Question bank

test nlgraph-shortest_path-test-41

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,6,6],[0,12,10],[0,11,5],[0,2,2],[0,10,2],[1,6,9],[1,11,3],[1,9,9],[1,10,5],[2,11,8],[2,17,8],[3,6,2],[3,5,8],[4,16,4],[4,10,7],[5,11,4],[5,9,6],[5,17,5],[6,16,3],[7,15,6],[7,9,4],[8,9,7],[9,16,1],[9,10,1],[10,13,5],[11,13,6],[11,16,5],[11,17,10],[12,13,1],[12,16,10],[12,17,4],[14,16,4]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"source":1,"target":12}

Model	Answer given
Gemma 4	{"path": [1, 11, 13, 12], "cost": 10}	✓ correct
Llama 3.3	{"path": [1, 11, 13, 12], "cost": 10}	✓ correct
Qwen · off	{"path": [1, 11, 13, 12], "cost": 10}	✓ correct
Qwen · on	{"path": [1, 11, 13, 12], "cost": 10}	✓ correct

test nlgraph-shortest_path-test-2

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,6,3],[0,5,8],[1,7,7],[1,11,2],[1,9,1],[2,3,2],[2,9,8],[2,5,6],[2,4,9],[3,8,3],[3,9,2],[4,11,3],[5,8,4],[5,10,2],[5,9,7],[6,8,2],[6,10,10],[6,11,6],[8,11,6],[8,9,2]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11],"source":7,"target":2}

Model	Answer given
Gemma 4	{"path": [7, 1, 9, 3, 2], "cost": 12}	✓ correct
Llama 3.3	{"path": [7, 1, 9, 3, 2], "cost": 12}	✓ correct
Qwen · off	{"path": [7, 1, 9, 3, 2], "cost": 12}	✓ correct
Qwen · on	{"path": [7, 1, 9, 3, 2], "cost": 12}	✓ correct

test nlgraph-shortest_path-test-5

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,2,1],[0,4,4],[0,1,4],[1,2,3],[1,3,4],[1,4,2],[2,3,4],[3,4,3]],"nodes":[0,1,2,3,4],"source":2,"target":4}

Model	Answer given
Gemma 4	{"path": [2, 1, 4], "cost": 5}	✓ correct
Llama 3.3	{"path": [2, 0, 4], "cost": 5}	✓ correct
Qwen · off	{"path": [2, 0, 4], "cost": 5}	✓ correct
Qwen · on	{"path": [2, 0, 4], "cost": 5}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,5,4],[0,3,2],[0,8,2],[0,7,4],[0,2,2],[0,1,1],[1,4,2],[1,5,1],[1,3,2],[1,8,4],[1,9,4],[1,2,4],[2,4,1],[2,8,4],[2,7,2],[3,4,4],[3,6,2],[4,5,1],[4,8,3],[4,9,4],[5,8,2],[5,7,1],[5,9,1],[5,6,2],[6,8,3],[6,7,3],[7,9,2]],"nodes":[0,1,2,3,4,5,6,7,8,9],"source":4,"target":7}

Model	Answer given
Gemma 4	{"path": [4, 5, 7], "cost": 2}	✓ correct
Llama 3.3	{"path": [4, 5, 7], "cost": 2}	✓ correct
Qwen · off	{"path": [4, 5, 7], "cost": 2}	✓ correct
Qwen · on	{"path": [4, 5, 7], "cost": 2}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,16,2],[0,10,7],[0,3,4],[0,18,3],[0,14,9],[1,3,1],[2,5,3],[2,7,10],[2,14,9],[2,15,1],[2,12,4],[3,9,1],[4,13,3],[4,8,8],[4,18,9],[4,14,3],[4,15,5],[4,12,2],[5,16,4],[5,9,7],[5,6,10],[5,11,1],[6,10,8],[7,13,8],[7,10,2],[7,9,4],[8,9,9],[8,14,8],[9,10,3],[10,13,2],[10,14,7],[10,12,2],[11,13,1],[11,16,2],[11,18,3],[11,17,8],[12,13,1],[12,16,10],[12,14,9],[12,15,4],[13,15,1],[14,17,5],[16,17,10]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"source":15,"target":1}

Model	Answer given
Gemma 4	{"path": [15, 13, 10, 9, 3, 1], "cost": 8}	✓ correct
Llama 3.3	{"path": [15, 13, 12, 3, 1], "cost": 5}	✗ wrong
Qwen · off	{"path": [15, 2, 12, 4, 14, 0, 16], "cost": 20}	✗ wrong
Qwen · on	{"path": [15, 13, 10, 9, 3, 1], "cost": 8}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,5,10],[1,13,6],[1,3,7],[1,2,4],[1,9,10],[1,14,1],[1,6,4],[2,12,10],[2,8,7],[2,14,4],[3,13,3],[3,8,3],[3,9,3],[4,10,3],[4,8,3],[4,7,2],[4,11,1],[5,10,8],[5,15,4],[5,7,2],[6,13,10],[6,12,4],[6,10,5],[6,11,4],[8,13,8],[8,14,1],[11,13,1],[11,15,9],[11,14,9],[13,15,6],[13,14,6]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"source":2,"target":0}

