10,1],[4,19,1],[4,16,1],[4,7,1],[4,8,1],[4,11,1],[4,18,1],[4,9,1],[4,5,1],[4,13,1],[5,17,1],[5,10,1],[5,19,1],[5,16,1],[5,7,1],[5,8,1],[5,11,1],[5,18,1],[5,9,1],[5,13,1],[6,15,1],[7,17,1],[7,10,1],[7,19,1],[7,16,1],[7,8,1],[7,11,1],[7,18,1],[7,9,1],[7,13,1],[8,17,1],[8,10,1],[8,19,1],[8,16,1],[8,11,1],[8,18,1],[8,9,1],[8,13,1],[9,17,1],[9,10,1],[9,19,1],[9,16,1],[9,11,1],[9,18,1],[9,13,1],[10,17,1],[10,19,1],[10,16,1],[10,11,1],[10,18,1],[10,13,1],[11,17,1],[11,19,1],[11,16,1],[11,18,1],[11,13,1],[12,14,1],[13,17,1],[13,19,1],[13,16,1],[13,18,1],[16,17,1],[16,19,1],[16,18,1],[17,19,1],[17,18,1],[18,19,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"source":6,"target":9}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-105

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,22,1],[0,6,1],[0,11,1],[0,10,1],[0,4,1],[0,5,1],[0,9,1],[0,1,1],[0,13,1],[0,21,1],[0,20,1],[0,12,1],[1,22,1],[1,11,1],[1,10,1],[1,5,1],[1,16,1],[1,9,1],[1,13,1],[1,21,1],[1,20,1],[2,8,1],[2,19,1],[2,3,1],[2,18,1],[2,24,1],[3,19,1],[3,17,1],[3,24,1],[3,23,1],[4,22,1],[4,6,1],[4,16,1],[4,9,1],[4,21,1],[4,20,1],[5,22,1],[5,6,1],[5,14,1],[5,11,1],[5,16,1],[5,15,1],[5,9,1],[5,13,1],[5,21,1],[5,20,1],[6,22,1],[6,11,1],[6,10,1],[6,16,1],[6,13,1],[6,21,1],[6,12,1],[7,8,1],[7,17,1],[7,18,1],[7,24,1],[7,23,1],[8,17,1],[8,24,1],[9,14,1],[9,11,1],[9,10,1],[9,16,1],[9,15,1],[9,21,1],[9,20,1],[9,12,1],[10,22,1],[10,14,1],[10,11,1],[10,16,1],[10,15,1],[10,21,1],[10,20,1],[11,22,1],[11,16,1],[11,15,1],[11,20,1],[12,22,1],[12,14,1],[12,15,1],[12,13,1],[12,21,1],[12,20,1],[13,14,1],[13,16,1],[13,15,1],[13,21,1],[13,20,1],[14,22,1],[14,16,1],[14,15,1],[14,21,1],[15,16,1],[15,21,1],[16,22,1],[16,21,1],[16,20,1],[17,19,1],[17,18,1],[17,24,1],[17,23,1],[18,23,1],[19,24,1],[23,24,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"source":3,"target":15}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-228

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,7,1],[0,15,1],[0,18,1],[0,27,1],[0,9,1],[0,13,1],[0,25,1],[0,3,1],[1,8,1],[1,5,1],[1,26,1],[1,12,1],[1,2,1],[1,16,1],[1,14,1],[2,8,1],[2,26,1],[2,12,1],[2,16,1],[2,14,1],[3,7,1],[3,4,1],[3,15,1],[3,18,1],[3,27,1],[3,13,1],[4,7,1],[4,15,1],[4,18,1],[4,27,1],[4,13,1],[5,8,1],[5,12,1],[5,11,1],[5,16,1],[5,14,1],[5,20,1],[6,17,1],[6,21,1],[6,29,1],[6,28,1],[7,15,1],[7,18,1],[7,27,1],[7,9,1],[7,13,1],[8,26,1],[8,23,1],[8,16,1],[8,14,1],[9,15,1],[10,29,1],[10,24,1],[11,12,1],[11,16,1],[11,14,1],[11,20,1],[12,22,1],[12,23,1],[12,14,1],[12,20,1],[13,18,1],[13,27,1],[14,26,1],[14,22,1],[14,23,1],[14,20,1],[15,18,1],[15,27,1],[15,25,1],[16,26,1],[16,22,1],[16,23,1],[16,20,1],[17,21,1],[17,19,1],[17,24,1],[17,28,1],[19,21,1],[19,29,1],[19,24,1],[19,28,1],[20,26,1],[20,22,1],[20,23,1],[21,29,1],[21,24,1],[22,26,1],[22,23,1],[24,29,1],[24,28,1],[25,27,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],"source":17,"target":14}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-305

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,12,1],[0,28,1],[0,1,1],[0,22,1],[0,20,1],[0,15,1],[0,18,1],[0,2,1],[0,5,1],[0,10,1],[0,8,1],[0,14,1],[0,6,1],[1,27,1],[1,12,1],[1,19,1],[1,28,1],[1,25,1],[1,29,1],[1,22,1],[1,4,1],[1,7,1],[1,15,1],[1,18,1],[1,3,1],[1,2,1],[1,24,1],[1,5,1],[1,11,1],[1,14,1],[1,13,1],[1,6,1],[2,12,1],[2,19,1],[2,28,1],[2,29,1],[2,4,1],[2,15,1],[2,16,1],[2,18,1],[2,3,1],[2,10,1],[2,13,1],[2,21,1],[2,6,1],[3,27,1],[3,19,1],[3,28,1],[3,20,1],[3,4,1],[3,7,1],[3,16,1],[3,18,1],[3,9,1],[3,24,1],[3,5,1],[3,11,1],[3,10,1],[3,8,1],[3,14,1],[3,23,1],[3,21,1],[3,6,1],[4,27,1],[4,12,1],[4,19,1],[4,28,1],[4,25,1],[4,20,1],[4,7,1],[4,15,1],[4,16,1],[4,5,1],[4,8,1],[4,14,1],[4,13,1],[4,21,1],[4,6,1],[5,27,1],[5,12,1],[5,19,1],[5,28,1],[5,25,1],[5,29,1],[5,22,1],[5,20,1],[5,7,1],[5,15,1],[5,16,1],[5,24,1],[5,11,1],[5,10,1],[5,8,1],[5,14,1],[5,23,1],[5,13,1],[5,21,1],[5,6,1],[6,27,1],[6,12,1],[6,28,1],[6,25,1],[6,29,1],[6,22,1],[6,20,1],[6,7,1],[6,16,1],[6,18,1],[6,9,1],[6,24,1],[6,8,1],[6,14,1],[6,21,1],[7,19,1],[7,25,1],[7,29,1],[7,22,1],[7,20,1],[7,15,1],[7,16,1],[7,24,1],[7,11,1],[7,10,1],[7,14,1],[7,23,1],[7,21,1],[8,27,1],[8,12,1],[8,19,1],[8,29,1],[8,22,1],[8,20,1],[8,15,1],[8,16,1],[8,9,1],[8,24,1],[8,11,1],[8,10,1],[8,14,1],[8,13,1],[9,12,1],[9,19,1],[9,25,1],[9,22,1],[9,20,1],[9,18,1],[9,24,1],[9,11,1],[9,10,1],[9,14,1],[9,23,1],[9,13,1],[9,21,1],[10,27,1],[10,12,1],[10,19,1],[10,28,1],[10,25,1],[10,29,1],[10,16,1],[10,18,1],[10,24,1],[10,14,1],[10,23,1],[10,13,1],[10,21,1],[11,27,1],[11,12,1],[11,25,1],[11,22,1],[11,20,1],[11,18,1],[11,24,1],[12,19,1],[12,28,1],[12,29,1],[12,22,1],[12,15,1],[12,16,1],[12,18,1],[12,14,1],[12,23,1],[12,13,1],[12,21,1],[13,27,1],[13,28,1],[13,25,1],[13,29,1],[13,22,1],[13,20,1],[13,15,1],[13,18,1],[13,24,1],[14,19,1],[14,28,1],[14,25,1],[14,29,1],[14,15,1],[14,16,1],[14,18,1],[14,24,1],[14,23,1],[15,27,1],[15,28,1],[15,25,1],[15,29,1],[15,20,1],[15,18,1],[15,23,1],[15,21,1],[16,27,1],[16,19,1],[16,28,1],[16,25,1],[16,29,1],[16,22,1],[16,20,1],[16,18,1],[16,24,1],[16,21,1],[18,19,1],[18,28,1],[18,29,1],[18,22,1],[18,20,1],[18,24,1],[18,23,1],[18,21,1],[19,27,1],[19,28,1],[19,25,1],[19,29,1],[19,22,1],[19,20,1],[19,24,1],[19,23,1],[19,21,1],[20,27,1],[20,28,1],[20,29,1],[20,22,1],[20,23,1],[20,21,1],[21,27,1],[21,28,1],[21,24,1],[21,23,1],[22,27,1],[22,28,1],[22,29,1],[22,23,1],[23,27,1],[23,28,1],[23,25,1],[23,29,1],[24,27,1],[24,28,1],[24,25,1],[24,29,1],[25,27,1],[25,29,1],[27,28,1],[27,29,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,27,28,29],"source":18,"target":24}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-60

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,23,1],[0,11,1],[0,8,1],[0,17,1],[0,13,1],[0,6,1],[0,3,1],[0,15,1],[0,7,1],[1,14,1],[1,19,1],[1,9,1],[1,21,1],[1,12,1],[1,22,1],[1,4,1],[1,18,1],[1,5,1],[1,10,1],[1,20,1],[2,16,1],[3,23,1],[3,11,1],[3,8,1],[3,17,1],[3,13,1],[3,6,1],[3,15,1],[3,7,1],[4,14,1],[4,19,1],[4,9,1],[4,21,1],[4,12,1],[4,22,1],[4,18,1],[4,5,1],[4,10,1],[4,20,1],[5,14,1],[5,19,1],[5,9,1],[5,21,1],[5,12,1],[5,22,1],[5,18,1],[5,10,1],[5,20,1],[6,23,1],[6,11,1],[6,8,1],[6,17,1],[6,13,1],[6,15,1],[6,7,1],[7,23,1],[7,11,1],[7,8,1],[7,17,1],[7,13,1],[7,15,1],[8,23,1],[8,11,1],[8,17,1],[8,13,1],[8,15,1],[9,14,1],[9,19,1],[9,21,1],[9,12,1],[9,22,1],[9,18,1],[9,10,1],[9,20,1],[10,14,1],[10,19,1],[10,21,1],[10,12,1],[10,22,1],[10,18,1],[10,20,1],[11,23,1],[11,17,1],[11,13,1],[11,15,1],[12,14,1],[12,19,1],[12,21,1],[12,22,1],[12,18,1],[12,20,1],[13,23,1],[13,17,1],[13,15,1],[14,19,1],[14,21,1],[14,22,1],[14,18,1],[14,20,1],[15,23,1],[15,17,1],[17,23,1],[18,19,1],[18,21,1],[18,22,1],[18,20,1],[19,21,1],[19,22,1],[19,20,1],[20,21,1],[20,22,1],[21,22,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"source":21,"target":3}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	false	✓ correct

test nlgraph-connectivity-test-273

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,25,1],[0,3,1],[1,25,1],[1,29,1],[2,14,1],[2,13,1],[2,20,1],[2,18,1],[2,31,1],[2,9,1],[2,27,1],[2,21,1],[2,12,1],[2,7,1],[2,33,1],[2,11,1],[2,24,1],[2,26,1],[2,30,1],[3,25,1],[4,23,1],[4,22,1],[4,34,1],[4,5,1],[5,23,1],[5,22,1],[5,34,1],[6,14,1],[6,13,1],[6,20,1],[6,18,1],[6,27,1],[6,21,1],[6,12,1],[6,7,1],[6,28,1],[6,24,1],[6,26,1],[6,30,1],[7,14,1],[7,13,1],[7,20,1],[7,31,1],[7,17,1],[7,9,1],[7,27,1],[7,21,1],[7,12,1],[7,10,1],[7,33,1],[7,28,1],[7,30,1],[8,14,1],[8,13,1],[8,31,1],[8,17,1],[8,9,1],[8,27,1],[8,12,1],[8,33,1],[8,11,1],[8,28,1],[8,26,1],[8,30,1],[9,14,1],[9,13,1],[9,20,1],[9,18,1],[9,27,1],[9,21,1],[9,12,1],[9,10,1],[9,33,1],[9,24,1],[9,26,1],[9,19,1],[9,30,1],[10,13,1],[10,20,1],[10,18,1],[10,31,1],[10,17,1],[10,27,1],[10,12,1],[10,33,1],[10,11,1],[10,28,1],[10,24,1],[11,14,1],[11,13,1],[11,20,1],[11,18,1],[11,31,1],[11,12,1],[11,33,1],[11,28,1],[11,24,1],[11,26,1],[11,30,1],[12,14,1],[12,13,1],[12,20,1],[12,18,1],[12,17,1],[12,27,1],[12,21,1],[12,33,1],[12,19,1],[13,14,1],[13,20,1],[13,18,1],[13,31,1],[13,17,1],[13,21,1],[13,28,1],[13,24,1],[13,26,1],[14,18,1],[14,31,1],[14,17,1],[14,27,1],[14,21,1],[14,33,1],[14,26,1],[15,32,1],[17,18,1],[17,31,1],[17,27,1],[17,33,1],[17,28,1],[17,24,1],[17,26,1],[17,19,1],[17,30,1],[18,20,1],[18,31,1],[18,33,1],[18,24,1],[18,26,1],[18,19,1],[18,30,1],[19,31,1],[19,27,1],[19,21,1],[19,33,1],[19,28,1],[19,26,1],[20,31,1],[20,27,1],[20,21,1],[20,33,1],[20,24,1],[20,26,1],[20,30,1],[21,27,1],[21,33,1],[21,28,1],[21,24,1],[21,30,1],[22,23,1],[22,34,1],[23,34,1],[24,33,1],[24,26,1],[25,29,1],[26,31,1],[26,33,1],[26,30,1],[27,31,1],[27,33,1],[27,28,1],[27,30,1],[28,31,1],[28,33,1],[28,30,1],[30,31,1],[30,33,1],[31,33,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],"source":1,"target":31}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-233

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,23,1],[0,4,1],[1,32,1],[1,22,1],[1,34,1],[1,7,1],[1,5,1],[1,28,1],[1,11,1],[1,13,1],[1,30,1],[1,31,1],[1,26,1],[2,12,1],[2,3,1],[2,24,1],[2,15,1],[2,18,1],[2,8,1],[2,20,1],[2,25,1],[2,19,1],[2,17,1],[2,16,1],[3,10,1],[3,24,1],[3,15,1],[3,18,1],[3,8,1],[3,20,1],[3,14,1],[3,19,1],[3,21,1],[4,23,1],[4,6,1],[5,32,1],[5,22,1],[5,7,1],[5,33,1],[5,11,1],[5,13,1],[5,27,1],[5,31,1],[5,26,1],[6,23,1],[7,22,1],[7,34,1],[7,28,1],[7,13,1],[7,27,1],[7,30,1],[7,26,1],[7,29,1],[8,10,1],[8,24,1],[8,15,1],[8,18,1],[8,20,1],[8,14,1],[8,17,1],[8,21,1],[8,16,1],[9,32,1],[9,22,1],[9,34,1],[9,28,1],[9,13,1],[9,27,1],[9,31,1],[9,26,1],[9,29,1],[10,12,1],[10,24,1],[10,15,1],[10,18,1],[10,20,1],[10,25,1],[10,17,1],[11,32,1],[11,22,1],[11,34,1],[11,28,1],[11,13,1],[11,27,1],[11,30,1],[11,31,1],[11,26,1],[12,24,1],[12,25,1],[12,14,1],[12,17,1],[12,21,1],[12,16,1],[13,34,1],[13,33,1],[13,27,1],[13,30,1],[13,31,1],[13,29,1],[14,15,1],[14,18,1],[14,20,1],[14,25,1],[14,19,1],[14,17,1],[14,21,1],[14,16,1],[15,24,1],[15,18,1],[15,20,1],[15,17,1],[15,21,1],[16,24,1],[16,20,1],[16,19,1],[16,17,1],[17,24,1],[17,20,1],[17,21,1],[18,20,1],[18,25,1],[18,19,1],[20,24,1],[20,25,1],[20,21,1],[21,25,1],[22,32,1],[22,28,1],[22,27,1],[22,30,1],[22,31,1],[22,26,1],[24,25,1],[26,34,1],[26,33,1],[26,31,1],[27,34,1],[27,33,1],[27,28,1],[27,30,1],[27,31,1],[27,29,1],[28,32,1],[28,33,1],[28,30,1],[28,31,1],[28,29,1],[29,32,1],[29,33,1],[30,32,1],[31,32,1],[31,34,1],[32,34,1],[32,33,1],[33,34,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34],"source":16,"target":4}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-291

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,19,1],[0,4,1],[0,12,1],[0,11,1],[0,10,1],[0,3,1],[0,17,1],[0,21,1],[0,27,1],[0,15,1],[0,23,1],[0,31,1],[0,29,1],[0,2,1],[0,8,1],[0,9,1],[0,14,1],[0,18,1],[1,5,1],[1,26,1],[1,13,1],[1,20,1],[1,32,1],[1,7,1],[2,19,1],[2,4,1],[2,28,1],[2,22,1],[2,16,1],[2,12,1],[2,10,1],[2,3,1],[2,17,1],[2,21,1],[2,27,1],[2,15,1],[2,23,1],[2,31,1],[2,29,1],[2,8,1],[2,9,1],[2,14,1],[2,18,1],[3,4,1],[3,22,1],[3,16,1],[3,12,1],[3,10,1],[3,17,1],[3,21,1],[3,27,1],[3,23,1],[3,31,1],[3,29,1],[3,6,1],[3,9,1],[3,14,1],[3,18,1],[4,16,1],[4,12,1],[4,11,1],[4,17,1],[4,21,1],[4,15,1],[4,30,1],[4,23,1],[4,29,1],[4,6,1],[4,8,1],[4,9,1],[4,18,1],[5,26,1],[5,13,1],[5,25,1],[5,24,1],[5,32,1],[5,7,1],[6,19,1],[6,22,1],[6,12,1],[6,11,1],[6,10,1],[6,17,1],[6,21,1],[6,27,1],[6,15,1],[6,30,1],[6,23,1],[6,31,1],[6,29,1],[6,9,1],[6,14,1],[7,26,1],[7,25,1],[7,32,1],[8,19,1],[8,28,1],[8,10,1],[8,17,1],[8,27,1],[8,15,1],[8,30,1],[8,23,1],[9,19,1],[9,28,1],[9,22,1],[9,16,1],[9,12,1],[9,10,1],[9,17,1],[9,21,1],[9,15,1],[9,30,1],[9,23,1],[9,29,1],[9,18,1],[10,19,1],[10,28,1],[10,22,1],[10,12,1],[10,11,1],[10,17,1],[10,21,1],[10,27,1],[10,15,1],[10,30,1],[10,23,1],[10,31,1],[10,29,1],[10,14,1],[10,18,1],[11,16,1],[11,12,1],[11,17,1],[11,21,1],[11,27,1],[11,15,1],[11,30,1],[11,31,1],[11,29,1],[11,14,1],[11,18,1],[12,19,1],[12,28,1],[12,22,1],[12,17,1],[12,27,1],[12,15,1],[12,30,1],[12,23,1],[12,31,1],[12,29,1],[12,14,1],[12,18,1],[13,26,1],[13,25,1],[13,20,1],[13,32,1],[14,28,1],[14,16,1],[14,17,1],[14,21,1],[14,27,1],[14,15,1],[14,31,1],[14,29,1],[14,18,1],[15,19,1],[15,22,1],[15,16,1],[15,17,1],[15,21,1],[15,27,1],[15,30,1],[15,23,1],[15,31,1],[15,29,1],[15,18,1],[16,19,1],[16,28,1],[16,22,1],[16,17,1],[16,21,1],[16,27,1],[16,30,1],[16,31,1],[16,18,1],[17,22,1],[17,21,1],[17,30,1],[17,31,1],[17,29,1],[17,18,1],[18,19,1],[18,28,1],[18,22,1],[18,21,1],[18,27,1],[18,29,1],[19,28,1],[19,22,1],[19,21,1],[19,30,1],[19,31,1],[19,29,1],[20,32,1],[21,28,1],[21,22,1],[21,27,1],[21,29,1],[22,28,1],[22,30,1],[22,23,1],[22,31,1],[22,29,1],[23,28,1],[23,27,1],[23,30,1],[23,31,1],[23,29,1],[24,26,1],[24,25,1],[25,26,1],[25,32,1],[26,32,1],[27,28,1],[27,30,1],[27,29,1],[28,30,1],[28,31,1],[28,29,1],[29,30,1],[29,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],"source":31,"target":26}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	false	✓ correct
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-287