Model	Answer given
Gemma 4	{"path": [2, 14, 8, 4, 7, 5, 0], "cost": 22}	✓ correct
Llama 3.3	{"path": [2, 1, 14, 8, 13, 5, 0], "cost": 24}	✗ wrong
Qwen · off	{"path": [2, 14, 8, 4, 7, 5, 0], "cost": 22}	✓ correct
Qwen · on	{"path": [2, 14, 8, 4, 7, 5, 0], "cost": 22}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,2,3],[0,6,2],[1,2,1],[1,7,4],[1,4,1],[2,3,2],[2,6,2],[2,7,4],[2,4,4],[3,5,2],[3,6,4],[3,7,1],[4,5,4],[4,6,3],[5,8,3],[5,6,4],[5,7,3],[6,7,3]],"nodes":[0,1,2,3,4,5,6,7,8],"source":2,"target":8}

Model	Answer given
Gemma 4	{"path": [2, 3, 5, 8], "cost": 7}	✓ correct
Llama 3.3	{"path": [2, 6, 5, 8], "cost": 9}	✗ wrong
Qwen · off	{"path": [2, 3, 5, 8], "cost": 7}	✓ correct
Qwen · on	{"path": [2, 3, 5, 8], "cost": 7}	✓ correct

test nlgraph-shortest_path-test-0

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,12,5],[0,2,4],[0,3,2],[1,3,3],[2,3,4],[2,5,8],[2,10,1],[3,6,10],[3,9,3],[3,7,6],[3,8,5],[4,12,5],[5,7,7],[5,11,6],[7,11,2],[8,9,1],[9,12,9],[9,11,5],[9,10,5],[10,12,6],[10,11,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12],"source":4,"target":2}

Model	Answer given
Gemma 4	{"path": [4, 12, 10, 2], "cost": 12}	✓ correct
Llama 3.3	{"path": [4, 12, 0, 2], "cost": 14}	✗ wrong
Qwen · off	{"path": [4, 12, 10, 2], "cost": 12}	✓ correct
Qwen · on	{"path": [4, 12, 10, 2], "cost": 12}	✓ correct

test nlgraph-shortest_path-test-42

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,6,2],[0,8,1],[0,2,4],[0,1,1],[0,4,1],[1,2,3],[1,7,2],[1,4,2],[1,5,3],[1,3,4],[2,6,2],[2,8,1],[2,4,3],[2,3,3],[3,7,4],[3,5,2],[4,8,3],[4,5,3],[5,6,4],[6,8,1],[6,7,1],[7,8,4]],"nodes":[0,1,2,3,4,5,6,7,8],"source":6,"target":1}

Model	Answer given
Gemma 4	{"path": [6, 7, 1], "cost": 3}	✓ correct
Llama 3.3	{"path": [6, 0, 1], "cost": 3}	✓ correct
Qwen · off	{"path": [6, 0, 1], "cost": 3}	✓ correct
Qwen · on	{"path": [6, 7, 1], "cost": 3}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,1,9],[0,2,9],[0,7,5],[0,5,1],[0,11,5],[0,3,10],[1,17,1],[2,17,4],[2,6,2],[2,8,8],[2,9,7],[3,14,8],[3,8,7],[3,7,2],[4,18,4],[5,18,1],[5,14,5],[5,8,1],[5,7,6],[5,11,6],[6,7,10],[7,14,9],[8,13,8],[8,12,8],[9,14,4],[9,11,3],[9,12,10],[10,16,6],[10,13,10],[11,18,1],[11,17,3],[12,18,4],[12,16,6],[12,13,9],[15,16,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"source":1,"target":15}

Model	Answer given
Gemma 4	{"path": [1, 17, 11, 18, 12, 16, 15], "cost": 16}	✓ correct
Llama 3.3	{"directed": false, "edges": [[0, 1, 9], [0, 2, 9], [0, 7, 5], [0, 5, 1], [0, 11, 5], [0, 3, 10], [1, 17, 1], [2, 17, 4], [2, 6, 2], [2, 8, …	✗ wrong
Qwen · off	{"path": [1, 17, 2, 6, 7, 3, 8, 5, 18, 11, 9, 14, 9, 11, 18, 12, 16, 15], "cost": 44}	✗ wrong
Qwen · on	{"path": [1, 17, 11, 18, 12, 16, 15], "cost": 16}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,2,9],[0,7,4],[1,8,10],[1,9,4],[1,10,4],[2,4,9],[3,4,6],[3,6,3],[3,7,8],[4,7,8],[5,7,6],[6,9,1],[6,10,1],[7,9,6],[8,11,9],[8,9,3]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11],"source":11,"target":2}

Model	Answer given
Gemma 4	{"path": [11, 8, 9, 7, 0, 2], "cost": 31}	✓ correct
Llama 3.3	{"path": [11, 8, 9, 6, 3, 4, 2], "cost": 31}	✓ correct
Qwen · off	{"path": [11, 8, 9, 6, 10, 1, 0, 2], "cost": 31}	✗ wrong
Qwen · on	{"path": [11, 8, 9, 6, 3, 4, 2], "cost": 31}	✓ correct

test nlgraph-shortest_path-test-59

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,1,1],[0,6,1],[0,5,1],[1,2,3],[1,6,4],[1,5,3],[2,4,3],[2,5,2],[3,5,3],[4,5,4]],"nodes":[0,1,2,3,4,5,6],"source":4,"target":0}

Model	Answer given
Gemma 4	{"path": [4, 2, 5, 0], "cost": 6}	✗ wrong
Llama 3.3	{"path": [4, 5, 0], "cost": 5}	✓ correct
Qwen · off	{"path": [4, 2, 5, 0], "cost": 6}	✗ wrong
Qwen · on	{"path": [4, 5, 0], "cost": 5}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,6,4],[0,8,2],[0,1,2],[0,4,3],[0,5,3],[0,3,2],[0,7,2],[1,9,1],[1,8,2],[1,3,4],[1,7,4],[2,9,3],[2,6,2],[2,4,4],[2,5,1],[2,3,1],[2,7,2],[3,9,4],[3,6,4],[3,8,4],[3,4,3],[3,5,2],[4,9,3],[4,6,1],[4,8,1],[4,5,4],[4,7,2],[5,9,4],[5,8,4],[5,7,2],[6,9,2],[6,7,1],[7,8,2]],"nodes":[0,1,2,3,4,5,6,7,8,9],"source":9,"target":0}

Model	Answer given
Gemma 4	{"path": [9, 1, 0], "cost": 3}	✓ correct
Llama 3.3	{"path": [9, 1, 0], "cost": 3}	✓ correct
Qwen · off	{"path": [9, 1, 0], "cost": 3}	✓ correct
Qwen · on	{"path": [9, 1, 0], "cost": 3}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,7,4],[0,3,1],[0,2,3],[0,1,4],[0,4,4],[0,5,2],[0,6,2],[1,7,4],[1,3,3],[1,2,2],[1,4,1],[1,5,3],[1,6,3],[2,7,3],[2,3,2],[2,4,1],[2,5,1],[2,6,2],[3,7,2],[3,4,3],[3,5,3],[3,6,1],[4,7,4],[4,5,1],[4,6,3],[5,7,2],[6,7,3]],"nodes":[0,1,2,3,4,5,6,7],"source":5,"target":6}

Model	Answer given
Gemma 4	{"path": [5, 2, 6], "cost": 3}	✓ correct
Llama 3.3	{"path": [5, 2, 3, 6], "cost": 4}	✗ wrong
Qwen · off	{"path": [5, 4, 2, 6], "cost": 3}	✗ wrong
Qwen · on	{"path": [5, 2, 6], "cost": 3}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,2,2],[0,3,1],[1,4,2],[1,6,2],[1,3,3],[2,4,4],[2,5,2],[3,4,2],[3,5,3],[3,6,2],[4,5,3],[4,6,2],[5,6,4]],"nodes":[0,1,2,3,4,5,6],"source":1,"target":0}

Model	Answer given
Gemma 4	{"path": [1, 3, 0], "cost": 4}	✓ correct
Llama 3.3	{"path": [1, 3, 0], "cost": 4}	✓ correct
Qwen · off	{"path": [1, 3, 0], "cost": 4}	✓ correct
Qwen · on	{"path": [1, 3, 0], "cost": 4}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,6,1],[0,3,2],[0,7,4],[0,1,2],[0,5,1],[1,2,3],[1,6,2],[1,4,3],[1,7,3],[1,5,4],[2,6,4],[2,4,1],[3,4,2],[3,5,1],[4,6,2],[4,7,1],[5,6,1],[5,7,4],[6,7,2]],"nodes":[0,1,2,3,4,5,6,7],"source":2,"target":3}