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,5,1],[0,11,1],[0,8,1],[0,6,1],[0,1,1],[1,10,1],[1,3,1],[1,5,1],[1,9,1],[1,6,1],[1,2,1],[2,10,1],[2,3,1],[2,5,1],[2,9,1],[2,8,1],[2,7,1],[2,6,1],[2,13,1],[3,9,1],[3,11,1],[3,8,1],[3,7,1],[4,12,1],[5,10,1],[5,9,1],[5,8,1],[5,7,1],[5,6,1],[6,10,1],[6,9,1],[6,11,1],[6,8,1],[7,10,1],[7,11,1],[7,8,1],[7,13,1],[8,10,1],[8,11,1],[8,13,1],[9,10,1],[9,11,1],[9,13,1],[10,11,1],[10,13,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"source":8,"target":12}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	true	✗ wrong
Qwen · off	false	✓ correct
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-274

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,11,1],[0,12,1],[0,5,1],[0,6,1],[0,4,1],[0,8,1],[0,2,1],[0,9,1],[0,1,1],[0,7,1],[1,12,1],[1,5,1],[1,6,1],[1,4,1],[1,8,1],[1,2,1],[1,9,1],[1,10,1],[1,7,1],[2,8,1],[2,10,1],[2,7,1],[4,11,1],[4,12,1],[4,5,1],[4,6,1],[4,8,1],[4,9,1],[4,7,1],[5,11,1],[5,6,1],[5,8,1],[5,10,1],[5,7,1],[6,11,1],[6,12,1],[6,8,1],[6,9,1],[7,11,1],[7,12,1],[7,9,1],[7,10,1],[8,12,1],[8,9,1],[8,10,1],[9,11,1],[9,12,1],[9,10,1],[10,11,1],[10,12,1],[11,12,1]],"nodes":[0,1,2,4,5,6,7,8,9,10,11,12],"source":0,"target":10}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-326

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,20,1],[0,4,1],[0,15,1],[0,19,1],[0,8,1],[0,17,1],[0,13,1],[0,3,1],[0,14,1],[0,5,1],[0,2,1],[0,16,1],[0,1,1],[0,10,1],[1,20,1],[1,4,1],[1,15,1],[1,19,1],[1,8,1],[1,17,1],[1,13,1],[1,3,1],[1,14,1],[1,5,1],[1,2,1],[1,16,1],[1,10,1],[2,20,1],[2,4,1],[2,15,1],[2,19,1],[2,8,1],[2,17,1],[2,13,1],[2,3,1],[2,14,1],[2,5,1],[2,16,1],[2,10,1],[3,20,1],[3,4,1],[3,15,1],[3,19,1],[3,8,1],[3,17,1],[3,13,1],[3,14,1],[3,5,1],[3,16,1],[3,10,1],[4,20,1],[4,15,1],[4,19,1],[4,8,1],[4,17,1],[4,13,1],[4,14,1],[4,5,1],[4,16,1],[4,10,1],[5,20,1],[5,15,1],[5,19,1],[5,8,1],[5,17,1],[5,13,1],[5,14,1],[5,16,1],[5,10,1],[6,12,1],[6,22,1],[6,9,1],[6,18,1],[6,21,1],[6,7,1],[6,11,1],[7,12,1],[7,22,1],[7,9,1],[7,18,1],[7,21,1],[7,11,1],[8,20,1],[8,15,1],[8,19,1],[8,17,1],[8,13,1],[8,14,1],[8,16,1],[8,10,1],[9,12,1],[9,22,1],[9,18,1],[9,21,1],[9,11,1],[10,20,1],[10,15,1],[10,19,1],[10,17,1],[10,13,1],[10,14,1],[10,16,1],[11,12,1],[11,22,1],[11,18,1],[11,21,1],[12,22,1],[12,18,1],[12,21,1],[13,20,1],[13,15,1],[13,19,1],[13,17,1],[13,14,1],[13,16,1],[14,20,1],[14,15,1],[14,19,1],[14,17,1],[14,16,1],[15,20,1],[15,19,1],[15,17,1],[15,16,1],[16,20,1],[16,19,1],[16,17,1],[17,20,1],[17,19,1],[18,22,1],[18,21,1],[19,20,1],[21,22,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],"source":19,"target":2}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-10

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,17,1],[0,10,1],[0,19,1],[0,16,1],[0,7,1],[0,8,1],[0,4,1],[0,3,1],[0,11,1],[0,1,1],[0,18,1],[0,9,1],[0,5,1],[0,2,1],[0,13,1],[1,17,1],[1,10,1],[1,19,1],[1,16,1],[1,7,1],[1,8,1],[1,4,1],[1,3,1],[1,11,1],[1,18,1],[1,9,1],[1,5,1],[1,2,1],[1,13,1],[2,17,1],[2,10,1],[2,19,1],[2,16,1],[2,7,1],[2,8,1],[2,4,1],[2,3,1],[2,11,1],[2,18,1],[2,9,1],[2,5,1],[2,13,1],[3,17,1],[3,10,1],[3,19,1],[3,16,1],[3,7,1],[3,8,1],[3,4,1],[3,11,1],[3,18,1],[3,9,1],[3,5,1],[3,13,1],[4,17,1],[4,10,1],[4,19,1],[4,16,1],[4,7,1],[4,8,1],[4,11,1],[4,18,1],[4,9,1],[4,5,1],[4,13,1],[5,17,1],[5,10,1],[5,19,1],[5,16,1],[5,7,1],[5,8,1],[5,11,1],[5,18,1],[5,9,1],[5,13,1],[6,15,1],[7,17,1],[7,10,1],[7,19,1],[7,16,1],[7,8,1],[7,11,1],[7,18,1],[7,9,1],[7,13,1],[8,17,1],[8,10,1],[8,19,1],[8,16,1],[8,11,1],[8,18,1],[8,9,1],[8,13,1],[9,17,1],[9,10,1],[9,19,1],[9,16,1],[9,11,1],[9,18,1],[9,13,1],[10,17,1],[10,19,1],[10,16,1],[10,11,1],[10,18,1],[10,13,1],[11,17,1],[11,19,1],[11,16,1],[11,18,1],[11,13,1],[12,14,1],[13,17,1],[13,19,1],[13,16,1],[13,18,1],[16,17,1],[16,19,1],[16,18,1],[17,19,1],[17,18,1],[18,19,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"source":2,"target":1}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-220

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,2,1],[0,3,1],[1,5,1],[2,4,1],[2,3,1],[3,4,1]],"nodes":[0,1,2,3,4,5],"source":3,"target":5}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-349

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,8,1],[0,1,1],[1,12,1],[1,15,1],[2,9,1],[2,6,1],[3,10,1],[3,17,1],[3,15,1],[5,7,1],[6,10,1],[6,9,1],[6,11,1],[7,13,1],[8,17,1],[8,16,1],[10,15,1],[11,12,1],[15,17,1]],"nodes":[0,1,2,3,5,6,7,8,9,10,11,12,13,14,15,16,17],"source":14,"target":9}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-7

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,15,1],[1,14,1],[1,3,1],[1,9,1],[1,10,1],[1,4,1],[1,7,1],[1,6,1],[1,13,1],[1,12,1],[1,11,1],[2,15,1],[3,14,1],[3,8,1],[3,9,1],[3,10,1],[3,4,1],[3,12,1],[3,11,1],[4,8,1],[4,9,1],[4,10,1],[4,7,1],[4,5,1],[4,11,1],[5,9,1],[5,7,1],[5,13,1],[5,12,1],[5,11,1],[6,14,1],[6,8,1],[6,7,1],[6,13,1],[6,11,1],[7,8,1],[7,9,1],[7,10,1],[7,11,1],[8,14,1],[8,10,1],[8,12,1],[8,11,1],[9,14,1],[9,10,1],[9,13,1],[9,12,1],[10,14,1],[10,13,1],[10,12,1],[11,14,1],[11,13,1],[11,12,1],[12,14,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"source":8,"target":3}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	true	✓ correct

test nlgraph-connectivity-test-132

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[0,4,1],[0,9,1],[0,5,1],[0,13,1],[1,14,1],[1,15,1],[1,12,1],[1,5,1],[1,7,1],[2,4,1],[2,6,1],[2,9,1],[2,12,1],[2,13,1],[4,11,1],[4,6,1],[4,15,1],[4,7,1],[4,8,1],[4,13,1],[5,11,1],[5,10,1],[5,14,1],[5,6,1],[5,9,1],[5,15,1],[5,12,1],[5,7,1],[5,13,1],[6,14,1],[7,14,1],[7,8,1],[9,13,1],[10,14,1],[12,15,1]],"nodes":[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15],"source":13,"target":14}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-55

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,8,1],[0,1,1],[1,12,1],[1,15,1],[2,9,1],[2,6,1],[3,10,1],[3,17,1],[3,15,1],[5,7,1],[6,10,1],[6,9,1],[6,11,1],[7,13,1],[8,17,1],[8,16,1],[10,15,1],[11,12,1],[15,17,1]],"nodes":[0,1,2,3,5,6,7,8,9,10,11,12,13,15,16,17],"source":15,"target":8}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-163

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,16,1],[0,13,1],[0,1,1],[0,9,1],[0,5,1],[0,7,1],[0,3,1],[0,10,1],[0,23,1],[0,26,1],[0,27,1],[0,8,1],[0,14,1],[0,22,1],[0,20,1],[0,15,1],[0,4,1],[0,2,1],[1,25,1],[1,11,1],[1,21,1],[1,13,1],[1,9,1],[1,3,1],[1,10,1],[1,23,1],[1,26,1],[1,27,1],[1,14,1],[1,20,1],[1,15,1],[1,2,1],[1,28,1],[2,25,1],[2,11,1],[2,16,1],[2,21,1],[2,6,1],[2,13,1],[2,9,1],[2,7,1],[2,23,1],[2,26,1],[2,8,1],[2,20,1],[2,15,1],[3,25,1],[3,6,1],[3,13,1],[3,9,1],[3,10,1],[3,27,1],[3,20,1],[3,15,1],[3,4,1],[3,28,1],[4,11,1],[4,16,1],[4,6,1],[4,13,1],[4,10,1],[4,23,1],[4,26,1],[4,27,1],[4,8,1],[4,14,1],[4,22,1],[4,15,1],[4,28,1],[5,25,1],[5,16,1],[5,21,1],[5,6,1],[5,13,1],[5,9,1],[5,7,1],[5,26,1],[5,8,1],[5,22,1],[5,15,1],[5,28,1],[6,11,1],[6,16,1],[6,21,1],[6,13,1],[6,9,1],[6,7,1],[6,10,1],[6,27,1],[6,22,1],[6,20,1],[6,15,1],[7,25,1],[7,16,1],[7,21,1],[7,9,1],[7,10,1],[7,27,1],[7,8,1],[7,14,1],[7,22,1],[7,20,1],[7,15,1],[7,28,1],[8,25,1],[8,13,1],[8,23,1],[8,26,1],[8,27,1],[8,14,1],[8,20,1],[8,28,1],[9,25,1],[9,11,1],[9,16,1],[9,21,1],[9,10,1],[9,23,1],[9,26,1],[9,27,1],[9,22,1],[9,20,1],[9,28,1],[10,11,1],[10,16,1],[10,21,1],[10,13,1],[10,23,1],[10,26,1],[10,27,1],[10,14,1],[10,22,1],[10,20,1],[10,15,1],[10,28,1],[11,25,1],[11,16,1],[11,21,1],[11,13,1],[11,23,1],[11,26,1],[11,27,1],[11,14,1],[11,22,1],[11,20,1],[12,24,1],[12,19,1],[13,25,1],[13,16,1],[13,14,1],[13,22,1],[13,15,1],[13,28,1],[14,25,1],[14,21,1],[14,23,1],[14,26,1],[14,20,1],[14,15,1],[15,16,1],[15,21,1],[15,26,1],[15,27,1],[15,22,1],[15,28,1],[16,21,1],[16,23,1],[16,26,1],[16,27,1],[16,28,1],[17,18,1],[20,25,1],[20,23,1],[20,26,1],[20,27,1],[20,22,1],[20,28,1],[21,25,1],[21,23,1],[21,26,1],[21,22,1],[22,25,1],[22,23,1],[22,27,1],[23,25,1],[23,26,1],[23,27,1],[23,28,1],[25,26,1],[25,27,1],[26,27,1],[27,28,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],"source":1,"target":19}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-272

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,8,1],[0,1,1],[0,6,1],[0,2,1],[0,3,1],[0,7,1],[0,5,1],[1,8,1],[1,6,1],[1,2,1],[1,3,1],[1,7,1],[1,5,1],[2,8,1],[2,6,1],[2,3,1],[2,7,1],[2,5,1],[3,8,1],[3,6,1],[3,7,1],[3,5,1],[5,8,1],[5,6,1],[5,7,1],[6,8,1],[6,7,1],[7,8,1]],"nodes":[0,1,2,3,5,6,7,8],"source":6,"target":3}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-212

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[0,17,1],[1,4,1],[2,10,1],[3,19,1],[3,30,1],[3,13,1],[3,25,1],[3,8,1],[4,31,1],[5,16,1],[6,29,1],[6,11,1],[6,32,1],[7,14,1],[7,17,1],[8,21,1],[8,30,1],[8,13,1],[8,28,1],[9,20,1],[9,25,1],[11,29,1],[11,26,1],[11,22,1],[13,21,1],[13,15,1],[13,28,1],[13,23,1],[15,31,1],[15,16,1],[15,28,1],[15,23,1],[16,21,1],[16,25,1],[16,23,1],[18,29,1],[18,24,1],[20,31,1],[20,30,1],[20,25,1],[21,25,1],[22,24,1],[23,25,1],[23,28,1],[24,29,1],[24,32,1],[25,30,1],[26,32,1],[28,30,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,23,24,25,26,28,29,30,31,32],"source":8,"target":19}

Model	Answer given
Gemma 4	false	✗ wrong
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-53

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,18,1],[1,20,1],[2,11,1],[2,23,1],[2,14,1],[2,8,1],[3,17,1],[3,14,1],[3,16,1],[4,7,1],[4,16,1],[4,8,1],[4,24,1],[5,6,1],[5,10,1],[5,20,1],[6,20,1],[7,12,1],[7,16,1],[7,8,1],[7,24,1],[8,12,1],[8,23,1],[8,21,1],[9,18,1],[10,18,1],[10,20,1],[11,17,1],[11,19,1],[11,24,1],[12,22,1],[12,17,1],[12,14,1],[13,24,1],[14,23,1],[14,24,1],[15,17,1],[15,19,1],[15,24,1],[16,22,1],[16,19,1],[17,19,1],[17,24,1],[19,24,1],[23,24,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"source":7,"target":10}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-147

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,15,1],[0,12,1],[0,1,1],[0,7,1],[0,16,1],[0,13,1],[0,9,1],[0,2,1],[0,10,1],[0,21,1],[0,19,1],[0,3,1],[0,20,1],[0,8,1],[0,23,1],[0,5,1],[0,4,1],[0,6,1],[0,22,1],[1,15,1],[1,12,1],[1,7,1],[1,16,1],[1,13,1],[1,9,1],[1,2,1],[1,10,1],[1,21,1],[1,19,1],[1,3,1],[1,20,1],[1,8,1],[1,23,1],[1,5,1],[1,4,1],[1,6,1],[1,22,1],[2,15,1],[2,12,1],[2,7,1],[2,16,1],[2,13,1],[2,9,1],[2,10,1],[2,21,1],[2,19,1],[2,3,1],[2,20,1],[2,8,1],[2,23,1],[2,5,1],[2,4,1],[2,6,1],[2,22,1],[3,15,1],[3,12,1],[3,7,1],[3,16,1],[3,13,1],[3,9,1],[3,10,1],[3,21,1],[3,19,1],[3,20,1],[3,8,1],[3,23,1],[3,5,1],[3,4,1],[3,6,1],[3,22,1],[4,15,1],[4,12,1],[4,7,1],[4,16,1],[4,13,1],[4,9,1],[4,10,1],[4,21,1],[4,19,1],[4,20,1],[4,8,1],[4,23,1],[4,5,1],[4,6,1],[4,22,1],[5,15,1],[5,12,1],[5,7,1],[5,16,1],[5,13,1],[5,9,1],[5,10,1],[5,21,1],[5,19,1],[5,20,1],[5,8,1],[5,23,1],[5,6,1],[5,22,1],[6,15,1],[6,12,1],[6,7,1],[6,16,1],[6,13,1],[6,9,1],[6,10,1],[6,21,1],[6,19,1],[6,20,1],[6,8,1],[6,23,1],[6,22,1],[7,15,1],[7,12,1],[7,16,1],[7,13,1],[7,9,1],[7,10,1],[7,21,1],[7,19,1],[7,20,1],[7,8,1],[7,23,1],[7,22,1],[8,15,1],[8,12,1],[8,16,1],[8,13,1],[8,9,1],[8,10,1],[8,21,1],[8,19,1],[8,20,1],[8,23,1],[8,22,1],[9,15,1],[9,12,1],[9,16,1],[9,13,1],[9,10,1],[9,21,1],[9,19,1],[9,20,1],[9,23,1],[9,22,1],[10,15,1],[10,12,1],[10,16,1],[10,13,1],[10,21,1],[10,19,1],[10,20,1],[10,23,1],[10,22,1],[11,17,1],[11,14,1],[11,18,1],[12,15,1],[12,16,1],[12,13,1],[12,21,1],[12,19,1],[12,20,1],[12,23,1],[12,22,1],[13,15,1],[13,16,1],[13,21,1],[13,19,1],[13,20,1],[13,23,1],[13,22,1],[14,17,1],[14,18,1],[15,16,1],[15,21,1],[15,19,1],[15,20,1],[15,23,1],[15,22,1],[16,21,1],[16,19,1],[16,20,1],[16,23,1],[16,22,1],[17,18,1],[19,21,1],[19,20,1],[19,23,1],[19,22,1],[20,21,1],[20,23,1],[20,22,1],[21,23,1],[21,22,1],[22,23,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"source":17,"target":19}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	false	✓ correct
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-254

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,11,1],[0,2,1],[0,7,1],[0,8,1],[0,16,1],[0,15,1],[1,11,1],[1,2,1],[1,7,1],[1,8,1],[1,16,1],[1,15,1],[1,14,1],[2,4,1],[2,11,1],[2,5,1],[2,7,1],[2,12,1],[2,16,1],[2,15,1],[3,13,1],[3,10,1],[4,6,1],[4,5,1],[4,7,1],[4,8,1],[4,12,1],[4,16,1],[4,15,1],[4,14,1],[5,6,1],[5,7,1],[5,8,1],[5,12,1],[5,16,1],[5,14,1],[6,11,1],[6,7,1],[6,8,1],[6,12,1],[6,16,1],[6,15,1],[6,14,1],[7,11,1],[7,8,1],[7,16,1],[7,14,1],[8,11,1],[8,12,1],[8,16,1],[11,12,1],[11,16,1],[11,15,1],[11,14,1],[12,14,1],[14,16,1],[14,15,1]],"nodes":[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16],"source":11,"target":10}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-63

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,11,1],[0,18,1],[0,19,1],[0,20,1],[0,23,1],[0,9,1],[0,10,1],[0,22,1],[0,13,1],[0,1,1],[0,12,1],[0,5,1],[0,7,1],[0,15,1],[0,4,1],[1,11,1],[1,18,1],[1,19,1],[1,20,1],[1,23,1],[1,9,1],[1,10,1],[1,22,1],[1,13,1],[1,12,1],[1,5,1],[1,7,1],[1,15,1],[1,4,1],[2,8,1],[2,6,1],[2,3,1],[2,24,1],[2,16,1],[2,21,1],[2,17,1],[2,14,1],[3,8,1],[3,6,1],[3,24,1],[3,16,1],[3,21,1],[3,17,1],[3,14,1],[4,11,1],[4,18,1],[4,19,1],[4,20,1],[4,23,1],[4,9,1],[4,10,1],[4,22,1],[4,13,1],[4,12,1],[4,5,1],[4,7,1],[4,15,1],[5,11,1],[5,18,1],[5,19,1],[5,20,1],[5,23,1],[5,9,1],[5,10,1],[5,22,1],[5,13,1],[5,12,1],[5,7,1],[5,15,1],[6,8,1],[6,24,1],[6,16,1],[6,21,1],[6,17,1],[6,14,1],[7,11,1],[7,18,1],[7,19,1],[7,20,1],[7,23,1],[7,9,1],[7,10,1],[7,22,1],[7,13,1],[7,12,1],[7,15,1],[8,24,1],[8,16,1],[8,21,1],[8,17,1],[8,14,1],[9,11,1],[9,18,1],[9,19,1],[9,20,1],[9,23,1],[9,10,1],[9,22,1],[9,13,1],[9,12,1],[9,15,1],[10,11,1],[10,18,1],[10,19,1],[10,20,1],[10,23,1],[10,22,1],[10,13,1],[10,12,1],[10,15,1],[11,18,1],[11,19,1],[11,20,1],[11,23,1],[11,22,1],[11,13,1],[11,12,1],[11,15,1],[12,18,1],[12,19,1],[12,20,1],[12,23,1],[12,22,1],[12,13,1],[12,15,1],[13,18,1],[13,19,1],[13,20,1],[13,23,1],[13,22,1],[13,15,1],[14,24,1],[14,16,1],[14,21,1],[14,17,1],[15,18,1],[15,19,1],[15,20,1],[15,23,1],[15,22,1],[16,24,1],[16,21,1],[16,17,1],[17,24,1],[17,21,1],[18,19,1],[18,20,1],[18,23,1],[18,22,1],[19,20,1],[19,23,1],[19,22,1],[20,23,1],[20,22,1],[21,24,1],[22,23,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"source":19,"target":4}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-87

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,1,1],[0,6,1],[0,21,1],[0,18,1],[1,24,1],[1,3,1],[3,24,1],[3,14,1],[4,6,1],[4,5,1],[4,23,1],[6,14,1],[6,21,1],[6,23,1],[7,11,1],[8,19,1],[8,13,1],[9,15,1],[9,19,1],[10,11,1],[10,12,1],[10,16,1],[10,17,1],[11,12,1],[11,16,1],[12,17,1],[13,15,1],[13,22,1],[14,23,1],[15,22,1],[16,17,1],[18,24,1],[18,21,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24],"source":12,"target":2}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-177

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,10,1],[0,12,1],[0,20,1],[0,14,1],[0,8,1],[0,3,1],[0,6,1],[0,5,1],[0,15,1],[0,19,1],[0,7,1],[0,9,1],[0,22,1],[0,2,1],[0,21,1],[0,18,1],[1,4,1],[1,10,1],[1,12,1],[1,20,1],[1,8,1],[1,5,1],[1,15,1],[1,16,1],[1,19,1],[1,7,1],[1,9,1],[1,22,1],[1,2,1],[1,18,1],[2,4,1],[2,10,1],[2,12,1],[2,14,1],[2,3,1],[2,5,1],[2,15,1],[2,19,1],[2,7,1],[2,22,1],[2,21,1],[2,18,1],[3,4,1],[3,12,1],[3,20,1],[3,14,1],[3,6,1],[3,5,1],[3,15,1],[3,16,1],[3,19,1],[3,7,1],[3,9,1],[3,22,1],[3,21,1],[3,18,1],[4,10,1],[4,12,1],[4,8,1],[4,6,1],[4,5,1],[4,15,1],[4,16,1],[4,19,1],[4,7,1],[4,9,1],[4,21,1],[4,18,1],[5,12,1],[5,14,1],[5,8,1],[5,6,1],[5,15,1],[5,16,1],[5,19,1],[5,7,1],[5,9,1],[5,22,1],[5,18,1],[6,10,1],[6,12,1],[6,20,1],[6,14,1],[6,16,1],[6,19,1],[6,7,1],[6,9,1],[6,22,1],[6,21,1],[6,18,1],[7,10,1],[7,12,1],[7,14,1],[7,8,1],[7,16,1],[7,9,1],[7,22,1],[7,21,1],[7,18,1],[8,10,1],[8,12,1],[8,14,1],[8,15,1],[8,16,1],[8,19,1],[8,9,1],[8,21,1],[9,12,1],[9,20,1],[9,15,1],[9,16,1],[9,22,1],[9,21,1],[9,18,1],[10,12,1],[10,20,1],[10,14,1],[10,15,1],[10,16,1],[10,18,1],[12,16,1],[12,19,1],[13,17,1],[14,20,1],[14,16,1],[15,16,1],[15,22,1],[15,21,1],[16,20,1],[16,21,1],[16,18,1],[18,22,1],[18,21,1],[19,20,1],[19,22,1],[19,21,1],[21,22,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,17,18,19,20,21,22],"source":5,"target":17}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-345

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,6,1],[0,10,1],[0,17,1],[0,4,1],[0,21,1],[0,1,1],[0,2,1],[0,18,1],[0,7,1],[0,19,1],[0,11,1],[0,3,1],[0,5,1],[0,14,1],[1,6,1],[1,10,1],[1,17,1],[1,21,1],[1,16,1],[1,18,1],[1,7,1],[1,8,1],[1,11,1],[2,6,1],[2,10,1],[2,17,1],[2,4,1],[2,21,1],[2,16,1],[2,13,1],[2,18,1],[2,7,1],[2,8,1],[2,19,1],[2,3,1],[2,5,1],[3,6,1],[3,10,1],[3,17,1],[3,4,1],[3,21,1],[3,16,1],[3,13,1],[3,18,1],[3,7,1],[3,19,1],[4,10,1],[4,16,1],[4,18,1],[4,7,1],[4,8,1],[4,19,1],[4,5,1],[5,6,1],[5,16,1],[5,13,1],[5,18,1],[5,7,1],[5,8,1],[5,19,1],[5,14,1],[6,10,1],[6,17,1],[6,21,1],[6,16,1],[6,13,1],[6,18,1],[6,7,1],[6,19,1],[6,11,1],[6,14,1],[7,10,1],[7,17,1],[7,21,1],[7,16,1],[7,13,1],[7,18,1],[7,8,1],[7,19,1],[7,11,1],[7,14,1],[8,10,1],[8,17,1],[8,21,1],[8,16,1],[8,13,1],[8,18,1],[8,19,1],[8,11,1],[9,20,1],[10,17,1],[10,21,1],[10,13,1],[10,18,1],[10,19,1],[10,11,1],[10,14,1],[11,17,1],[11,16,1],[11,13,1],[11,18,1],[11,19,1],[12,15,1],[13,21,1],[13,16,1],[13,18,1],[13,19,1],[13,14,1],[14,17,1],[14,21,1],[14,16,1],[14,18,1],[14,19,1],[16,17,1],[16,21,1],[16,18,1],[17,18,1],[18,21,1],[18,19,1],[19,21,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],"source":13,"target":17}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-92

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,7,1],[0,10,1],[0,6,1],[0,2,1],[0,8,1],[0,4,1],[0,1,1],[1,3,1],[1,7,1],[1,10,1],[1,6,1],[1,2,1],[1,8,1],[1,4,1],[2,3,1],[2,7,1],[2,10,1],[2,6,1],[2,8,1],[2,4,1],[3,7,1],[3,10,1],[3,6,1],[3,8,1],[3,4,1],[4,7,1],[4,10,1],[4,6,1],[4,8,1],[5,9,1],[6,7,1],[6,10,1],[6,8,1],[7,10,1],[7,8,1],[8,10,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10],"source":6,"target":3}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-27

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,18,1],[1,20,1],[2,11,1],[2,23,1],[2,14,1],[2,8,1],[3,17,1],[3,14,1],[3,16,1],[4,7,1],[4,16,1],[4,8,1],[4,24,1],[5,6,1],[5,10,1],[5,20,1],[6,20,1],[7,12,1],[7,16,1],[7,8,1],[7,24,1],[8,12,1],[8,23,1],[8,21,1],[9,18,1],[10,18,1],[10,20,1],[11,17,1],[11,19,1],[11,24,1],[12,22,1],[12,17,1],[12,14,1],[13,24,1],[14,23,1],[14,24,1],[15,17,1],[15,19,1],[15,24,1],[16,22,1],[16,19,1],[17,19,1],[17,24,1],[19,24,1],[23,24,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"source":8,"target":18}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-369

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,6,1],[1,15,1],[1,16,1],[2,18,1],[2,17,1],[2,7,1],[3,14,1],[3,7,1],[5,11,1],[6,13,1],[7,17,1],[8,15,1],[8,13,1],[9,17,1],[10,17,1],[13,15,1],[13,16,1],[16,19,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19],"source":3,"target":4}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-76

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,19,1],[0,17,1],[0,1,1],[0,4,1],[0,15,1],[0,2,1],[0,13,1],[0,10,1],[0,6,1],[0,18,1],[0,11,1],[0,12,1],[0,5,1],[1,19,1],[1,17,1],[1,4,1],[1,15,1],[1,2,1],[1,13,1],[1,10,1],[1,6,1],[1,18,1],[1,11,1],[1,12,1],[1,5,1],[2,19,1],[2,17,1],[2,4,1],[2,15,1],[2,13,1],[2,10,1],[2,6,1],[2,18,1],[2,11,1],[2,12,1],[2,5,1],[3,20,1],[3,16,1],[3,14,1],[3,8,1],[4,19,1],[4,17,1],[4,15,1],[4,13,1],[4,10,1],[4,6,1],[4,18,1],[4,11,1],[4,12,1],[4,5,1],[5,19,1],[5,17,1],[5,15,1],[5,13,1],[5,10,1],[5,6,1],[5,18,1],[5,11,1],[5,12,1],[6,19,1],[6,17,1],[6,15,1],[6,13,1],[6,10,1],[6,18,1],[6,11,1],[6,12,1],[7,9,1],[8,20,1],[8,16,1],[8,14,1],[10,19,1],[10,17,1],[10,15,1],[10,13,1],[10,18,1],[10,11,1],[10,12,1],[11,19,1],[11,17,1],[11,15,1],[11,13,1],[11,18,1],[11,12,1],[12,19,1],[12,17,1],[12,15,1],[12,13,1],[12,18,1],[13,19,1],[13,17,1],[13,15,1],[13,18,1],[14,20,1],[14,16,1],[15,19,1],[15,17,1],[15,18,1],[16,20,1],[17,19,1],[17,18,1],[18,19,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"source":15,"target":2}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-69

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,20,1],[0,34,1],[0,1,1],[0,10,1],[0,12,1],[1,12,1],[2,24,1],[3,31,1],[3,30,1],[3,25,1],[4,19,1],[4,6,1],[5,8,1],[7,26,1],[10,20,1],[10,28,1],[10,17,1],[10,18,1],[12,20,1],[12,32,1],[12,17,1],[13,14,1],[13,15,1],[13,21,1],[13,26,1],[13,23,1],[14,15,1],[14,21,1],[15,26,1],[15,23,1],[16,21,1],[16,30,1],[17,20,1],[17,27,1],[17,32,1],[18,27,1],[18,34,1],[19,33,1],[20,27,1],[21,31,1],[21,22,1],[22,26,1],[22,31,1],[23,31,1],[26,31,1],[28,34,1],[30,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,30,31,32,33,34],"source":25,"target":9}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-181

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,1,1],[0,20,1],[0,8,1],[0,31,1],[0,22,1],[1,4,1],[1,24,1],[1,19,1],[1,16,1],[1,5,1],[1,2,1],[1,8,1],[1,18,1],[1,27,1],[2,4,1],[2,19,1],[2,12,1],[2,17,1],[2,21,1],[2,31,1],[2,22,1],[3,25,1],[3,20,1],[3,14,1],[3,31,1],[3,22,1],[3,27,1],[4,7,1],[4,21,1],[4,26,1],[4,27,1],[5,11,1],[5,24,1],[5,20,1],[5,19,1],[5,12,1],[5,16,1],[5,17,1],[5,21,1],[5,9,1],[5,22,1],[6,15,1],[7,24,1],[7,20,1],[7,19,1],[7,16,1],[7,29,1],[7,17,1],[7,21,1],[7,14,1],[7,9,1],[7,8,1],[7,18,1],[7,22,1],[7,30,1],[8,20,1],[8,12,1],[8,14,1],[9,20,1],[9,16,1],[9,14,1],[9,18,1],[9,26,1],[9,23,1],[10,15,1],[11,25,1],[11,28,1],[11,20,1],[11,21,1],[11,26,1],[12,28,1],[12,24,1],[12,20,1],[12,29,1],[12,14,1],[12,18,1],[12,26,1],[12,22,1],[12,27,1],[12,23,1],[14,24,1],[14,16,1],[14,18,1],[14,31,1],[16,25,1],[16,26,1],[16,31,1],[16,23,1],[17,31,1],[17,27,1],[18,25,1],[18,28,1],[18,24,1],[18,21,1],[18,26,1],[18,27,1],[19,29,1],[19,21,1],[19,22,1],[20,25,1],[20,21,1],[20,26,1],[21,24,1],[21,29,1],[21,31,1],[21,23,1],[22,29,1],[22,26,1],[22,23,1],[23,25,1],[23,26,1],[24,25,1],[24,26,1],[24,30,1],[25,29,1],[25,31,1],[26,29,1],[26,31,1],[27,28,1],[27,31,1],[28,29,1],[29,31,1],[29,30,1],[30,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],"source":14,"target":22}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-337

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,7,1],[0,8,1],[0,10,1],[0,3,1],[1,4,1],[1,11,1],[1,9,1],[1,6,1],[1,12,1],[1,2,1],[2,4,1],[2,11,1],[2,9,1],[2,6,1],[2,12,1],[3,5,1],[3,7,1],[3,8,1],[3,10,1],[4,11,1],[4,9,1],[4,6,1],[4,12,1],[5,7,1],[5,8,1],[5,10,1],[6,11,1],[6,9,1],[6,12,1],[7,8,1],[7,10,1],[8,10,1],[9,11,1],[9,12,1],[11,12,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12],"source":12,"target":10}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-94

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[1,10,1],[2,9,1],[2,5,1],[3,12,1],[3,14,1],[3,4,1],[3,8,1],[3,18,1],[4,19,1],[4,16,1],[4,11,1],[5,20,1],[5,12,1],[5,14,1],[5,11,1],[6,18,1],[6,16,1],[7,15,1],[8,20,1],[8,12,1],[8,18,1],[8,16,1],[9,20,1],[9,14,1],[9,19,1],[9,11,1],[11,13,1],[11,12,1],[11,18,1],[11,16,1],[12,18,1],[13,19,1],[13,18,1],[14,19,1],[16,20,1],[18,19,1]],"nodes":[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"source":17,"target":10}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-219

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,14,1],[0,20,1],[0,13,1],[0,24,1],[0,4,1],[1,21,1],[1,3,1],[1,11,1],[1,10,1],[1,23,1],[1,8,1],[1,2,1],[1,22,1],[1,19,1],[1,18,1],[2,21,1],[2,3,1],[2,11,1],[2,10,1],[2,23,1],[2,8,1],[2,22,1],[2,19,1],[2,18,1],[3,21,1],[3,11,1],[3,10,1],[3,23,1],[3,8,1],[3,22,1],[3,19,1],[3,18,1],[4,14,1],[4,20,1],[4,13,1],[4,24,1],[5,7,1],[5,9,1],[5,12,1],[5,16,1],[5,15,1],[5,17,1],[5,6,1],[6,7,1],[6,9,1],[6,12,1],[6,16,1],[6,15,1],[6,17,1],[7,9,1],[7,12,1],[7,16,1],[7,15,1],[7,17,1],[8,21,1],[8,11,1],[8,10,1],[8,23,1],[8,22,1],[8,19,1],[8,18,1],[9,12,1],[9,16,1],[9,15,1],[9,17,1],[10,21,1],[10,11,1],[10,23,1],[10,22,1],[10,19,1],[10,18,1],[11,21,1],[11,23,1],[11,22,1],[11,19,1],[11,18,1],[12,16,1],[12,15,1],[12,17,1],[13,14,1],[13,20,1],[13,24,1],[14,20,1],[14,24,1],[15,16,1],[15,17,1],[16,17,1],[18,21,1],[18,23,1],[18,22,1],[18,19,1],[19,21,1],[19,23,1],[19,22,1],[20,24,1],[21,23,1],[21,22,1],[22,23,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"source":12,"target":7}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-158