Model	Answer given
Gemma 4	{"path": [2, 4, 3], "cost": 3}	✓ correct
Llama 3.3	{"path": [2, 4, 3], "cost": 3}	✓ correct
Qwen · off	{"path": [2, 4, 3], "cost": 3}	✓ correct
Qwen · on	{"path": [2, 4, 3], "cost": 3}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,8,3],[0,11,7],[0,4,1],[0,12,8],[0,2,5],[1,13,5],[1,4,7],[1,5,10],[1,6,3],[1,12,7],[2,11,4],[2,10,8],[2,15,8],[2,12,1],[3,10,10],[3,4,6],[3,17,6],[4,16,8],[4,10,10],[4,5,5],[4,15,8],[4,6,3],[5,17,1],[5,7,1],[5,12,1],[6,12,5],[7,13,5],[7,11,2],[7,14,3],[8,10,2],[8,9,5],[8,12,4],[9,10,5],[9,17,5],[10,13,2],[10,16,5],[10,11,3],[10,14,7],[10,15,2],[11,15,8],[12,15,5],[14,17,5],[15,16,10]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"source":8,"target":4}

Model	Answer given
Gemma 4	{"path": [8, 0, 4], "cost": 4}	✓ correct
Llama 3.3	{"path": [8, 12, 5, 4], "cost": 10}	✗ wrong
Qwen · off	{"path": [8, 10, 15, 4], "cost": 15}	✗ wrong
Qwen · on	{"path": [8, 0, 4], "cost": 4}	✓ correct

test nlgraph-shortest_path-test-26

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,17,8],[1,13,5],[1,5,6],[1,14,9],[2,5,5],[2,6,9],[3,13,2],[3,5,2],[4,9,7],[4,12,9],[5,10,8],[5,15,10],[6,10,4],[6,7,10],[7,11,9],[8,18,6],[8,16,7],[9,17,7],[9,15,10],[10,11,4],[10,15,4],[11,13,2],[13,19,5],[13,17,2],[14,19,4],[14,15,9],[15,18,2],[16,19,9]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"source":2,"target":17}

Model	Answer given
Gemma 4	{"path": [2, 5, 3, 13, 17], "cost": 11}	✓ correct
Llama 3.3	{"path": [2, 5, 3, 13, 17], "cost": 11}	✓ correct
Qwen · off	{"path": [2, 5, 3, 13, 17], "cost": 11}	✓ correct
Qwen · on	{"path": [2, 5, 3, 13, 17], "cost": 11}	✓ correct

test nlgraph-shortest_path-test-1

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,6,6],[0,9,1],[0,5,8],[1,15,10],[1,4,7],[1,16,6],[2,9,2],[2,13,3],[3,14,6],[3,9,3],[3,4,2],[4,6,2],[4,13,6],[4,16,10],[4,12,7],[5,6,9],[5,9,4],[6,14,4],[6,8,1],[6,10,3],[7,17,2],[8,10,2],[8,15,1],[8,12,6],[9,17,9],[9,10,7],[11,12,10],[13,15,9],[14,15,10]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"source":11,"target":7}

Model	Answer given
Gemma 4	{"path": [11, 12, 8, 6, 0, 9, 17, 7], "cost": 35}	✗ wrong
Llama 3.3	{"path": [11, 12, 4, 3, 9, 17, 7], "cost": 37}	✗ wrong
Qwen · off	{"path": [11, 12, 4, 3, 9, 17, 7], "cost": 33}	✓ correct
Qwen · on	{"path": [11, 12, 4, 3, 9, 17, 7], "cost": 33}	✓ correct

test nlgraph-shortest_path-test-23

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,1,1],[0,3,4],[0,4,1],[0,5,4],[0,7,3],[1,6,2],[1,5,4],[1,7,4],[2,6,3],[2,5,3],[2,7,2],[3,6,1],[3,4,4],[3,7,4],[4,6,3],[4,8,3],[4,5,3],[4,7,4],[5,6,2],[5,8,3],[6,7,4],[7,8,2]],"nodes":[0,1,2,3,4,5,6,7,8],"source":1,"target":3}

Model	Answer given
Gemma 4	{"path": [1, 6, 3], "cost": 3}	✓ correct
Llama 3.3	{"path": [1, 6, 3], "cost": 3}	✓ correct
Qwen · off	{"path": [1, 0, 3], "cost": 5}	✗ wrong
Qwen · on	{"path": [1, 6, 3], "cost": 3}	✓ correct

test nlgraph-shortest_path-test-37

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,7,2],[0,8,2],[0,4,3],[0,2,3],[0,1,4],[0,3,3],[1,5,1],[1,8,4],[1,4,4],[1,6,4],[1,3,2],[2,5,2],[2,4,3],[2,6,2],[2,3,3],[3,5,1],[3,7,2],[3,8,1],[3,4,1],[5,8,3],[5,6,4],[6,7,4],[6,8,2]],"nodes":[0,1,2,3,4,5,6,7,8],"source":5,"target":7}

Model	Answer given
Gemma 4	{"path": [5, 3, 7], "cost": 3}	✓ correct
Llama 3.3	{"path": [5, 3, 7], "cost": 3}	✓ correct
Qwen · off	{"path": [5, 3, 7], "cost": 3}	✓ correct
Qwen · on	{"path": [5, 3, 7], "cost": 3}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,13,6],[1,17,2],[1,11,5],[1,9,4],[2,5,10],[3,11,2],[3,12,2],[3,6,1],[4,16,1],[4,14,8],[4,17,9],[4,7,9],[5,12,1],[5,10,2],[5,8,1],[5,7,10],[6,15,8],[6,19,6],[7,16,2],[8,13,9],[9,15,9],[9,18,6],[10,19,5],[10,11,1],[10,12,10],[11,16,1],[12,15,3],[14,15,2],[15,16,5]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"source":9,"target":19}

Model	Answer given
Gemma 4	{"path": [9, 1, 11, 10, 19], "cost": 15}	✓ correct
Llama 3.3	{"path": [9, 10, 19], "cost": 11}	✗ wrong
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	{"path": [9, 1, 11, 10, 19], "cost": 15}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,4,4],[0,3,1],[0,1,1],[0,5,1],[0,2,2],[1,4,2],[1,3,1],[1,5,2],[1,2,4],[2,4,3],[2,3,2],[2,5,3],[3,4,3],[3,5,3]],"nodes":[0,1,2,3,4,5],"source":4,"target":5}

Model	Answer given
Gemma 4	{"path": [4, 1, 5], "cost": 4}	✓ correct
Llama 3.3	{"path": [4, 0, 5], "cost": 5}	✗ wrong
Qwen · off	{"path": [4, 0, 5], "cost": 5}	✗ wrong
Qwen · on	{"path": [4, 1, 5], "cost": 4}	✓ correct

test nlgraph-shortest_path-test-14

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,4,1],[1,5,4],[1,4,1],[2,5,1],[2,4,3],[3,5,4],[4,5,3]],"nodes":[0,1,2,3,4,5],"source":5,"target":0}

Model	Answer given
Gemma 4	{"path": [5, 4, 0], "cost": 4}	✓ correct
Llama 3.3	{"path": [5, 4, 0], "cost": 4}	✓ correct
Qwen · off	{"path": [5, 1, 4, 0], "cost": 6}	✗ wrong
Qwen · on	{"path": [5, 4, 0], "cost": 4}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,5,3],[0,3,4],[0,6,1],[0,4,1],[0,2,2],[0,1,4],[0,7,1],[0,8,1],[1,5,4],[1,3,2],[1,6,4],[1,4,4],[1,2,2],[1,7,2],[1,8,1],[2,3,2],[2,6,4],[2,4,3],[2,7,3],[2,8,2],[3,6,2],[3,8,1],[4,5,4],[4,6,1],[4,7,1],[5,8,4],[6,7,2],[6,8,1],[7,8,4]],"nodes":[0,1,2,3,4,5,6,7,8],"source":5,"target":3}

Model	Answer given
Gemma 4	{"path": [5, 8, 3], "cost": 5}	✓ correct
Llama 3.3	{"path": [5, 8, 3], "cost": 5}	✓ correct
Qwen · off	{"path": [5, 0, 3], "cost": 7}	✗ wrong
Qwen · on	{"path": [5, 0, 8, 3], "cost": 5}	✓ correct

test nlgraph-shortest_path-test-56

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,8,8],[1,11,1],[1,4,5],[1,2,1],[2,4,2],[3,6,10],[3,12,6],[4,10,4],[5,6,8],[5,14,3],[6,14,8],[6,13,9],[7,13,3],[8,11,6],[8,9,4],[9,10,7],[11,12,9]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"source":9,"target":3}

Model	Answer given
Gemma 4	{"path": [9, 8, 11, 12, 3], "cost": 25}	✓ correct
Llama 3.3	{"path": [9, 8, 11, 12, 3], "cost": 25}	✓ correct
Qwen · off	{"path": [9, 8, 11, 1, 2, 4, 10, 9, 10, 4, 2, 1, 11, 12, 3], "cost": 35}	✗ wrong
Qwen · on	{"path": [9, 8, 11, 12, 3], "cost": 25}	✓ correct

test nlgraph-shortest_path-test-13

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,10,4],[0,12,4],[0,4,6],[1,5,3],[1,6,5],[1,13,8],[2,10,10],[2,7,3],[2,6,3],[3,9,3],[3,7,2],[4,12,1],[4,9,9],[4,7,10],[5,9,10],[5,7,10],[5,8,4],[6,13,9],[7,10,8],[7,8,5],[9,10,7],[9,11,1]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"source":0,"target":9}