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,19,1],[0,4,1],[1,23,1],[1,7,1],[1,18,1],[1,24,1],[1,32,1],[1,31,1],[1,21,1],[1,27,1],[1,11,1],[1,6,1],[1,29,1],[1,17,1],[1,20,1],[2,23,1],[2,7,1],[2,18,1],[2,33,1],[2,24,1],[2,31,1],[2,21,1],[2,8,1],[2,27,1],[2,11,1],[2,29,1],[2,17,1],[2,26,1],[3,9,1],[3,22,1],[3,13,1],[3,5,1],[3,30,1],[3,28,1],[3,16,1],[3,14,1],[3,15,1],[4,19,1],[4,10,1],[5,9,1],[5,22,1],[5,13,1],[5,28,1],[5,16,1],[5,14,1],[6,18,1],[6,32,1],[6,25,1],[6,21,1],[6,8,1],[6,11,1],[6,17,1],[6,20,1],[6,26,1],[7,18,1],[7,33,1],[7,24,1],[7,32,1],[7,25,1],[7,31,1],[7,21,1],[7,17,1],[7,20,1],[7,26,1],[8,18,1],[8,33,1],[8,32,1],[8,25,1],[8,31,1],[8,27,1],[8,11,1],[8,29,1],[8,20,1],[8,26,1],[9,22,1],[9,13,1],[9,30,1],[9,28,1],[9,14,1],[9,15,1],[10,19,1],[10,12,1],[11,18,1],[11,33,1],[11,24,1],[11,25,1],[11,31,1],[11,27,1],[11,29,1],[11,26,1],[12,19,1],[13,28,1],[13,15,1],[14,30,1],[14,28,1],[14,16,1],[14,15,1],[15,22,1],[15,30,1],[15,16,1],[16,22,1],[17,23,1],[17,18,1],[17,33,1],[17,25,1],[17,31,1],[17,21,1],[17,27,1],[17,29,1],[17,20,1],[17,26,1],[18,23,1],[18,32,1],[18,25,1],[18,21,1],[18,29,1],[18,20,1],[18,26,1],[20,23,1],[20,33,1],[20,32,1],[20,25,1],[20,31,1],[20,21,1],[20,27,1],[20,29,1],[20,26,1],[21,23,1],[21,33,1],[21,24,1],[21,25,1],[21,29,1],[23,33,1],[23,24,1],[23,25,1],[23,31,1],[23,27,1],[23,29,1],[23,26,1],[24,33,1],[24,32,1],[24,25,1],[24,27,1],[24,29,1],[24,26,1],[25,32,1],[25,31,1],[25,27,1],[25,29,1],[25,26,1],[26,33,1],[26,31,1],[26,27,1],[27,31,1],[27,29,1],[28,30,1],[31,32,1],[32,33,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],"source":13,"target":8}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-35

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,2,1],[0,1,1],[0,4,1],[1,3,1],[1,2,1],[1,4,1],[1,6,1],[2,3,1],[2,4,1],[2,5,1],[3,4,1],[3,6,1],[4,6,1],[5,6,1]],"nodes":[0,1,2,3,4,5,6],"source":2,"target":6}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-179

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,12,1],[0,7,1],[0,13,1],[0,24,1],[0,19,1],[0,5,1],[0,10,1],[0,4,1],[0,2,1],[0,21,1],[0,17,1],[0,23,1],[0,9,1],[0,20,1],[0,15,1],[0,22,1],[1,3,1],[1,18,1],[1,6,1],[1,14,1],[1,8,1],[1,11,1],[2,12,1],[2,7,1],[2,13,1],[2,24,1],[2,19,1],[2,5,1],[2,10,1],[2,4,1],[2,21,1],[2,17,1],[2,23,1],[2,9,1],[2,20,1],[2,15,1],[2,22,1],[3,18,1],[3,6,1],[3,14,1],[3,8,1],[3,11,1],[4,12,1],[4,7,1],[4,13,1],[4,24,1],[4,19,1],[4,5,1],[4,10,1],[4,21,1],[4,17,1],[4,23,1],[4,9,1],[4,20,1],[4,15,1],[4,22,1],[5,12,1],[5,7,1],[5,13,1],[5,24,1],[5,19,1],[5,10,1],[5,21,1],[5,17,1],[5,23,1],[5,9,1],[5,20,1],[5,15,1],[5,22,1],[6,18,1],[6,14,1],[6,8,1],[6,11,1],[7,12,1],[7,13,1],[7,24,1],[7,19,1],[7,10,1],[7,21,1],[7,17,1],[7,23,1],[7,9,1],[7,20,1],[7,15,1],[7,22,1],[8,18,1],[8,14,1],[8,11,1],[9,12,1],[9,13,1],[9,24,1],[9,19,1],[9,10,1],[9,21,1],[9,17,1],[9,23,1],[9,20,1],[9,15,1],[9,22,1],[10,12,1],[10,13,1],[10,24,1],[10,19,1],[10,21,1],[10,17,1],[10,23,1],[10,20,1],[10,15,1],[10,22,1],[11,18,1],[11,14,1],[12,13,1],[12,24,1],[12,19,1],[12,21,1],[12,17,1],[12,23,1],[12,20,1],[12,15,1],[12,22,1],[13,24,1],[13,19,1],[13,21,1],[13,17,1],[13,23,1],[13,20,1],[13,15,1],[13,22,1],[14,18,1],[15,24,1],[15,19,1],[15,21,1],[15,17,1],[15,23,1],[15,20,1],[15,22,1],[17,24,1],[17,19,1],[17,21,1],[17,23,1],[17,20,1],[17,22,1],[19,24,1],[19,21,1],[19,23,1],[19,20,1],[19,22,1],[20,24,1],[20,21,1],[20,23,1],[20,22,1],[21,24,1],[21,23,1],[21,22,1],[22,24,1],[22,23,1],[23,24,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24],"source":24,"target":14}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-46

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,7,1],[0,15,1],[0,6,1],[0,17,1],[0,4,1],[0,12,1],[0,16,1],[0,9,1],[1,14,1],[1,23,1],[1,18,1],[1,19,1],[1,3,1],[1,21,1],[2,14,1],[2,5,1],[2,11,1],[2,23,1],[2,22,1],[2,8,1],[2,18,1],[2,19,1],[2,3,1],[2,20,1],[3,14,1],[3,5,1],[3,23,1],[3,22,1],[3,8,1],[3,18,1],[3,19,1],[3,20,1],[3,21,1],[4,7,1],[4,15,1],[4,6,1],[4,17,1],[4,13,1],[4,10,1],[4,16,1],[5,14,1],[5,8,1],[5,18,1],[5,19,1],[5,21,1],[6,13,1],[6,10,1],[6,16,1],[6,9,1],[7,15,1],[7,13,1],[7,9,1],[8,14,1],[8,11,1],[8,23,1],[8,22,1],[8,18,1],[8,19,1],[8,20,1],[8,21,1],[9,15,1],[9,13,1],[9,12,1],[9,16,1],[10,15,1],[10,17,1],[10,13,1],[10,12,1],[11,14,1],[11,23,1],[11,22,1],[11,18,1],[11,19,1],[12,17,1],[12,16,1],[13,17,1],[13,16,1],[14,23,1],[14,19,1],[15,17,1],[16,17,1],[18,23,1],[18,22,1],[18,19,1],[18,21,1],[19,23,1],[19,22,1],[19,20,1],[20,23,1],[20,21,1],[21,23,1],[22,23,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"source":9,"target":4}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-283

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,2,1],[1,5,1],[1,2,1],[2,5,1],[2,10,1],[3,10,1],[3,4,1],[3,8,1],[4,5,1],[5,10,1],[5,8,1],[7,11,1],[8,10,1],[9,11,1]],"nodes":[0,1,2,3,4,5,7,8,9,10,11],"source":3,"target":8}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-16

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,21,1],[0,11,1],[0,15,1],[0,4,1],[0,22,1],[0,5,1],[0,3,1],[0,6,1],[0,20,1],[0,13,1],[0,18,1],[0,9,1],[0,1,1],[0,12,1],[0,24,1],[0,16,1],[0,8,1],[0,23,1],[0,2,1],[1,21,1],[1,11,1],[1,15,1],[1,4,1],[1,22,1],[1,5,1],[1,3,1],[1,6,1],[1,20,1],[1,13,1],[1,18,1],[1,9,1],[1,12,1],[1,24,1],[1,16,1],[1,8,1],[1,23,1],[1,2,1],[2,21,1],[2,11,1],[2,15,1],[2,4,1],[2,22,1],[2,5,1],[2,3,1],[2,6,1],[2,20,1],[2,13,1],[2,18,1],[2,9,1],[2,12,1],[2,24,1],[2,16,1],[2,8,1],[2,23,1],[3,21,1],[3,11,1],[3,15,1],[3,4,1],[3,22,1],[3,5,1],[3,6,1],[3,20,1],[3,13,1],[3,18,1],[3,9,1],[3,12,1],[3,24,1],[3,16,1],[3,8,1],[3,23,1],[4,21,1],[4,11,1],[4,15,1],[4,22,1],[4,5,1],[4,6,1],[4,20,1],[4,13,1],[4,18,1],[4,9,1],[4,12,1],[4,24,1],[4,16,1],[4,8,1],[4,23,1],[5,21,1],[5,11,1],[5,15,1],[5,22,1],[5,6,1],[5,20,1],[5,13,1],[5,18,1],[5,9,1],[5,12,1],[5,24,1],[5,16,1],[5,8,1],[5,23,1],[6,21,1],[6,11,1],[6,15,1],[6,22,1],[6,20,1],[6,13,1],[6,18,1],[6,9,1],[6,12,1],[6,24,1],[6,16,1],[6,8,1],[6,23,1],[7,10,1],[7,14,1],[7,17,1],[7,19,1],[8,21,1],[8,11,1],[8,15,1],[8,22,1],[8,20,1],[8,13,1],[8,18,1],[8,9,1],[8,12,1],[8,24,1],[8,16,1],[8,23,1],[9,21,1],[9,11,1],[9,15,1],[9,22,1],[9,20,1],[9,13,1],[9,18,1],[9,12,1],[9,24,1],[9,16,1],[9,23,1],[10,14,1],[10,17,1],[10,19,1],[11,21,1],[11,15,1],[11,22,1],[11,20,1],[11,13,1],[11,18,1],[11,12,1],[11,24,1],[11,16,1],[11,23,1],[12,21,1],[12,15,1],[12,22,1],[12,20,1],[12,13,1],[12,18,1],[12,24,1],[12,16,1],[12,23,1],[13,21,1],[13,15,1],[13,22,1],[13,20,1],[13,18,1],[13,24,1],[13,16,1],[13,23,1],[14,17,1],[14,19,1],[15,21,1],[15,22,1],[15,20,1],[15,18,1],[15,24,1],[15,16,1],[15,23,1],[16,21,1],[16,22,1],[16,20,1],[16,18,1],[16,24,1],[16,23,1],[17,19,1],[18,21,1],[18,22,1],[18,20,1],[18,24,1],[18,23,1],[20,21,1],[20,22,1],[20,24,1],[20,23,1],[21,22,1],[21,24,1],[21,23,1],[22,24,1],[22,23,1],[23,24,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"source":11,"target":20}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"reachable": true}	✓ correct

test nlgraph-connectivity-test-335

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,6,1],[0,10,1],[0,17,1],[0,4,1],[0,21,1],[0,1,1],[0,2,1],[0,18,1],[0,7,1],[0,19,1],[0,11,1],[0,3,1],[0,5,1],[0,14,1],[1,6,1],[1,10,1],[1,17,1],[1,21,1],[1,16,1],[1,18,1],[1,7,1],[1,8,1],[1,11,1],[2,6,1],[2,10,1],[2,17,1],[2,4,1],[2,21,1],[2,16,1],[2,13,1],[2,18,1],[2,7,1],[2,8,1],[2,19,1],[2,3,1],[2,5,1],[3,6,1],[3,10,1],[3,17,1],[3,4,1],[3,21,1],[3,16,1],[3,13,1],[3,18,1],[3,7,1],[3,19,1],[4,10,1],[4,16,1],[4,18,1],[4,7,1],[4,8,1],[4,19,1],[4,5,1],[5,6,1],[5,16,1],[5,13,1],[5,18,1],[5,7,1],[5,8,1],[5,19,1],[5,14,1],[6,10,1],[6,17,1],[6,21,1],[6,16,1],[6,13,1],[6,18,1],[6,7,1],[6,19,1],[6,11,1],[6,14,1],[7,10,1],[7,17,1],[7,21,1],[7,16,1],[7,13,1],[7,18,1],[7,8,1],[7,19,1],[7,11,1],[7,14,1],[8,10,1],[8,17,1],[8,21,1],[8,16,1],[8,13,1],[8,18,1],[8,19,1],[8,11,1],[9,20,1],[10,17,1],[10,21,1],[10,13,1],[10,18,1],[10,19,1],[10,11,1],[10,14,1],[11,17,1],[11,16,1],[11,13,1],[11,18,1],[11,19,1],[12,15,1],[13,21,1],[13,16,1],[13,18,1],[13,19,1],[13,14,1],[14,17,1],[14,21,1],[14,16,1],[14,18,1],[14,19,1],[16,17,1],[16,21,1],[16,18,1],[17,18,1],[18,21,1],[18,19,1],[19,21,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],"source":1,"target":0}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-114

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,20,1],[0,1,1],[0,15,1],[0,6,1],[0,9,1],[0,4,1],[0,16,1],[0,19,1],[1,20,1],[1,15,1],[1,6,1],[1,9,1],[1,4,1],[1,16,1],[1,19,1],[2,14,1],[2,10,1],[2,3,1],[2,11,1],[2,7,1],[2,18,1],[2,5,1],[2,12,1],[2,17,1],[2,8,1],[3,14,1],[3,10,1],[3,11,1],[3,7,1],[3,18,1],[3,5,1],[3,12,1],[3,17,1],[3,8,1],[4,20,1],[4,15,1],[4,6,1],[4,9,1],[4,16,1],[4,19,1],[5,14,1],[5,10,1],[5,11,1],[5,7,1],[5,18,1],[5,12,1],[5,17,1],[5,8,1],[6,20,1],[6,15,1],[6,9,1],[6,16,1],[6,19,1],[7,14,1],[7,10,1],[7,11,1],[7,18,1],[7,12,1],[7,17,1],[7,8,1],[8,14,1],[8,10,1],[8,11,1],[8,18,1],[8,12,1],[8,17,1],[9,20,1],[9,15,1],[9,16,1],[9,19,1],[10,14,1],[10,11,1],[10,18,1],[10,12,1],[10,17,1],[11,14,1],[11,18,1],[11,12,1],[11,17,1],[12,14,1],[12,18,1],[12,17,1],[14,18,1],[14,17,1],[15,20,1],[15,16,1],[15,19,1],[16,20,1],[16,19,1],[17,18,1],[19,20,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20],"source":2,"target":12}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-338

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,14,1],[0,6,1],[0,11,1],[0,19,1],[0,20,1],[0,1,1],[0,15,1],[0,12,1],[0,7,1],[0,22,1],[0,5,1],[0,21,1],[0,3,1],[0,4,1],[0,18,1],[0,17,1],[1,14,1],[1,6,1],[1,11,1],[1,19,1],[1,20,1],[1,15,1],[1,12,1],[1,7,1],[1,22,1],[1,5,1],[1,21,1],[1,3,1],[1,4,1],[1,18,1],[1,17,1],[2,13,1],[2,10,1],[2,8,1],[2,16,1],[2,9,1],[3,14,1],[3,6,1],[3,11,1],[3,19,1],[3,20,1],[3,15,1],[3,12,1],[3,7,1],[3,22,1],[3,5,1],[3,21,1],[3,4,1],[3,18,1],[3,17,1],[4,14,1],[4,6,1],[4,11,1],[4,19,1],[4,20,1],[4,15,1],[4,12,1],[4,7,1],[4,22,1],[4,5,1],[4,21,1],[4,18,1],[4,17,1],[5,14,1],[5,6,1],[5,11,1],[5,19,1],[5,20,1],[5,15,1],[5,12,1],[5,7,1],[5,22,1],[5,21,1],[5,18,1],[5,17,1],[6,14,1],[6,11,1],[6,19,1],[6,20,1],[6,15,1],[6,12,1],[6,7,1],[6,22,1],[6,21,1],[6,18,1],[6,17,1],[7,14,1],[7,11,1],[7,19,1],[7,20,1],[7,15,1],[7,12,1],[7,22,1],[7,21,1],[7,18,1],[7,17,1],[8,13,1],[8,10,1],[8,16,1],[8,9,1],[9,13,1],[9,10,1],[9,16,1],[10,13,1],[10,16,1],[11,14,1],[11,19,1],[11,20,1],[11,15,1],[11,12,1],[11,22,1],[11,21,1],[11,18,1],[11,17,1],[12,14,1],[12,19,1],[12,20,1],[12,15,1],[12,22,1],[12,21,1],[12,18,1],[12,17,1],[13,16,1],[14,19,1],[14,20,1],[14,15,1],[14,22,1],[14,21,1],[14,18,1],[14,17,1],[15,19,1],[15,20,1],[15,22,1],[15,21,1],[15,18,1],[15,17,1],[17,19,1],[17,20,1],[17,22,1],[17,21,1],[17,18,1],[18,19,1],[18,20,1],[18,22,1],[18,21,1],[19,20,1],[19,22,1],[19,21,1],[20,22,1],[20,21,1],[21,22,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],"source":13,"target":20}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	false	✓ correct
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-316

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,12,1],[0,10,1],[0,25,1],[0,16,1],[0,24,1],[0,4,1],[0,8,1],[0,27,1],[0,19,1],[1,5,1],[1,28,1],[2,15,1],[3,12,1],[3,13,1],[3,21,1],[3,24,1],[3,4,1],[3,8,1],[4,26,1],[4,20,1],[4,21,1],[4,11,1],[4,9,1],[6,13,1],[6,14,1],[6,22,1],[6,21,1],[6,7,1],[6,23,1],[6,11,1],[7,12,1],[7,26,1],[7,20,1],[7,17,1],[7,14,1],[7,10,1],[7,25,1],[7,24,1],[7,8,1],[7,11,1],[7,19,1],[7,9,1],[8,25,1],[8,27,1],[8,11,1],[9,17,1],[9,14,1],[9,21,1],[9,23,1],[9,27,1],[9,11,1],[10,26,1],[10,20,1],[10,14,1],[10,25,1],[10,23,1],[10,24,1],[11,13,1],[11,17,1],[11,21,1],[11,25,1],[11,23,1],[11,19,1],[12,20,1],[12,17,1],[12,24,1],[13,26,1],[13,20,1],[13,17,1],[13,22,1],[13,25,1],[13,24,1],[13,19,1],[14,20,1],[14,16,1],[15,28,1],[15,18,1],[16,26,1],[16,21,1],[16,23,1],[17,26,1],[17,22,1],[17,23,1],[17,27,1],[18,28,1],[19,22,1],[20,23,1],[20,24,1],[20,27,1],[21,26,1],[21,27,1],[23,25,1],[24,25,1],[24,27,1],[25,27,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],"source":6,"target":10}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-202