Model	Answer given
Gemma 4	{"path": [0, 10, 9], "cost": 11}	✓ correct
Llama 3.3	{"path": [0, 12, 4, 9], "cost": 14}	✗ wrong
Qwen · off	{"path": [0, 12, 4, 9], "cost": 16}	✗ wrong
Qwen · on	{"path": [0, 10, 9], "cost": 11}	✓ correct

test nlgraph-shortest_path-test-54

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,1,1],[0,5,4],[0,2,1],[1,4,1],[1,3,4],[1,2,3],[2,4,2],[3,4,1]],"nodes":[0,1,2,3,4,5],"source":4,"target":0}

Model	Answer given
Gemma 4	{"path": [4, 1, 0], "cost": 2}	✓ correct
Llama 3.3	{"path": [4, 1, 0], "cost": 2}	✓ correct
Qwen · off	{"path": [4, 2, 0], "cost": 3}	✗ wrong
Qwen · on	{"path": [4, 1, 0], "cost": 2}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,11,8],[0,12,6],[0,13,5],[1,9,9],[1,6,2],[1,5,4],[1,8,7],[2,9,8],[2,6,1],[2,4,9],[3,6,8],[3,12,3],[3,10,10],[5,8,9],[6,9,8],[6,7,3],[7,12,9]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"source":11,"target":9}

Model	Answer given
Gemma 4	{"path": [11, 0, 12, 3, 6, 9], "cost": 33}	✓ correct
Llama 3.3	{"path": [11, 0, 1, 6, 9], "cost": 23}	✗ wrong
Qwen · off	{"path": [11, 0, 13], "cost": 13}	✗ wrong
Qwen · on	{"path": [11, 0, 12, 3, 6, 9], "cost": 33}	✓ correct

test nlgraph-shortest_path-test-47

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,6,4],[0,5,3],[1,4,4],[1,5,8],[2,8,9],[2,11,7],[2,4,4],[2,5,2],[3,11,4],[4,11,9],[5,10,3],[6,10,7],[7,10,3],[8,9,2],[9,11,4]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11],"source":0,"target":9}

Model	Answer given
Gemma 4	{"path": [0, 5, 2, 11, 9], "cost": 16}	✓ correct
Llama 3.3	{"path": [0, 5, 2, 8, 9], "cost": 16}	✓ correct
Qwen · off	{"path": [0, 5, 2, 8, 9], "cost": 16}	✓ correct
Qwen · on	{"path": [0, 5, 2, 11, 9], "cost": 16}	✓ correct

test nlgraph-shortest_path-test-33

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,1,2],[0,4,3],[0,3,2],[0,8,2],[0,6,1],[0,2,1],[0,7,3],[1,5,4],[1,4,2],[1,3,3],[1,8,2],[1,6,3],[1,2,1],[1,7,3],[2,5,2],[2,3,3],[2,8,3],[2,6,1],[2,7,4],[3,5,1],[3,4,4],[3,8,1],[3,6,2],[3,7,2],[4,8,3],[4,6,1],[4,7,3],[5,8,4],[5,6,1],[5,7,4],[6,8,3],[6,7,1]],"nodes":[0,1,2,3,4,5,6,7,8],"source":5,"target":4}

Model	Answer given
Gemma 4	{"path": [5, 6, 4], "cost": 2}	✓ correct
Llama 3.3	{"path": [5, 6, 4], "cost": 2}	✓ correct
Qwen · off	{"path": [5, 6, 4], "cost": 2}	✓ correct
Qwen · on	{"path": [5, 6, 4], "cost": 2}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,1,2],[1,16,9],[1,11,2],[1,6,10],[1,5,9],[1,9,6],[2,6,4],[2,7,8],[2,12,5],[2,14,4],[2,15,4],[3,18,7],[3,13,3],[4,16,5],[4,10,2],[4,17,10],[5,16,10],[5,11,1],[5,9,9],[6,17,8],[6,12,8],[7,16,6],[7,12,4],[7,14,8],[7,15,4],[8,16,1],[8,11,10],[8,13,3],[10,19,1],[10,18,6],[10,15,5],[11,19,2],[11,13,8],[13,16,8],[14,15,9],[15,16,6],[16,19,7],[16,17,9],[17,19,10]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"source":9,"target":18}

Model	Answer given
Gemma 4	{"path": [9, 1, 11, 19, 10, 18], "cost": 17}	✓ correct
Llama 3.3	{"path": [9, 1, 11, 19, 18], "cost": 22}	✗ wrong
Qwen · off	TokenLimit	✗ no usable answer
Qwen · on	{"path": [9, 1, 11, 19, 10, 18], "cost": 17}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,1,1],[1,5,7],[1,4,8],[2,5,5],[3,12,5],[3,6,2],[3,4,4],[4,11,9],[4,13,10],[5,11,3],[5,8,5],[6,12,6],[7,12,10],[8,9,8],[8,12,3],[9,12,9],[9,10,10],[10,13,4],[11,12,3]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"source":7,"target":0}