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,1,1],[1,11,1],[1,5,1],[1,8,1],[2,14,1],[2,10,1],[2,6,1],[2,3,1],[2,13,1],[2,4,1],[3,7,1],[3,14,1],[3,6,1],[3,12,1],[3,13,1],[3,4,1],[4,9,1],[4,7,1],[4,10,1],[4,12,1],[4,13,1],[5,11,1],[5,8,1],[6,7,1],[6,10,1],[6,12,1],[6,13,1],[7,9,1],[7,14,1],[7,10,1],[7,13,1],[8,11,1],[10,14,1],[10,12,1],[10,13,1],[12,14,1],[12,13,1],[13,14,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"source":12,"target":7}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InternalServerError	✗ no usable answer

test nlgraph-connectivity-test-187

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,21,1],[0,8,1],[0,11,1],[0,16,1],[0,13,1],[0,10,1],[0,20,1],[0,6,1],[0,4,1],[1,14,1],[1,17,1],[1,18,1],[1,5,1],[1,19,1],[1,2,1],[2,22,1],[2,14,1],[2,5,1],[3,8,1],[3,11,1],[3,10,1],[3,12,1],[3,6,1],[4,11,1],[4,13,1],[4,20,1],[4,12,1],[5,22,1],[5,14,1],[5,17,1],[5,18,1],[5,9,1],[5,19,1],[6,8,1],[6,11,1],[6,16,1],[6,13,1],[6,10,1],[6,20,1],[6,12,1],[7,15,1],[8,11,1],[8,13,1],[8,10,1],[8,20,1],[8,12,1],[9,22,1],[9,14,1],[9,17,1],[9,18,1],[9,19,1],[10,21,1],[10,13,1],[11,16,1],[11,13,1],[11,20,1],[11,12,1],[12,21,1],[12,16,1],[12,13,1],[12,20,1],[13,21,1],[13,16,1],[13,20,1],[14,22,1],[14,18,1],[16,21,1],[16,20,1],[17,22,1],[17,18,1],[17,19,1],[18,19,1],[20,21,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],"source":14,"target":5}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-171

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,11,1],[0,2,1],[0,14,1],[0,7,1],[0,13,1],[1,17,1],[1,3,1],[1,10,1],[1,6,1],[2,11,1],[2,12,1],[2,14,1],[2,13,1],[3,17,1],[3,10,1],[3,6,1],[4,9,1],[4,5,1],[5,9,1],[5,16,1],[6,17,1],[6,8,1],[6,10,1],[7,11,1],[7,12,1],[7,14,1],[7,13,1],[8,17,1],[8,15,1],[9,18,1],[9,16,1],[10,17,1],[12,14,1],[12,13,1],[13,14,1],[15,17,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"source":3,"target":10}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-58

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[0,5,1],[0,6,1],[1,3,1],[1,4,1],[2,5,1],[2,6,1],[3,4,1],[5,6,1]],"nodes":[0,1,2,3,4,5,6],"source":5,"target":4}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-78

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,18,1],[0,25,1],[0,19,1],[0,16,1],[0,22,1],[0,8,1],[0,10,1],[0,31,1],[0,13,1],[0,5,1],[0,14,1],[0,24,1],[0,27,1],[0,1,1],[0,15,1],[0,23,1],[1,9,1],[1,30,1],[1,25,1],[1,19,1],[1,16,1],[1,17,1],[1,22,1],[1,8,1],[1,21,1],[1,4,1],[1,31,1],[1,13,1],[1,14,1],[1,24,1],[1,12,1],[1,27,1],[1,15,1],[2,11,1],[2,28,1],[2,29,1],[2,7,1],[3,9,1],[3,18,1],[3,25,1],[3,19,1],[3,16,1],[3,22,1],[3,10,1],[3,4,1],[3,31,1],[3,13,1],[3,5,1],[3,14,1],[3,24,1],[3,12,1],[3,20,1],[3,27,1],[3,15,1],[3,23,1],[4,18,1],[4,30,1],[4,19,1],[4,22,1],[4,8,1],[4,21,1],[4,31,1],[4,5,1],[4,24,1],[4,12,1],[4,27,1],[4,23,1],[5,18,1],[5,30,1],[5,25,1],[5,19,1],[5,17,1],[5,10,1],[5,21,1],[5,31,1],[5,12,1],[5,20,1],[5,15,1],[5,23,1],[6,28,1],[6,29,1],[6,7,1],[6,26,1],[7,28,1],[8,9,1],[8,25,1],[8,19,1],[8,16,1],[8,22,1],[8,10,1],[8,13,1],[8,14,1],[8,24,1],[8,12,1],[8,27,1],[8,15,1],[8,23,1],[9,18,1],[9,30,1],[9,19,1],[9,16,1],[9,17,1],[9,22,1],[9,10,1],[9,31,1],[9,13,1],[9,27,1],[9,15,1],[9,23,1],[10,18,1],[10,30,1],[10,25,1],[10,16,1],[10,22,1],[10,21,1],[10,31,1],[10,14,1],[10,24,1],[10,12,1],[10,20,1],[10,15,1],[11,28,1],[11,26,1],[12,19,1],[12,22,1],[12,21,1],[12,13,1],[12,24,1],[12,15,1],[12,23,1],[13,25,1],[13,19,1],[13,16,1],[13,17,1],[13,22,1],[13,31,1],[13,14,1],[13,27,1],[14,30,1],[14,25,1],[14,16,1],[14,17,1],[14,22,1],[14,31,1],[14,24,1],[14,20,1],[14,15,1],[14,23,1],[15,18,1],[15,30,1],[15,25,1],[15,19,1],[15,16,1],[15,22,1],[15,31,1],[15,24,1],[16,18,1],[16,30,1],[16,22,1],[16,21,1],[16,31,1],[16,20,1],[16,27,1],[17,18,1],[17,30,1],[17,25,1],[17,19,1],[17,22,1],[17,21,1],[17,31,1],[17,24,1],[17,27,1],[17,23,1],[18,30,1],[18,25,1],[18,19,1],[18,22,1],[18,21,1],[18,31,1],[18,24,1],[18,27,1],[18,23,1],[19,30,1],[19,25,1],[19,21,1],[19,24,1],[19,20,1],[19,27,1],[19,23,1],[20,21,1],[20,31,1],[20,24,1],[20,27,1],[20,23,1],[21,25,1],[21,22,1],[21,31,1],[21,24,1],[21,27,1],[21,23,1],[22,30,1],[22,31,1],[22,24,1],[22,23,1],[23,30,1],[23,25,1],[23,24,1],[23,27,1],[24,30,1],[24,25,1],[24,31,1],[24,27,1],[25,30,1],[25,27,1],[26,28,1],[27,30,1],[27,31,1],[28,29,1],[30,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],"source":26,"target":1}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-208

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,20,1],[0,34,1],[0,1,1],[0,10,1],[0,12,1],[1,12,1],[2,24,1],[3,31,1],[3,30,1],[3,25,1],[4,19,1],[4,6,1],[5,8,1],[7,26,1],[10,20,1],[10,28,1],[10,17,1],[10,18,1],[12,20,1],[12,32,1],[12,17,1],[13,14,1],[13,15,1],[13,21,1],[13,26,1],[13,23,1],[14,15,1],[14,21,1],[15,26,1],[15,23,1],[16,21,1],[16,30,1],[17,20,1],[17,27,1],[17,32,1],[18,27,1],[18,34,1],[19,33,1],[20,27,1],[21,31,1],[21,22,1],[22,26,1],[22,31,1],[23,31,1],[26,31,1],[28,34,1],[30,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,30,31,32,33,34],"source":31,"target":18}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-203

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,9,1],[1,18,1],[1,8,1],[1,4,1],[2,15,1],[2,18,1],[2,11,1],[2,23,1],[2,4,1],[3,12,1],[3,5,1],[4,23,1],[4,25,1],[5,12,1],[5,17,1],[6,22,1],[6,13,1],[7,18,1],[7,23,1],[7,8,1],[9,17,1],[10,19,1],[10,17,1],[11,15,1],[12,24,1],[14,20,1],[14,22,1],[15,18,1],[16,20,1],[16,22,1],[20,22,1],[21,22,1],[23,25,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],"source":24,"target":11}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	false	✓ correct

test nlgraph-connectivity-test-357

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,10,1],[0,12,1],[0,20,1],[0,14,1],[0,8,1],[0,3,1],[0,6,1],[0,5,1],[0,15,1],[0,19,1],[0,7,1],[0,9,1],[0,22,1],[0,2,1],[0,21,1],[0,18,1],[1,4,1],[1,10,1],[1,12,1],[1,20,1],[1,8,1],[1,5,1],[1,15,1],[1,16,1],[1,19,1],[1,7,1],[1,9,1],[1,22,1],[1,2,1],[1,18,1],[2,4,1],[2,10,1],[2,12,1],[2,14,1],[2,3,1],[2,5,1],[2,15,1],[2,19,1],[2,7,1],[2,22,1],[2,21,1],[2,18,1],[3,4,1],[3,12,1],[3,20,1],[3,14,1],[3,6,1],[3,5,1],[3,15,1],[3,16,1],[3,19,1],[3,7,1],[3,9,1],[3,22,1],[3,21,1],[3,18,1],[4,10,1],[4,12,1],[4,8,1],[4,6,1],[4,5,1],[4,15,1],[4,16,1],[4,19,1],[4,7,1],[4,9,1],[4,21,1],[4,18,1],[5,12,1],[5,14,1],[5,8,1],[5,6,1],[5,15,1],[5,16,1],[5,19,1],[5,7,1],[5,9,1],[5,22,1],[5,18,1],[6,10,1],[6,12,1],[6,20,1],[6,14,1],[6,16,1],[6,19,1],[6,7,1],[6,9,1],[6,22,1],[6,21,1],[6,18,1],[7,10,1],[7,12,1],[7,14,1],[7,8,1],[7,16,1],[7,9,1],[7,22,1],[7,21,1],[7,18,1],[8,10,1],[8,12,1],[8,14,1],[8,15,1],[8,16,1],[8,19,1],[8,9,1],[8,21,1],[9,12,1],[9,20,1],[9,15,1],[9,16,1],[9,22,1],[9,21,1],[9,18,1],[10,12,1],[10,20,1],[10,14,1],[10,15,1],[10,16,1],[10,18,1],[12,16,1],[12,19,1],[13,17,1],[14,20,1],[14,16,1],[15,16,1],[15,22,1],[15,21,1],[16,20,1],[16,21,1],[16,18,1],[18,22,1],[18,21,1],[19,20,1],[19,22,1],[19,21,1],[21,22,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,17,18,19,20,21,22],"source":7,"target":14}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-131

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,17,1],[0,24,1],[1,11,1],[1,9,1],[1,3,1],[2,19,1],[2,29,1],[2,27,1],[3,7,1],[3,20,1],[4,23,1],[4,25,1],[5,17,1],[6,22,1],[7,29,1],[7,27,1],[7,9,1],[8,16,1],[8,30,1],[8,26,1],[8,18,1],[8,31,1],[9,11,1],[9,27,1],[10,13,1],[10,12,1],[11,19,1],[11,27,1],[12,26,1],[12,18,1],[14,28,1],[15,27,1],[16,30,1],[17,23,1],[18,26,1],[19,28,1],[20,29,1],[21,22,1],[23,24,1],[24,25,1],[27,28,1],[30,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],"source":5,"target":13}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	true	✗ wrong
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-211

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,17,1],[0,24,1],[1,11,1],[1,9,1],[1,3,1],[2,19,1],[2,29,1],[2,27,1],[3,7,1],[3,20,1],[4,23,1],[4,25,1],[5,17,1],[6,22,1],[7,29,1],[7,27,1],[7,9,1],[8,16,1],[8,30,1],[8,26,1],[8,18,1],[8,31,1],[9,11,1],[9,27,1],[10,13,1],[10,12,1],[11,19,1],[11,27,1],[12,26,1],[12,18,1],[14,28,1],[15,27,1],[16,30,1],[17,23,1],[18,26,1],[19,28,1],[20,29,1],[21,22,1],[23,24,1],[24,25,1],[27,28,1],[30,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],"source":13,"target":20}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-290

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,21,1],[0,8,1],[0,11,1],[0,16,1],[0,13,1],[0,10,1],[0,20,1],[0,6,1],[0,4,1],[1,14,1],[1,17,1],[1,18,1],[1,5,1],[1,19,1],[1,2,1],[2,22,1],[2,14,1],[2,5,1],[3,8,1],[3,11,1],[3,10,1],[3,12,1],[3,6,1],[4,11,1],[4,13,1],[4,20,1],[4,12,1],[5,22,1],[5,14,1],[5,17,1],[5,18,1],[5,9,1],[5,19,1],[6,8,1],[6,11,1],[6,16,1],[6,13,1],[6,10,1],[6,20,1],[6,12,1],[7,15,1],[8,11,1],[8,13,1],[8,10,1],[8,20,1],[8,12,1],[9,22,1],[9,14,1],[9,17,1],[9,18,1],[9,19,1],[10,21,1],[10,13,1],[11,16,1],[11,13,1],[11,20,1],[11,12,1],[12,21,1],[12,16,1],[12,13,1],[12,20,1],[13,21,1],[13,16,1],[13,20,1],[14,22,1],[14,18,1],[16,21,1],[16,20,1],[17,22,1],[17,18,1],[17,19,1],[18,19,1],[20,21,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],"source":15,"target":10}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-57

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,8,1],[0,19,1],[0,17,1],[0,7,1],[0,16,1],[0,21,1],[1,22,1],[1,19,1],[1,20,1],[1,21,1],[2,23,1],[2,6,1],[3,13,1],[3,18,1],[3,4,1],[3,10,1],[3,21,1],[4,19,1],[4,10,1],[4,16,1],[5,14,1],[5,12,1],[5,9,1],[5,11,1],[6,14,1],[6,23,1],[7,15,1],[7,22,1],[7,18,1],[7,8,1],[7,17,1],[7,20,1],[8,13,1],[8,21,1],[9,12,1],[9,11,1],[10,17,1],[13,19,1],[13,17,1],[13,21,1],[15,20,1],[16,18,1],[16,20,1],[19,20,1],[19,21,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"source":11,"target":8}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-193

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,2,1],[0,1,1],[0,4,1],[1,3,1],[1,2,1],[1,4,1],[1,6,1],[2,3,1],[2,4,1],[2,5,1],[3,4,1],[3,6,1],[4,6,1],[5,6,1]],"nodes":[0,1,2,3,4,5,6],"source":5,"target":2}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-317

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[1,6,1],[1,4,1],[1,3,1],[1,2,1],[1,7,1],[2,10,1],[2,4,1],[2,8,1],[3,10,1],[3,6,1],[3,4,1],[3,8,1],[3,5,1],[4,6,1],[4,8,1],[4,5,1],[4,7,1],[5,10,1],[5,8,1],[6,10,1],[6,8,1],[7,10,1]],"nodes":[0,1,2,3,4,5,6,7,8,10],"source":0,"target":7}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-301

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,29,1],[0,30,1],[0,27,1],[0,33,1],[0,11,1],[0,5,1],[0,12,1],[0,20,1],[0,7,1],[0,28,1],[0,17,1],[0,6,1],[0,4,1],[0,32,1],[0,13,1],[0,3,1],[0,22,1],[0,31,1],[1,25,1],[1,29,1],[1,30,1],[1,27,1],[1,33,1],[1,2,1],[1,5,1],[1,12,1],[1,20,1],[1,28,1],[1,18,1],[1,16,1],[1,24,1],[1,6,1],[1,13,1],[1,3,1],[1,22,1],[1,31,1],[2,25,1],[2,23,1],[2,29,1],[2,30,1],[2,27,1],[2,33,1],[2,11,1],[2,5,1],[2,12,1],[2,7,1],[2,18,1],[2,16,1],[2,17,1],[2,24,1],[2,13,1],[2,22,1],[2,15,1],[3,25,1],[3,23,1],[3,29,1],[3,30,1],[3,12,1],[3,7,1],[3,18,1],[3,16,1],[3,24,1],[3,4,1],[3,13,1],[3,22,1],[3,31,1],[4,23,1],[4,29,1],[4,27,1],[4,33,1],[4,11,1],[4,5,1],[4,7,1],[4,18,1],[4,24,1],[4,32,1],[4,15,1],[4,31,1],[5,25,1],[5,23,1],[5,30,1],[5,27,1],[5,33,1],[5,11,1],[5,12,1],[5,20,1],[5,7,1],[5,28,1],[5,24,1],[5,6,1],[5,32,1],[5,13,1],[5,22,1],[5,15,1],[5,31,1],[6,25,1],[6,23,1],[6,30,1],[6,27,1],[6,33,1],[6,12,1],[6,20,1],[6,7,1],[6,18,1],[6,24,1],[6,32,1],[6,13,1],[7,25,1],[7,30,1],[7,27,1],[7,33,1],[7,20,1],[7,28,1],[7,18,1],[7,24,1],[7,32,1],[7,13,1],[7,22,1],[7,15,1],[7,31,1],[8,14,1],[8,26,1],[8,19,1],[9,14,1],[9,26,1],[9,19,1],[9,21,1],[9,10,1],[10,14,1],[10,26,1],[10,19,1],[11,23,1],[11,29,1],[11,30,1],[11,27,1],[11,33,1],[11,20,1],[11,18,1],[11,16,1],[11,17,1],[11,32,1],[11,13,1],[11,22,1],[11,15,1],[11,31,1],[12,25,1],[12,23,1],[12,29,1],[12,27,1],[12,33,1],[12,28,1],[12,16,1],[12,24,1],[12,13,1],[12,22,1],[12,15,1],[12,31,1],[13,25,1],[13,23,1],[13,29,1],[13,27,1],[13,33,1],[13,20,1],[13,28,1],[13,18,1],[13,16,1],[13,17,1],[13,24,1],[13,32,1],[13,15,1],[13,31,1],[14,26,1],[15,25,1],[15,23,1],[15,29,1],[15,30,1],[15,33,1],[15,16,1],[15,17,1],[15,24,1],[15,22,1],[15,31,1],[16,25,1],[16,23,1],[16,29,1],[16,30,1],[16,27,1],[16,28,1],[16,17,1],[16,24,1],[16,32,1],[16,22,1],[17,25,1],[17,23,1],[17,29,1],[17,33,1],[17,20,1],[17,18,1],[17,24,1],[17,31,1],[18,25,1],[18,29,1],[18,30,1],[18,33,1],[18,28,1],[18,24,1],[18,31,1],[20,25,1],[20,23,1],[20,30,1],[20,24,1],[20,32,1],[20,22,1],[20,31,1],[21,26,1],[22,25,1],[22,29,1],[22,30,1],[22,28,1],[22,24,1],[23,25,1],[23,29,1],[23,27,1],[23,28,1],[23,24,1],[23,32,1],[24,25,1],[24,29,1],[24,27,1],[24,33,1],[24,28,1],[24,31,1],[25,29,1],[25,30,1],[25,27,1],[25,28,1],[25,32,1],[25,31,1],[27,29,1],[27,30,1],[27,33,1],[27,28,1],[28,29,1],[28,30,1],[28,33,1],[28,32,1],[28,31,1],[29,30,1],[29,33,1],[29,32,1],[29,31,1],[30,33,1],[30,32,1],[30,31,1],[31,33,1],[31,32,1],[32,33,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],"source":33,"target":27}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-40

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,7,1],[0,3,1],[0,2,1],[0,9,1],[0,8,1],[1,6,1],[1,4,1],[2,7,1],[2,10,1],[2,3,1],[2,8,1],[2,5,1],[3,10,1],[3,9,1],[3,8,1],[4,6,1],[5,7,1],[5,10,1],[5,9,1],[7,8,1],[8,9,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10],"source":0,"target":1}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	false	✓ correct

test nlgraph-connectivity-test-112

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,1,1],[0,11,1],[0,17,1],[0,3,1],[0,19,1],[0,9,1],[0,16,1],[0,15,1],[0,7,1],[0,12,1],[0,2,1],[1,11,1],[1,10,1],[1,3,1],[1,4,1],[1,8,1],[1,19,1],[1,13,1],[1,9,1],[1,16,1],[1,15,1],[1,7,1],[1,12,1],[1,2,1],[2,17,1],[2,5,1],[2,16,1],[2,15,1],[3,17,1],[3,10,1],[3,5,1],[3,6,1],[3,8,1],[3,13,1],[3,9,1],[3,16,1],[3,15,1],[3,7,1],[3,12,1],[4,11,1],[4,5,1],[4,8,1],[4,19,1],[4,13,1],[4,9,1],[4,7,1],[4,12,1],[5,11,1],[5,10,1],[5,6,1],[5,8,1],[5,19,1],[5,13,1],[5,7,1],[6,11,1],[6,17,1],[6,10,1],[6,8,1],[6,19,1],[6,13,1],[6,16,1],[6,15,1],[6,7,1],[6,12,1],[7,11,1],[7,17,1],[7,10,1],[7,19,1],[7,9,1],[7,16,1],[7,15,1],[8,11,1],[8,17,1],[8,10,1],[8,19,1],[8,13,1],[8,15,1],[8,12,1],[9,11,1],[9,17,1],[9,10,1],[9,13,1],[9,16,1],[9,15,1],[10,11,1],[10,17,1],[10,19,1],[10,13,1],[10,15,1],[10,12,1],[11,19,1],[11,15,1],[11,12,1],[12,17,1],[12,19,1],[12,13,1],[13,19,1],[13,16,1],[13,15,1],[14,18,1],[15,19,1],[15,16,1],[16,17,1],[17,19,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"source":18,"target":16}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-204

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,16,1],[0,7,1],[0,12,1],[0,32,1],[0,22,1],[0,9,1],[0,20,1],[0,2,1],[0,5,1],[0,14,1],[0,4,1],[0,26,1],[0,21,1],[1,11,1],[1,8,1],[1,24,1],[1,3,1],[1,31,1],[1,28,1],[1,6,1],[2,16,1],[2,7,1],[2,32,1],[2,22,1],[2,9,1],[2,20,1],[2,14,1],[2,4,1],[2,21,1],[3,11,1],[3,8,1],[3,24,1],[3,31,1],[3,28,1],[4,16,1],[4,32,1],[4,22,1],[4,9,1],[4,20,1],[4,5,1],[4,14,1],[4,26,1],[5,16,1],[5,7,1],[5,12,1],[5,32,1],[5,22,1],[5,9,1],[5,20,1],[5,14,1],[5,26,1],[5,21,1],[6,8,1],[6,24,1],[6,31,1],[6,28,1],[7,12,1],[7,32,1],[7,22,1],[7,9,1],[7,14,1],[7,26,1],[7,21,1],[8,24,1],[8,31,1],[8,28,1],[9,16,1],[9,12,1],[9,32,1],[9,20,1],[9,26,1],[9,21,1],[10,23,1],[10,13,1],[10,29,1],[10,19,1],[10,25,1],[10,18,1],[12,32,1],[12,22,1],[12,20,1],[12,26,1],[12,21,1],[13,30,1],[13,27,1],[13,29,1],[13,19,1],[13,25,1],[13,18,1],[14,16,1],[14,32,1],[14,22,1],[14,20,1],[14,26,1],[15,30,1],[15,29,1],[15,25,1],[15,18,1],[16,32,1],[16,22,1],[16,20,1],[16,26,1],[16,21,1],[17,30,1],[17,27,1],[18,30,1],[18,29,1],[19,30,1],[19,23,1],[19,27,1],[19,25,1],[20,32,1],[20,22,1],[20,26,1],[21,32,1],[21,26,1],[22,32,1],[22,26,1],[23,30,1],[23,29,1],[23,25,1],[24,28,1],[26,32,1],[27,30,1],[27,29,1],[28,31,1],[29,30,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],"source":15,"target":19}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-145

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,11,1],[0,6,1],[1,5,1],[1,8,1],[1,10,1],[1,15,1],[1,17,1],[1,13,1],[1,16,1],[2,5,1],[2,4,1],[2,8,1],[2,10,1],[2,14,1],[2,17,1],[2,13,1],[2,16,1],[3,9,1],[3,6,1],[3,12,1],[4,8,1],[4,15,1],[4,14,1],[4,17,1],[4,13,1],[5,8,1],[5,15,1],[5,17,1],[6,7,1],[6,9,1],[7,11,1],[7,9,1],[8,15,1],[8,17,1],[8,13,1],[8,16,1],[9,11,1],[10,15,1],[10,14,1],[10,17,1],[11,12,1],[13,15,1],[13,14,1],[13,16,1],[14,15,1],[14,17,1],[14,16,1],[15,17,1],[15,16,1],[16,17,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"source":16,"target":13}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-365

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[2,3,1],[2,5,1],[3,5,1],[4,6,1]],"nodes":[0,2,3,4,5,6],"source":2,"target":3}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-116

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,9,1],[0,1,1],[0,2,1],[0,7,1],[0,6,1],[1,2,1],[1,8,1],[1,7,1],[1,4,1],[1,6,1],[2,7,1],[2,4,1],[2,6,1],[3,5,1],[4,9,1],[4,8,1],[4,7,1],[6,9,1],[6,7,1],[7,8,1]],"nodes":[0,1,2,3,4,5,6,7,8,9],"source":1,"target":2}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	true	✓ correct

test nlgraph-connectivity-test-82

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,9,1],[0,30,1],[0,6,1],[0,12,1],[1,15,1],[2,17,1],[2,4,1],[3,25,1],[3,30,1],[3,12,1],[4,18,1],[4,16,1],[4,20,1],[4,22,1],[4,28,1],[4,8,1],[4,17,1],[5,12,1],[5,11,1],[6,19,1],[7,9,1],[7,10,1],[8,22,1],[8,28,1],[8,21,1],[9,23,1],[10,12,1],[10,11,1],[11,30,1],[11,19,1],[11,12,1],[12,25,1],[12,19,1],[13,27,1],[13,26,1],[15,26,1],[16,18,1],[16,29,1],[16,20,1],[16,24,1],[16,22,1],[16,28,1],[16,17,1],[17,22,1],[17,28,1],[17,21,1],[18,29,1],[18,20,1],[18,24,1],[18,22,1],[19,30,1],[20,22,1],[20,28,1],[21,24,1],[24,28,1],[25,30,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],"source":26,"target":30}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-138

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,20,1],[0,14,1],[0,12,1],[1,20,1],[1,12,1],[2,13,1],[2,18,1],[3,17,1],[4,20,1],[7,21,1],[8,18,1],[9,20,1],[9,15,1],[10,13,1],[10,19,1],[13,18,1],[14,16,1],[14,15,1],[15,20,1]],"nodes":[0,1,2,3,4,7,8,9,10,12,13,14,15,16,17,18,19,20,21],"source":0,"target":4}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-136

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,23,1],[1,6,1],[1,19,1],[1,7,1],[2,17,1],[2,24,1],[2,10,1],[2,20,1],[3,22,1],[3,27,1],[4,17,1],[4,15,1],[5,19,1],[5,12,1],[5,25,1],[6,19,1],[6,7,1],[7,18,1],[7,23,1],[8,16,1],[8,13,1],[9,27,1],[9,13,1],[10,21,1],[10,15,1],[10,11,1],[11,17,1],[11,26,1],[11,24,1],[11,14,1],[12,25,1],[12,23,1],[14,17,1],[14,26,1],[15,21,1],[17,26,1],[17,21,1],[17,24,1],[20,21,1],[20,24,1],[21,26,1],[21,24,1],[23,25,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],"source":3,"target":0}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-50

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,18,1],[0,24,1],[0,5,1],[0,12,1],[0,26,1],[0,14,1],[0,16,1],[0,21,1],[0,9,1],[0,1,1],[0,28,1],[0,25,1],[1,3,1],[1,18,1],[1,24,1],[1,5,1],[1,12,1],[1,26,1],[1,14,1],[1,16,1],[1,21,1],[1,2,1],[1,23,1],[1,20,1],[1,28,1],[1,25,1],[2,3,1],[2,18,1],[2,10,1],[2,24,1],[2,5,1],[2,12,1],[2,26,1],[2,14,1],[2,16,1],[2,9,1],[2,23,1],[2,20,1],[2,28,1],[2,7,1],[2,25,1],[2,22,1],[2,13,1],[3,18,1],[3,24,1],[3,12,1],[3,26,1],[3,16,1],[3,9,1],[3,19,1],[3,7,1],[3,25,1],[3,22,1],[4,11,1],[4,27,1],[4,17,1],[4,15,1],[4,8,1],[5,18,1],[5,24,1],[5,12,1],[5,26,1],[5,14,1],[5,16,1],[5,21,1],[5,9,1],[5,23,1],[5,19,1],[5,20,1],[5,7,1],[5,13,1],[6,11,1],[6,27,1],[6,29,1],[6,15,1],[6,8,1],[7,18,1],[7,10,1],[7,12,1],[7,26,1],[7,14,1],[7,16,1],[7,21,1],[7,9,1],[7,20,1],[7,25,1],[7,22,1],[7,13,1],[8,11,1],[8,27,1],[8,29,1],[8,17,1],[8,15,1],[9,18,1],[9,10,1],[9,24,1],[9,16,1],[9,21,1],[9,19,1],[9,20,1],[9,28,1],[9,25,1],[9,13,1],[10,18,1],[10,24,1],[10,12,1],[10,26,1],[10,14,1],[10,16,1],[10,23,1],[10,20,1],[10,28,1],[10,25,1],[10,22,1],[10,13,1],[11,27,1],[11,29,1],[12,18,1],[12,24,1],[12,16,1],[12,21,1],[12,23,1],[12,20,1],[12,28,1],[12,22,1],[12,13,1],[13,18,1],[13,24,1],[13,26,1],[13,14,1],[13,16,1],[13,21,1],[13,23,1],[13,20,1],[13,28,1],[13,25,1],[13,22,1],[14,26,1],[14,16,1],[14,21,1],[14,23,1],[14,19,1],[14,20,1],[14,28,1],[14,25,1],[15,27,1],[15,17,1],[16,18,1],[16,24,1],[16,26,1],[16,20,1],[16,25,1],[16,22,1],[17,29,1],[18,24,1],[18,26,1],[18,23,1],[18,19,1],[18,20,1],[18,25,1],[18,22,1],[19,21,1],[19,23,1],[19,28,1],[19,25,1],[20,26,1],[20,23,1],[20,28,1],[20,25,1],[20,22,1],[21,26,1],[21,23,1],[21,28,1],[21,22,1],[22,26,1],[22,23,1],[22,25,1],[23,24,1],[23,26,1],[24,26,1],[24,28,1],[25,26,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29],"source":12,"target":13}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"reachable": true}	✓ correct

test nlgraph-connectivity-test-260

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,11,1],[0,25,1],[0,13,1],[0,3,1],[0,1,1],[1,11,1],[1,25,1],[1,13,1],[1,2,1],[1,3,1],[1,8,1],[2,21,1],[2,22,1],[2,25,1],[2,13,1],[2,3,1],[3,18,1],[3,22,1],[3,11,1],[3,13,1],[4,23,1],[4,14,1],[4,6,1],[4,12,1],[4,27,1],[4,15,1],[4,5,1],[4,16,1],[4,26,1],[4,20,1],[4,7,1],[4,19,1],[5,14,1],[5,6,1],[5,12,1],[5,27,1],[5,15,1],[5,16,1],[5,9,1],[5,20,1],[5,7,1],[6,23,1],[6,14,1],[6,12,1],[6,24,1],[6,15,1],[6,16,1],[6,9,1],[6,17,1],[6,26,1],[6,20,1],[6,7,1],[6,19,1],[7,23,1],[7,14,1],[7,12,1],[7,24,1],[7,10,1],[7,16,1],[7,9,1],[7,17,1],[7,26,1],[7,20,1],[7,19,1],[8,21,1],[8,18,1],[8,22,1],[8,11,1],[8,25,1],[8,13,1],[9,23,1],[9,12,1],[9,10,1],[9,16,1],[9,17,1],[9,26,1],[9,20,1],[10,23,1],[10,14,1],[10,12,1],[10,24,1],[10,27,1],[10,16,1],[10,17,1],[10,26,1],[10,19,1],[11,21,1],[11,22,1],[11,25,1],[11,13,1],[12,23,1],[12,14,1],[12,24,1],[12,27,1],[12,16,1],[12,26,1],[12,20,1],[12,19,1],[13,22,1],[13,25,1],[14,23,1],[14,24,1],[14,16,1],[14,26,1],[14,19,1],[15,24,1],[15,27,1],[15,16,1],[15,26,1],[16,23,1],[16,27,1],[16,17,1],[16,26,1],[16,20,1],[17,27,1],[17,26,1],[17,20,1],[17,19,1],[18,22,1],[19,23,1],[19,24,1],[19,27,1],[19,26,1],[19,20,1],[20,23,1],[20,26,1],[21,22,1],[21,25,1],[22,25,1],[23,24,1],[23,27,1],[24,27,1],[24,26,1],[26,27,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27],"source":2,"target":0}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"reachable": true}	✓ correct

test nlgraph-connectivity-test-125

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,9,1],[0,30,1],[0,6,1],[0,12,1],[1,15,1],[2,17,1],[2,4,1],[3,25,1],[3,30,1],[3,12,1],[4,18,1],[4,16,1],[4,20,1],[4,22,1],[4,28,1],[4,8,1],[4,17,1],[5,12,1],[5,11,1],[6,19,1],[7,9,1],[7,10,1],[8,22,1],[8,28,1],[8,21,1],[9,23,1],[10,12,1],[10,11,1],[11,30,1],[11,19,1],[11,12,1],[12,25,1],[12,19,1],[13,27,1],[13,26,1],[15,26,1],[16,18,1],[16,29,1],[16,20,1],[16,24,1],[16,22,1],[16,28,1],[16,17,1],[17,22,1],[17,28,1],[17,21,1],[18,29,1],[18,20,1],[18,24,1],[18,22,1],[19,30,1],[20,22,1],[20,28,1],[21,24,1],[24,28,1],[25,30,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],"source":25,"target":4}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-62

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,9,1],[0,10,1],[0,1,1],[1,8,1],[1,3,1],[1,14,1],[3,5,1],[3,6,1],[3,9,1],[3,12,1],[4,9,1],[4,16,1],[6,7,1],[6,12,1],[7,14,1],[8,16,1],[8,14,1],[10,11,1],[10,14,1],[10,12,1],[11,14,1],[12,14,1]],"nodes":[0,1,3,4,5,6,7,8,9,10,11,12,14,16],"source":7,"target":3}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-209

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[0,17,1],[1,4,1],[2,10,1],[3,19,1],[3,30,1],[3,13,1],[3,25,1],[3,8,1],[4,31,1],[5,16,1],[6,29,1],[6,11,1],[6,32,1],[7,14,1],[7,17,1],[8,21,1],[8,30,1],[8,13,1],[8,28,1],[9,20,1],[9,25,1],[11,29,1],[11,26,1],[11,22,1],[13,21,1],[13,15,1],[13,28,1],[13,23,1],[15,31,1],[15,16,1],[15,28,1],[15,23,1],[16,21,1],[16,25,1],[16,23,1],[18,29,1],[18,24,1],[20,31,1],[20,30,1],[20,25,1],[21,25,1],[22,24,1],[23,25,1],[23,28,1],[24,29,1],[24,32,1],[25,30,1],[26,32,1],[28,30,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,23,24,25,26,28,29,30,31,32],"source":31,"target":28}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-98

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,11,1],[0,12,1],[0,5,1],[0,6,1],[0,4,1],[0,8,1],[0,2,1],[0,9,1],[0,1,1],[0,7,1],[1,12,1],[1,5,1],[1,6,1],[1,4,1],[1,8,1],[1,2,1],[1,9,1],[1,10,1],[1,7,1],[2,8,1],[2,10,1],[2,7,1],[4,11,1],[4,12,1],[4,5,1],[4,6,1],[4,8,1],[4,9,1],[4,7,1],[5,11,1],[5,6,1],[5,8,1],[5,10,1],[5,7,1],[6,11,1],[6,12,1],[6,8,1],[6,9,1],[7,11,1],[7,12,1],[7,9,1],[7,10,1],[8,12,1],[8,9,1],[8,10,1],[9,11,1],[9,12,1],[9,10,1],[10,11,1],[10,12,1],[11,12,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12],"source":11,"target":3}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	false	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-213

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,19,1],[1,12,1],[1,19,1],[2,13,1],[3,20,1],[3,11,1],[4,7,1],[4,16,1],[4,18,1],[5,17,1],[5,7,1],[6,15,1],[6,20,1],[6,11,1],[7,20,1],[7,11,1],[8,12,1],[8,13,1],[8,19,1],[11,17,1],[11,15,1],[12,19,1],[16,17,1],[16,20,1],[17,20,1],[18,20,1]],"nodes":[0,1,2,3,4,5,6,7,8,11,12,13,15,16,17,18,19,20,21],"source":0,"target":21}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-11

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,9,1],[0,30,1],[0,6,1],[0,12,1],[1,15,1],[2,17,1],[2,4,1],[3,25,1],[3,30,1],[3,12,1],[4,18,1],[4,16,1],[4,20,1],[4,22,1],[4,28,1],[4,8,1],[4,17,1],[5,12,1],[5,11,1],[6,19,1],[7,9,1],[7,10,1],[8,22,1],[8,28,1],[8,21,1],[9,23,1],[10,12,1],[10,11,1],[11,30,1],[11,19,1],[11,12,1],[12,25,1],[12,19,1],[13,27,1],[13,26,1],[15,26,1],[16,18,1],[16,29,1],[16,20,1],[16,24,1],[16,22,1],[16,28,1],[16,17,1],[17,22,1],[17,28,1],[17,21,1],[18,29,1],[18,20,1],[18,24,1],[18,22,1],[19,30,1],[20,22,1],[20,28,1],[21,24,1],[24,28,1],[25,30,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],"source":10,"target":14}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-244