Model	Answer given
Gemma 4	{"path": [7, 12, 11, 5, 1, 0], "cost": 24}	✓ correct
Llama 3.3	{"path": [7, 12, 11, 5, 1, 0], "cost": 24}	✓ correct
Qwen · off	{"path": [7, 12, 8, 5, 1, 0], "cost": 28}	✗ wrong
Qwen · on	{"path": [7, 12, 11, 5, 1, 0], "cost": 24}	✓ correct

test nlgraph-shortest_path-test-19

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,1,10],[0,11,7],[0,9,4],[0,10,1],[1,7,3],[1,18,8],[1,9,6],[1,14,3],[1,3,2],[2,13,8],[2,18,10],[2,16,1],[2,14,2],[3,15,7],[4,7,3],[4,8,6],[4,16,8],[5,13,9],[5,8,7],[6,13,9],[6,8,10],[6,14,7],[8,18,7],[8,14,8],[9,11,2],[9,10,10],[10,17,4],[11,13,7],[11,12,2],[12,16,6],[13,15,10]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"source":18,"target":15}

Model	Answer given
Gemma 4	{"path": [18, 1, 3, 15], "cost": 17}	✓ correct
Llama 3.3	{"path": [18, 8, 14, 2, 3, 15], "cost": 27}	✗ wrong
Qwen · off	{"path": [18, 1, 3, 15], "cost": 17}	✓ correct
Qwen · on	{"path": [18, 1, 3, 15], "cost": 17}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,3,9],[0,2,2],[1,8,7],[1,15,8],[1,16,2],[2,6,6],[2,10,6],[3,5,1],[3,15,9],[3,4,8],[4,13,6],[4,11,2],[4,5,10],[4,10,1],[5,15,10],[6,12,6],[6,7,3],[7,13,9],[7,16,4],[7,10,9],[7,9,6],[8,11,5],[8,9,1],[9,12,1],[9,16,6],[9,10,7],[12,16,1],[14,16,10]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"source":14,"target":0}

Model	Answer given
Gemma 4	{"path": [14, 16, 12, 6, 2, 0], "cost": 25}	✓ correct
Llama 3.3	{"path": [14, 16, 9, 10, 2, 0], "cost": 25}	✗ wrong
Qwen · off	{"path": [14, 16, 12, 9, 8, 1, 16, 7, 6, 2, 0], "cost": 33}	✗ wrong
Qwen · on	{"path": [14, 16, 12, 6, 2, 0], "cost": 25}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,7,1],[0,11,3],[1,13,8],[1,9,3],[1,8,3],[2,14,4],[3,11,8],[3,4,1],[3,9,3],[3,16,9],[4,11,6],[4,13,9],[4,5,1],[4,16,8],[5,12,3],[5,10,1],[6,13,9],[6,10,3],[6,16,1],[7,16,9],[9,13,1],[10,14,1],[12,13,1],[13,15,4],[13,16,10]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"source":2,"target":0}

Model	Answer given
Gemma 4	APITimeoutError	✗ no usable answer
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	{"path": [2, 14, 10, 5, 4, 3, 11, 0], "cost": 18}	✗ wrong
Qwen · on	{"path": [2, 14, 10, 5, 4, 11, 0], "cost": 16}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,6,4],[0,1,4],[1,5,3],[1,4,4],[1,3,4],[1,6,1],[2,5,2],[2,4,4],[2,3,1],[2,6,2],[3,5,2],[3,4,3],[3,6,2],[4,6,4],[5,6,4]],"nodes":[0,1,2,3,4,5,6],"source":5,"target":4}

Model	Answer given
Gemma 4	{"path": [5, 3, 4], "cost": 5}	✓ correct
Llama 3.3	{"path": [5, 3, 4], "cost": 5}	✓ correct
Qwen · off	{"path": [5, 3, 4], "cost": 5}	✓ correct
Qwen · on	{"path": [5, 3, 4], "cost": 5}	✓ correct

test nlgraph-shortest_path-test-12

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,8,3],[0,5,6],[0,10,8],[1,8,5],[2,3,4],[2,10,1],[3,6,6],[3,10,8],[4,9,10],[4,6,2],[6,9,6],[6,8,10],[6,10,5],[7,10,9]],"nodes":[0,1,2,3,4,5,6,7,8,9,10],"source":5,"target":6}

Model	Answer given
Gemma 4	{"path": [5, 0, 8, 6], "cost": 19}	✓ correct
Llama 3.3	{"path": [5, 0, 2, 3, 6], "cost": 17}	✗ wrong
Qwen · off	{"path": [5, 0, 8, 6], "cost": 19}	✓ correct
Qwen · on	{"path": [5, 0, 8, 6], "cost": 19}	✓ correct

test nlgraph-shortest_path-test-31

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,5,10],[0,7,2],[0,3,5],[0,2,7],[1,5,6],[1,9,5],[1,8,9],[1,6,3],[2,9,7],[4,7,2],[5,9,4],[5,6,8],[6,9,3],[6,8,6],[6,10,3],[7,9,5],[8,10,5]],"nodes":[0,1,2,3,4,5,6,7,8,9,10],"source":10,"target":3}