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,29,1],[0,27,1],[0,23,1],[0,4,1],[0,20,1],[0,17,1],[0,6,1],[1,5,1],[1,22,1],[1,11,1],[1,19,1],[1,24,1],[1,2,1],[1,15,1],[1,8,1],[1,30,1],[1,9,1],[1,28,1],[1,18,1],[2,5,1],[2,22,1],[2,24,1],[2,15,1],[2,8,1],[2,30,1],[2,9,1],[2,28,1],[2,18,1],[3,26,1],[3,13,1],[4,21,1],[4,29,1],[4,23,1],[4,20,1],[4,17,1],[4,6,1],[5,22,1],[5,19,1],[5,24,1],[5,14,1],[5,30,1],[5,28,1],[5,18,1],[6,21,1],[6,29,1],[6,27,1],[6,23,1],[6,20,1],[6,17,1],[7,26,1],[7,10,1],[7,13,1],[7,16,1],[7,12,1],[8,11,1],[8,24,1],[8,14,1],[8,30,1],[8,9,1],[8,28,1],[8,18,1],[9,22,1],[9,11,1],[9,19,1],[9,15,1],[9,28,1],[10,16,1],[10,12,1],[11,15,1],[11,30,1],[11,28,1],[11,18,1],[12,13,1],[12,16,1],[13,26,1],[13,16,1],[13,25,1],[14,22,1],[14,19,1],[14,15,1],[14,30,1],[15,19,1],[15,30,1],[15,28,1],[15,18,1],[16,26,1],[16,25,1],[17,29,1],[17,23,1],[18,19,1],[18,24,1],[18,28,1],[19,30,1],[19,28,1],[20,21,1],[20,27,1],[21,29,1],[21,27,1],[21,23,1],[22,24,1],[22,28,1],[23,27,1],[24,30,1],[24,28,1],[25,26,1],[28,30,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],"source":13,"target":26}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-39

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[1,11,1],[1,9,1],[1,19,1],[1,31,1],[1,20,1],[2,15,1],[2,11,1],[2,27,1],[2,29,1],[2,16,1],[2,31,1],[3,8,1],[3,4,1],[3,12,1],[3,18,1],[3,17,1],[3,10,1],[3,25,1],[3,31,1],[3,20,1],[4,30,1],[4,24,1],[4,19,1],[5,26,1],[5,23,1],[6,13,1],[7,15,1],[7,9,1],[7,30,1],[7,12,1],[7,16,1],[7,19,1],[7,10,1],[7,25,1],[8,15,1],[8,11,1],[8,30,1],[8,24,1],[8,10,1],[8,31,1],[9,11,1],[9,30,1],[9,27,1],[9,29,1],[9,10,1],[10,15,1],[10,30,1],[10,12,1],[10,18,1],[10,19,1],[10,17,1],[10,14,1],[11,30,1],[11,29,1],[11,19,1],[12,15,1],[12,19,1],[12,14,1],[12,20,1],[13,28,1],[14,27,1],[14,24,1],[14,20,1],[15,27,1],[15,18,1],[15,25,1],[15,20,1],[16,29,1],[16,24,1],[16,19,1],[17,29,1],[17,19,1],[17,31,1],[18,30,1],[18,24,1],[18,19,1],[18,31,1],[19,30,1],[19,25,1],[21,28,1],[21,23,1],[22,23,1],[25,27,1],[25,31,1],[26,28,1],[29,31,1]],"nodes":[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],"source":22,"target":12}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-80

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[0,1,1],[3,4,1]],"nodes":[0,1,2,3,4],"source":1,"target":0}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	{"result": true}	✓ correct

test nlgraph-connectivity-test-70

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,20,1],[0,13,1],[0,30,1],[0,1,1],[0,4,1],[0,2,1],[0,22,1],[1,30,1],[1,17,1],[1,5,1],[1,4,1],[1,25,1],[1,29,1],[2,3,1],[2,5,1],[2,23,1],[3,28,1],[3,24,1],[3,4,1],[3,6,1],[3,8,1],[3,12,1],[4,15,1],[4,24,1],[4,25,1],[4,7,1],[4,6,1],[4,29,1],[5,21,1],[5,23,1],[5,7,1],[5,12,1],[6,20,1],[6,28,1],[6,23,1],[7,13,1],[7,15,1],[7,16,1],[7,8,1],[7,12,1],[8,20,1],[8,30,1],[8,24,1],[8,17,1],[8,23,1],[10,19,1],[11,19,1],[11,26,1],[12,20,1],[12,16,1],[12,25,1],[12,18,1],[13,28,1],[13,18,1],[14,20,1],[15,28,1],[15,24,1],[15,23,1],[16,20,1],[16,30,1],[16,24,1],[16,29,1],[17,21,1],[17,28,1],[17,25,1],[18,21,1],[18,23,1],[18,29,1],[20,24,1],[20,23,1],[20,22,1],[20,29,1],[21,25,1],[21,23,1],[21,22,1],[22,25,1],[23,24,1],[23,29,1],[24,28,1],[24,29,1],[25,28,1],[26,27,1],[29,30,1]],"nodes":[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30],"source":0,"target":11}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	true	✗ wrong
Qwen · off	false	✓ correct
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-310

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,20,1],[0,15,1],[1,3,1],[1,20,1],[2,11,1],[3,12,1],[3,6,1],[3,16,1],[3,20,1],[5,14,1],[5,7,1],[6,20,1],[6,21,1],[7,13,1],[7,18,1],[8,14,1],[8,13,1],[9,12,1],[9,16,1],[9,21,1],[10,21,1],[11,17,1],[12,16,1],[14,18,1],[15,16,1],[15,21,1],[16,20,1],[20,21,1]],"nodes":[0,1,2,3,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21],"source":10,"target":0}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-195

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,6,1],[0,14,1],[1,21,1],[1,3,1],[1,15,1],[1,7,1],[3,12,1],[4,10,1],[5,10,1],[6,22,1],[7,21,1],[7,15,1],[9,12,1],[11,13,1],[11,21,1],[14,20,1],[15,17,1],[15,21,1],[16,18,1],[18,22,1]],"nodes":[0,1,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,20,21,22],"source":22,"target":6}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-91

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,1,1],[0,12,1],[0,4,1],[1,13,1],[1,3,1],[1,6,1],[1,9,1],[2,15,1],[2,14,1],[2,11,1],[4,7,1],[5,16,1],[5,6,1],[5,9,1],[6,13,1],[6,8,1],[10,13,1],[10,12,1],[11,15,1],[11,14,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"source":7,"target":17}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-32

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,7,1],[0,10,1],[0,6,1],[0,2,1],[0,8,1],[0,4,1],[0,1,1],[1,3,1],[1,7,1],[1,10,1],[1,6,1],[1,2,1],[1,8,1],[1,4,1],[2,3,1],[2,7,1],[2,10,1],[2,6,1],[2,8,1],[2,4,1],[3,7,1],[3,10,1],[3,6,1],[3,8,1],[3,4,1],[4,7,1],[4,10,1],[4,6,1],[4,8,1],[5,9,1],[6,7,1],[6,10,1],[6,8,1],[7,10,1],[7,8,1],[8,10,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10],"source":4,"target":2}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-263

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,19,1],[0,4,1],[0,12,1],[0,11,1],[0,10,1],[0,3,1],[0,17,1],[0,21,1],[0,27,1],[0,15,1],[0,23,1],[0,31,1],[0,29,1],[0,2,1],[0,8,1],[0,9,1],[0,14,1],[0,18,1],[1,5,1],[1,26,1],[1,13,1],[1,20,1],[1,32,1],[1,7,1],[2,19,1],[2,4,1],[2,28,1],[2,22,1],[2,16,1],[2,12,1],[2,10,1],[2,3,1],[2,17,1],[2,21,1],[2,27,1],[2,15,1],[2,23,1],[2,31,1],[2,29,1],[2,8,1],[2,9,1],[2,14,1],[2,18,1],[3,4,1],[3,22,1],[3,16,1],[3,12,1],[3,10,1],[3,17,1],[3,21,1],[3,27,1],[3,23,1],[3,31,1],[3,29,1],[3,6,1],[3,9,1],[3,14,1],[3,18,1],[4,16,1],[4,12,1],[4,11,1],[4,17,1],[4,21,1],[4,15,1],[4,30,1],[4,23,1],[4,29,1],[4,6,1],[4,8,1],[4,9,1],[4,18,1],[5,26,1],[5,13,1],[5,25,1],[5,24,1],[5,32,1],[5,7,1],[6,19,1],[6,22,1],[6,12,1],[6,11,1],[6,10,1],[6,17,1],[6,21,1],[6,27,1],[6,15,1],[6,30,1],[6,23,1],[6,31,1],[6,29,1],[6,9,1],[6,14,1],[7,26,1],[7,25,1],[7,32,1],[8,19,1],[8,28,1],[8,10,1],[8,17,1],[8,27,1],[8,15,1],[8,30,1],[8,23,1],[9,19,1],[9,28,1],[9,22,1],[9,16,1],[9,12,1],[9,10,1],[9,17,1],[9,21,1],[9,15,1],[9,30,1],[9,23,1],[9,29,1],[9,18,1],[10,19,1],[10,28,1],[10,22,1],[10,12,1],[10,11,1],[10,17,1],[10,21,1],[10,27,1],[10,15,1],[10,30,1],[10,23,1],[10,31,1],[10,29,1],[10,14,1],[10,18,1],[11,16,1],[11,12,1],[11,17,1],[11,21,1],[11,27,1],[11,15,1],[11,30,1],[11,31,1],[11,29,1],[11,14,1],[11,18,1],[12,19,1],[12,28,1],[12,22,1],[12,17,1],[12,27,1],[12,15,1],[12,30,1],[12,23,1],[12,31,1],[12,29,1],[12,14,1],[12,18,1],[13,26,1],[13,25,1],[13,20,1],[13,32,1],[14,28,1],[14,16,1],[14,17,1],[14,21,1],[14,27,1],[14,15,1],[14,31,1],[14,29,1],[14,18,1],[15,19,1],[15,22,1],[15,16,1],[15,17,1],[15,21,1],[15,27,1],[15,30,1],[15,23,1],[15,31,1],[15,29,1],[15,18,1],[16,19,1],[16,28,1],[16,22,1],[16,17,1],[16,21,1],[16,27,1],[16,30,1],[16,31,1],[16,18,1],[17,22,1],[17,21,1],[17,30,1],[17,31,1],[17,29,1],[17,18,1],[18,19,1],[18,28,1],[18,22,1],[18,21,1],[18,27,1],[18,29,1],[19,28,1],[19,22,1],[19,21,1],[19,30,1],[19,31,1],[19,29,1],[20,32,1],[21,28,1],[21,22,1],[21,27,1],[21,29,1],[22,28,1],[22,30,1],[22,23,1],[22,31,1],[22,29,1],[23,28,1],[23,27,1],[23,30,1],[23,31,1],[23,29,1],[24,26,1],[24,25,1],[25,26,1],[25,32,1],[26,32,1],[27,28,1],[27,30,1],[27,29,1],[28,30,1],[28,31,1],[28,29,1],[29,30,1],[29,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],"source":0,"target":25}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✗ wrong
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-22

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,17,1],[0,1,1],[0,14,1],[0,18,1],[1,17,1],[1,14,1],[1,18,1],[2,19,1],[2,7,1],[2,10,1],[2,3,1],[2,12,1],[2,16,1],[2,11,1],[2,5,1],[2,9,1],[2,15,1],[2,6,1],[2,20,1],[2,8,1],[2,4,1],[2,13,1],[3,19,1],[3,7,1],[3,10,1],[3,12,1],[3,16,1],[3,11,1],[3,5,1],[3,9,1],[3,15,1],[3,6,1],[3,20,1],[3,8,1],[3,4,1],[3,13,1],[4,19,1],[4,7,1],[4,10,1],[4,12,1],[4,16,1],[4,11,1],[4,5,1],[4,9,1],[4,15,1],[4,6,1],[4,20,1],[4,8,1],[4,13,1],[5,19,1],[5,7,1],[5,10,1],[5,12,1],[5,16,1],[5,11,1],[5,9,1],[5,15,1],[5,6,1],[5,20,1],[5,8,1],[5,13,1],[6,19,1],[6,7,1],[6,10,1],[6,12,1],[6,16,1],[6,11,1],[6,9,1],[6,15,1],[6,20,1],[6,8,1],[6,13,1],[7,19,1],[7,10,1],[7,12,1],[7,16,1],[7,11,1],[7,9,1],[7,15,1],[7,20,1],[7,8,1],[7,13,1],[8,19,1],[8,10,1],[8,12,1],[8,16,1],[8,11,1],[8,9,1],[8,15,1],[8,20,1],[8,13,1],[9,19,1],[9,10,1],[9,12,1],[9,16,1],[9,11,1],[9,15,1],[9,20,1],[9,13,1],[10,19,1],[10,12,1],[10,16,1],[10,11,1],[10,15,1],[10,20,1],[10,13,1],[11,19,1],[11,12,1],[11,16,1],[11,15,1],[11,20,1],[11,13,1],[12,19,1],[12,16,1],[12,15,1],[12,20,1],[12,13,1],[13,19,1],[13,16,1],[13,15,1],[13,20,1],[14,17,1],[14,18,1],[15,19,1],[15,16,1],[15,20,1],[16,19,1],[16,20,1],[17,18,1],[19,20,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"source":9,"target":18}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	{"result": true}	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-353

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,22,1],[0,15,1],[0,8,1],[0,12,1],[0,14,1],[0,2,1],[0,9,1],[0,1,1],[1,15,1],[1,20,1],[1,12,1],[2,20,1],[2,12,1],[2,7,1],[2,16,1],[3,15,1],[3,7,1],[3,16,1],[3,13,1],[3,14,1],[3,17,1],[3,21,1],[4,22,1],[4,8,1],[4,12,1],[4,17,1],[4,11,1],[6,23,1],[7,15,1],[7,17,1],[7,11,1],[7,21,1],[7,18,1],[8,22,1],[8,15,1],[8,20,1],[8,16,1],[8,9,1],[9,22,1],[9,13,1],[9,11,1],[9,21,1],[9,18,1],[10,22,1],[10,13,1],[10,21,1],[11,22,1],[11,15,1],[11,20,1],[11,12,1],[11,21,1],[11,18,1],[12,15,1],[12,13,1],[13,20,1],[13,18,1],[14,20,1],[17,22,1],[17,18,1],[18,20,1],[19,23,1],[20,22,1],[21,22,1]],"nodes":[0,1,2,3,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"source":8,"target":10}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-327

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,7,1],[0,8,1],[0,10,1],[0,3,1],[1,4,1],[1,11,1],[1,9,1],[1,6,1],[1,12,1],[1,2,1],[2,4,1],[2,11,1],[2,9,1],[2,6,1],[2,12,1],[3,5,1],[3,7,1],[3,8,1],[3,10,1],[4,11,1],[4,9,1],[4,6,1],[4,12,1],[5,7,1],[5,8,1],[5,10,1],[6,11,1],[6,9,1],[6,12,1],[7,8,1],[7,10,1],[8,10,1],[9,11,1],[9,12,1],[11,12,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12],"source":3,"target":11}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-175

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,21,1],[0,14,1],[0,1,1],[0,22,1],[0,16,1],[0,19,1],[0,5,1],[0,10,1],[0,20,1],[0,11,1],[0,24,1],[0,13,1],[1,21,1],[1,9,1],[1,3,1],[1,14,1],[1,22,1],[1,10,1],[1,20,1],[1,12,1],[1,11,1],[1,24,1],[1,13,1],[1,23,1],[2,8,1],[2,4,1],[2,18,1],[2,15,1],[3,9,1],[3,14,1],[3,16,1],[3,19,1],[3,7,1],[3,6,1],[3,5,1],[3,10,1],[3,11,1],[4,8,1],[4,17,1],[4,18,1],[4,15,1],[5,9,1],[5,14,1],[5,22,1],[5,7,1],[5,6,1],[5,10,1],[5,20,1],[5,12,1],[5,11,1],[5,13,1],[5,23,1],[6,21,1],[6,9,1],[6,22,1],[6,19,1],[6,7,1],[6,20,1],[6,12,1],[6,11,1],[6,13,1],[6,23,1],[7,21,1],[7,9,1],[7,14,1],[7,16,1],[7,19,1],[7,10,1],[7,20,1],[7,12,1],[7,11,1],[7,24,1],[7,13,1],[7,23,1],[8,17,1],[8,18,1],[8,15,1],[9,21,1],[9,16,1],[9,10,1],[9,20,1],[9,12,1],[9,11,1],[9,24,1],[9,13,1],[9,23,1],[10,22,1],[10,19,1],[10,12,1],[10,11,1],[10,13,1],[10,23,1],[11,21,1],[11,22,1],[11,19,1],[11,20,1],[11,12,1],[11,24,1],[11,13,1],[11,23,1],[12,21,1],[12,14,1],[12,22,1],[12,20,1],[12,24,1],[12,13,1],[12,23,1],[13,21,1],[13,14,1],[13,22,1],[13,16,1],[13,20,1],[13,23,1],[14,21,1],[14,16,1],[14,20,1],[14,24,1],[14,23,1],[15,18,1],[16,21,1],[16,22,1],[16,19,1],[16,20,1],[16,24,1],[16,23,1],[17,18,1],[19,21,1],[19,20,1],[19,24,1],[19,23,1],[20,21,1],[20,24,1],[20,23,1],[21,24,1],[21,23,1],[22,23,1],[23,24,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"source":23,"target":3}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-20

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,19,1],[0,18,1],[0,1,1],[0,8,1],[0,10,1],[0,11,1],[0,7,1],[0,4,1],[0,2,1],[0,6,1],[0,17,1],[0,14,1],[1,19,1],[1,18,1],[1,8,1],[1,10,1],[1,11,1],[1,7,1],[1,4,1],[1,2,1],[1,6,1],[1,17,1],[1,14,1],[2,19,1],[2,18,1],[2,8,1],[2,10,1],[2,11,1],[2,7,1],[2,4,1],[2,6,1],[2,17,1],[2,14,1],[3,13,1],[3,9,1],[3,15,1],[4,19,1],[4,18,1],[4,8,1],[4,10,1],[4,11,1],[4,7,1],[4,6,1],[4,17,1],[4,14,1],[5,12,1],[5,16,1],[6,19,1],[6,18,1],[6,8,1],[6,10,1],[6,11,1],[6,7,1],[6,17,1],[6,14,1],[7,19,1],[7,18,1],[7,8,1],[7,10,1],[7,11,1],[7,17,1],[7,14,1],[8,19,1],[8,18,1],[8,10,1],[8,11,1],[8,17,1],[8,14,1],[9,13,1],[9,15,1],[10,19,1],[10,18,1],[10,11,1],[10,17,1],[10,14,1],[11,19,1],[11,18,1],[11,17,1],[11,14,1],[12,16,1],[13,15,1],[14,19,1],[14,18,1],[14,17,1],[17,19,1],[17,18,1],[18,19,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"source":7,"target":12}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-71

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,1,1],[0,20,1],[0,8,1],[0,31,1],[0,22,1],[1,4,1],[1,24,1],[1,19,1],[1,16,1],[1,5,1],[1,2,1],[1,8,1],[1,18,1],[1,27,1],[2,4,1],[2,19,1],[2,12,1],[2,17,1],[2,21,1],[2,31,1],[2,22,1],[3,25,1],[3,20,1],[3,14,1],[3,31,1],[3,22,1],[3,27,1],[4,7,1],[4,21,1],[4,26,1],[4,27,1],[5,11,1],[5,24,1],[5,20,1],[5,19,1],[5,12,1],[5,16,1],[5,17,1],[5,21,1],[5,9,1],[5,22,1],[6,15,1],[7,24,1],[7,20,1],[7,19,1],[7,16,1],[7,29,1],[7,17,1],[7,21,1],[7,14,1],[7,9,1],[7,8,1],[7,18,1],[7,22,1],[7,30,1],[8,20,1],[8,12,1],[8,14,1],[9,20,1],[9,16,1],[9,14,1],[9,18,1],[9,26,1],[9,23,1],[10,15,1],[11,25,1],[11,28,1],[11,20,1],[11,21,1],[11,26,1],[12,28,1],[12,24,1],[12,20,1],[12,29,1],[12,14,1],[12,18,1],[12,26,1],[12,22,1],[12,27,1],[12,23,1],[14,24,1],[14,16,1],[14,18,1],[14,31,1],[16,25,1],[16,26,1],[16,31,1],[16,23,1],[17,31,1],[17,27,1],[18,25,1],[18,28,1],[18,24,1],[18,21,1],[18,26,1],[18,27,1],[19,29,1],[19,21,1],[19,22,1],[20,25,1],[20,21,1],[20,26,1],[21,24,1],[21,29,1],[21,31,1],[21,23,1],[22,29,1],[22,26,1],[22,23,1],[23,25,1],[23,26,1],[24,25,1],[24,26,1],[24,30,1],[25,29,1],[25,31,1],[26,29,1],[26,31,1],[27,28,1],[27,31,1],[28,29,1],[29,31,1],[29,30,1],[30,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],"source":14,"target":21}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-189

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,20,1],[0,14,1],[0,5,1],[0,9,1],[0,8,1],[0,6,1],[0,21,1],[1,4,1],[1,15,1],[1,18,1],[1,11,1],[1,10,1],[1,12,1],[2,20,1],[2,14,1],[2,5,1],[2,9,1],[2,22,1],[2,6,1],[2,16,1],[3,9,1],[3,23,1],[3,22,1],[3,6,1],[3,21,1],[4,15,1],[4,11,1],[4,19,1],[4,13,1],[5,20,1],[5,14,1],[5,9,1],[5,8,1],[5,6,1],[5,21,1],[6,20,1],[6,14,1],[6,9,1],[6,23,1],[6,8,1],[6,16,1],[7,18,1],[7,11,1],[7,10,1],[7,12,1],[7,19,1],[7,13,1],[8,20,1],[8,14,1],[8,23,1],[8,21,1],[9,20,1],[9,23,1],[9,22,1],[9,21,1],[10,15,1],[10,18,1],[10,11,1],[10,12,1],[10,19,1],[10,13,1],[11,15,1],[11,13,1],[12,18,1],[12,19,1],[13,18,1],[13,19,1],[14,23,1],[14,22,1],[14,21,1],[15,19,1],[16,23,1],[16,22,1],[20,21,1],[22,23,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23],"source":21,"target":11}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-109

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,6,1],[0,3,1],[0,14,1],[1,8,1],[1,6,1],[1,14,1],[2,6,1],[2,12,1],[2,18,1],[3,8,1],[3,6,1],[3,12,1],[3,18,1],[4,12,1],[4,9,1],[4,14,1],[5,15,1],[5,16,1],[5,7,1],[6,8,1],[6,12,1],[6,14,1],[7,10,1],[9,11,1],[9,18,1],[15,17,1],[15,16,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18],"source":10,"target":5}

Model	Answer given
Gemma 4	false	✗ wrong
Llama 3.3	true	✓ correct
Qwen · off	false	✗ wrong
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-150

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[0,1,1],[3,4,1]],"nodes":[0,1,2,3,4],"source":1,"target":4}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	false	✓ correct
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-302

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,24,1],[0,2,1],[0,7,1],[0,15,1],[0,14,1],[0,22,1],[0,10,1],[0,18,1],[0,5,1],[0,9,1],[0,4,1],[0,11,1],[0,8,1],[0,20,1],[0,13,1],[1,2,1],[1,7,1],[1,15,1],[1,14,1],[1,18,1],[1,5,1],[1,16,1],[1,9,1],[1,4,1],[1,11,1],[1,8,1],[1,13,1],[2,24,1],[2,7,1],[2,15,1],[2,14,1],[2,22,1],[2,18,1],[2,16,1],[2,9,1],[2,4,1],[2,11,1],[2,8,1],[2,20,1],[2,23,1],[3,21,1],[4,7,1],[4,14,1],[4,22,1],[4,18,1],[4,16,1],[4,13,1],[4,23,1],[5,24,1],[5,7,1],[5,15,1],[5,14,1],[5,22,1],[5,10,1],[5,18,1],[5,20,1],[5,23,1],[6,12,1],[7,24,1],[7,15,1],[7,14,1],[7,10,1],[7,18,1],[7,16,1],[7,9,1],[7,11,1],[7,8,1],[7,20,1],[7,13,1],[7,23,1],[8,24,1],[8,14,1],[8,10,1],[8,18,1],[8,9,1],[8,13,1],[8,23,1],[9,24,1],[9,15,1],[9,14,1],[9,22,1],[9,10,1],[9,16,1],[9,20,1],[9,23,1],[10,24,1],[10,15,1],[10,14,1],[10,22,1],[10,18,1],[10,16,1],[10,20,1],[11,15,1],[11,14,1],[11,18,1],[11,16,1],[11,20,1],[11,13,1],[11,23,1],[13,24,1],[13,15,1],[13,18,1],[13,16,1],[13,23,1],[14,24,1],[14,15,1],[14,22,1],[14,18,1],[14,16,1],[14,23,1],[15,24,1],[15,22,1],[15,18,1],[15,16,1],[15,20,1],[15,23,1],[16,24,1],[16,20,1],[16,23,1],[18,22,1],[18,20,1],[18,23,1],[19,21,1],[20,22,1],[22,24,1],[22,23,1],[23,24,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24],"source":0,"target":20}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-248

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,9,1],[0,2,1],[0,5,1],[0,10,1],[0,1,1],[1,4,1],[1,9,1],[1,2,1],[1,5,1],[1,10,1],[2,4,1],[2,9,1],[2,5,1],[2,10,1],[3,11,1],[3,8,1],[3,12,1],[3,7,1],[3,6,1],[4,9,1],[4,5,1],[4,10,1],[5,9,1],[5,10,1],[6,11,1],[6,8,1],[6,12,1],[6,7,1],[7,11,1],[7,8,1],[7,12,1],[8,11,1],[8,12,1],[9,10,1],[11,12,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12],"source":7,"target":12}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-164

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,2,1],[0,5,1],[0,12,1],[0,11,1],[0,8,1],[0,1,1],[0,13,1],[0,10,1],[0,3,1],[1,2,1],[1,5,1],[1,12,1],[1,11,1],[1,8,1],[1,13,1],[1,10,1],[1,3,1],[2,5,1],[2,12,1],[2,11,1],[2,8,1],[2,13,1],[2,10,1],[2,3,1],[3,5,1],[3,12,1],[3,11,1],[3,8,1],[3,13,1],[3,10,1],[4,9,1],[4,6,1],[4,7,1],[4,14,1],[5,12,1],[5,11,1],[5,8,1],[5,13,1],[5,10,1],[6,9,1],[6,7,1],[6,14,1],[7,9,1],[7,14,1],[8,12,1],[8,11,1],[8,13,1],[8,10,1],[9,14,1],[10,12,1],[10,11,1],[10,13,1],[11,12,1],[11,13,1],[12,13,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"source":14,"target":13}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-214

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,11,1],[0,6,1],[0,2,1],[0,5,1],[1,7,1],[1,16,1],[1,14,1],[1,17,1],[1,3,1],[1,9,1],[1,13,1],[1,10,1],[2,11,1],[2,6,1],[2,5,1],[3,7,1],[3,16,1],[3,14,1],[3,17,1],[3,9,1],[3,13,1],[3,10,1],[4,8,1],[4,15,1],[4,12,1],[5,11,1],[5,6,1],[6,11,1],[7,16,1],[7,14,1],[7,17,1],[7,9,1],[7,13,1],[7,10,1],[8,15,1],[8,12,1],[9,16,1],[9,14,1],[9,17,1],[9,13,1],[9,10,1],[10,16,1],[10,14,1],[10,17,1],[10,13,1],[12,15,1],[13,16,1],[13,14,1],[13,17,1],[14,16,1],[14,17,1],[16,17,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"source":2,"target":7}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	true	✗ wrong
Qwen · off	true	✗ wrong
Qwen · on	{"result": false}	✓ correct

test nlgraph-connectivity-test-166

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[1,3,1],[1,2,1],[1,6,1],[2,5,1],[2,6,1],[3,5,1],[5,6,1]],"nodes":[0,1,2,3,4,5,6],"source":2,"target":5}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-206

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,3,1],[0,10,1],[0,26,1],[0,13,1],[0,23,1],[0,14,1],[0,27,1],[0,30,1],[0,31,1],[0,28,1],[0,2,1],[0,8,1],[0,12,1],[0,9,1],[0,24,1],[0,5,1],[1,19,1],[1,15,1],[1,6,1],[1,11,1],[1,29,1],[1,17,1],[1,21,1],[1,4,1],[1,25,1],[1,7,1],[2,3,1],[2,14,1],[2,31,1],[2,28,1],[2,18,1],[2,8,1],[2,12,1],[2,9,1],[2,24,1],[2,5,1],[3,10,1],[3,13,1],[3,23,1],[3,27,1],[3,30,1],[3,31,1],[3,28,1],[3,18,1],[3,8,1],[3,12,1],[3,9,1],[3,24,1],[3,5,1],[4,20,1],[4,19,1],[4,15,1],[4,11,1],[4,29,1],[4,16,1],[4,22,1],[4,7,1],[5,10,1],[5,13,1],[5,23,1],[5,14,1],[5,27,1],[5,31,1],[5,18,1],[5,8,1],[5,12,1],[5,9,1],[6,20,1],[6,15,1],[6,11,1],[6,29,1],[6,17,1],[6,21,1],[6,16,1],[6,25,1],[6,7,1],[7,20,1],[7,15,1],[7,11,1],[7,29,1],[7,17,1],[7,21,1],[7,25,1],[8,10,1],[8,26,1],[8,13,1],[8,23,1],[8,14,1],[8,27,1],[8,30,1],[8,12,1],[8,24,1],[9,10,1],[9,26,1],[9,13,1],[9,14,1],[9,27,1],[9,30,1],[9,31,1],[9,18,1],[9,24,1],[10,26,1],[10,13,1],[10,23,1],[10,14,1],[10,27,1],[10,30,1],[10,31,1],[10,18,1],[11,20,1],[11,19,1],[11,15,1],[11,29,1],[11,17,1],[11,21,1],[11,16,1],[11,25,1],[11,22,1],[12,13,1],[12,23,1],[12,14,1],[12,27,1],[12,28,1],[13,26,1],[13,23,1],[13,14,1],[13,27,1],[13,31,1],[13,28,1],[14,23,1],[14,30,1],[14,28,1],[14,18,1],[14,24,1],[15,19,1],[15,29,1],[15,21,1],[15,16,1],[15,22,1],[16,20,1],[16,19,1],[16,29,1],[16,17,1],[16,21,1],[16,25,1],[17,20,1],[17,19,1],[17,29,1],[17,21,1],[17,25,1],[17,22,1],[18,26,1],[18,27,1],[18,30,1],[18,31,1],[18,28,1],[19,29,1],[19,21,1],[19,25,1],[19,22,1],[20,29,1],[20,22,1],[21,29,1],[21,25,1],[21,22,1],[22,25,1],[23,26,1],[23,27,1],[23,30,1],[23,31,1],[23,24,1],[24,27,1],[24,30,1],[24,31,1],[25,29,1],[26,27,1],[26,30,1],[26,28,1],[27,30,1],[27,31,1],[28,30,1],[28,31,1],[30,31,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31],"source":6,"target":28}

Model	Answer given
Gemma 4	true	✗ wrong
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	true	✗ wrong
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-210

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,12,1],[0,13,1],[0,6,1],[0,5,1],[0,15,1],[0,14,1],[0,1,1],[0,10,1],[0,8,1],[0,7,1],[0,2,1],[0,11,1],[0,3,1],[1,12,1],[1,13,1],[1,6,1],[1,5,1],[1,15,1],[1,14,1],[1,10,1],[1,8,1],[1,7,1],[1,2,1],[1,11,1],[1,3,1],[2,12,1],[2,13,1],[2,6,1],[2,5,1],[2,15,1],[2,14,1],[2,10,1],[2,8,1],[2,7,1],[2,11,1],[2,3,1],[3,12,1],[3,13,1],[3,6,1],[3,5,1],[3,15,1],[3,14,1],[3,10,1],[3,8,1],[3,7,1],[3,11,1],[4,9,1],[5,12,1],[5,13,1],[5,6,1],[5,15,1],[5,14,1],[5,10,1],[5,8,1],[5,7,1],[5,11,1],[6,12,1],[6,13,1],[6,15,1],[6,14,1],[6,10,1],[6,8,1],[6,7,1],[6,11,1],[7,12,1],[7,13,1],[7,15,1],[7,14,1],[7,10,1],[7,8,1],[7,11,1],[8,12,1],[8,13,1],[8,15,1],[8,14,1],[8,10,1],[8,11,1],[10,12,1],[10,13,1],[10,15,1],[10,14,1],[10,11,1],[11,12,1],[11,13,1],[11,15,1],[11,14,1],[12,13,1],[12,15,1],[12,14,1],[13,15,1],[13,14,1],[14,15,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"source":4,"target":11}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	{"reachable": false}	✓ correct

test nlgraph-connectivity-test-113

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,4,1],[0,13,1],[0,12,1],[0,14,1],[0,8,1],[0,3,1],[0,6,1],[0,2,1],[0,9,1],[0,5,1],[1,10,1],[1,7,1],[1,11,1],[2,4,1],[2,13,1],[2,12,1],[2,14,1],[2,8,1],[2,3,1],[2,6,1],[2,9,1],[2,5,1],[3,4,1],[3,13,1],[3,12,1],[3,14,1],[3,8,1],[3,6,1],[3,9,1],[3,5,1],[4,13,1],[4,12,1],[4,14,1],[4,8,1],[4,6,1],[4,9,1],[4,5,1],[5,13,1],[5,12,1],[5,14,1],[5,8,1],[5,6,1],[5,9,1],[6,13,1],[6,12,1],[6,14,1],[6,8,1],[6,9,1],[7,10,1],[7,11,1],[8,13,1],[8,12,1],[8,14,1],[8,9,1],[9,13,1],[9,12,1],[9,14,1],[10,11,1],[12,13,1],[12,14,1],[13,14,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"source":14,"target":12}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-241

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,5,1],[0,1,1],[0,3,1],[1,5,1],[1,3,1],[2,4,1],[3,5,1]],"nodes":[0,1,2,3,4,5],"source":3,"target":0}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-90

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[2,3,1]],"nodes":[1,2,3,4],"source":4,"target":1}

Model	Answer given
Gemma 4	false	✓ correct
Llama 3.3	false	✓ correct
Qwen · off	false	✓ correct
Qwen · on	false	✓ correct

test nlgraph-connectivity-test-205

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,6,1],[0,13,1],[1,6,1],[1,8,1],[1,3,1],[1,4,1],[2,5,1],[2,9,1],[3,12,1],[3,9,1],[3,13,1],[4,6,1],[4,10,1],[5,6,1],[5,9,1],[6,12,1],[6,8,1],[8,9,1],[9,10,1],[12,13,1]],"nodes":[0,1,2,3,4,5,6,8,9,10,12,13],"source":10,"target":8}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-67

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,16,1],[0,3,1],[0,12,1],[0,6,1],[0,11,1],[1,16,1],[1,3,1],[1,12,1],[1,6,1],[1,11,1],[1,14,1],[1,10,1],[2,15,1],[2,7,1],[2,13,1],[2,5,1],[2,9,1],[2,4,1],[2,18,1],[3,17,1],[3,12,1],[3,11,1],[3,14,1],[4,15,1],[4,7,1],[4,5,1],[4,9,1],[4,8,1],[5,15,1],[5,13,1],[5,9,1],[5,8,1],[5,18,1],[6,16,1],[6,17,1],[6,12,1],[6,14,1],[6,10,1],[7,15,1],[7,13,1],[7,9,1],[7,18,1],[8,15,1],[8,9,1],[8,18,1],[9,13,1],[9,18,1],[10,16,1],[10,17,1],[10,12,1],[10,11,1],[11,16,1],[11,17,1],[11,12,1],[12,16,1],[12,17,1],[12,14,1],[13,15,1],[13,18,1],[14,16,1],[14,17,1],[15,18,1],[16,17,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"source":13,"target":7}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer

test nlgraph-connectivity-test-15

This is a synthetic transport-network capability problem, not an observed city. Use only the complete network below. Node IDs are locations. Edges are bidirectional usable links. Is the target reachable from the source? Return only the JSON boolean true or false.
Network: {"directed":false,"edges":[[0,12,1],[0,10,1],[0,17,1],[0,5,1],[0,13,1],[0,15,1],[0,16,1],[0,3,1],[0,7,1],[0,11,1],[0,1,1],[0,4,1],[0,14,1],[1,12,1],[1,10,1],[1,17,1],[1,5,1],[1,13,1],[1,15,1],[1,16,1],[1,3,1],[1,7,1],[1,11,1],[1,4,1],[1,14,1],[2,8,1],[2,6,1],[3,12,1],[3,10,1],[3,17,1],[3,5,1],[3,13,1],[3,15,1],[3,16,1],[3,7,1],[3,11,1],[3,4,1],[3,14,1],[4,12,1],[4,10,1],[4,17,1],[4,5,1],[4,13,1],[4,15,1],[4,16,1],[4,7,1],[4,11,1],[4,14,1],[5,12,1],[5,10,1],[5,17,1],[5,13,1],[5,15,1],[5,16,1],[5,7,1],[5,11,1],[5,14,1],[6,8,1],[7,12,1],[7,10,1],[7,17,1],[7,13,1],[7,15,1],[7,16,1],[7,11,1],[7,14,1],[10,12,1],[10,17,1],[10,13,1],[10,15,1],[10,16,1],[10,11,1],[10,14,1],[11,12,1],[11,17,1],[11,13,1],[11,15,1],[11,16,1],[11,14,1],[12,17,1],[12,13,1],[12,15,1],[12,16,1],[12,14,1],[13,17,1],[13,15,1],[13,16,1],[13,14,1],[14,17,1],[14,15,1],[14,16,1],[15,17,1],[15,16,1],[16,17,1]],"nodes":[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17],"source":4,"target":17}

Model	Answer given
Gemma 4	true	✓ correct
Llama 3.3	true	✓ correct
Qwen · off	true	✓ correct
Qwen · on	InvalidJSON	✗ no usable answer