Model	Answer given
Gemma 4	{"path": [10, 6, 9, 7, 0, 3], "cost": 18}	✓ correct
Llama 3.3	{"path": [10, 6, 9, 7, 0, 3], "cost": 18}	✓ correct
Qwen · off	{"path": [10, 6, 1, 0, 3], "cost": 20}	✗ wrong
Qwen · on	{"path": [10, 6, 9, 7, 0, 3], "cost": 18}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,6,7],[0,8,1],[1,5,1],[2,4,6],[2,9,1],[3,6,10],[3,7,6],[3,8,6],[4,10,7],[4,6,9],[4,7,3],[4,8,6],[5,9,10],[7,11,4],[8,9,9]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11],"source":6,"target":11}

Model	Answer given
Gemma 4	{"path": [6, 4, 7, 11], "cost": 16}	✓ correct
Llama 3.3	{"path": [6, 7, 11], "cost": 7}	✗ wrong
Qwen · off	{"path": [6, 0, 8, 3, 7, 11], "cost": 24}	✗ wrong
Qwen · on	{"path": [6, 4, 7, 11], "cost": 16}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,13,5],[0,1,5],[0,14,5],[1,2,2],[1,12,10],[1,4,1],[1,6,2],[2,12,5],[2,11,4],[2,14,2],[2,8,9],[2,7,7],[3,16,7],[3,8,5],[3,6,2],[4,9,5],[4,16,7],[4,14,4],[4,10,6],[5,8,3],[5,10,4],[5,7,2],[6,11,5],[7,13,6],[7,12,3],[7,15,6],[7,10,8],[9,10,3],[10,15,10],[10,16,7],[12,15,4],[15,16,2]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"source":3,"target":0}

Model	Answer given
Gemma 4	{"path": [3, 6, 1, 0], "cost": 9}	✓ correct
Llama 3.3	{"path": [3, 6, 1, 0], "cost": 9}	✓ correct
Qwen · off	{"path": [3, 6, 1, 0], "cost": 9}	✓ correct
Qwen · on	{"path": [3, 6, 1, 0], "cost": 9}	✓ correct

test nlgraph-shortest_path-test-45

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,13,10],[0,2,9],[0,8,10],[0,1,2],[0,12,4],[0,14,7],[1,13,4],[1,2,7],[1,15,5],[1,16,1],[1,11,9],[2,15,1],[2,6,2],[2,11,6],[2,3,4],[3,17,1],[3,6,2],[3,12,5],[4,8,4],[4,5,5],[4,10,3],[6,12,5],[7,8,2],[7,11,2],[7,14,4],[8,11,2],[8,10,7],[8,14,3],[9,10,3],[9,14,4],[10,16,9],[10,11,5],[10,14,4],[12,13,8],[12,16,5],[13,17,8],[13,16,10],[15,18,3],[16,17,5]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"source":3,"target":5}

Model	Answer given
Gemma 4	{"path": [3, 2, 11, 8, 4, 5], "cost": 21}	✓ correct
Llama 3.3	TokenLimit	✗ no usable answer
Qwen · off	{"path": [3, 2, 0, 1, 16, 10, 4, 5], "cost": 24}	✗ wrong
Qwen · on	{"path": [3, 2, 11, 8, 4, 5], "cost": 21}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,5,2],[0,2,1],[0,1,2],[0,9,1],[0,8,4],[0,7,3],[0,6,2],[1,5,3],[1,4,2],[1,2,1],[1,8,4],[1,6,3],[2,3,3],[2,4,1],[2,9,3],[2,7,3],[3,9,3],[3,8,3],[4,5,3],[4,7,3],[4,6,1],[5,9,3],[5,7,3],[5,6,2],[6,9,1],[7,9,4],[7,8,3],[8,9,1]],"nodes":[0,1,2,3,4,5,6,7,8,9],"source":5,"target":3}

Model	Answer given
Gemma 4	{"path": [5, 0, 2, 3], "cost": 6}	✓ correct
Llama 3.3	{"path": [5, 0, 2, 3], "cost": 6}	✓ correct
Qwen · off	{"path": [5, 0, 2, 3], "cost": 7}	✗ wrong
Qwen · on	{"path": [5, 0, 2, 3], "cost": 6}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,6,10],[0,11,4],[0,1,3],[0,10,2],[0,4,8],[1,7,7],[1,10,10],[1,4,3],[2,7,5],[2,9,1],[2,11,7],[2,3,4],[2,10,5],[2,12,3],[3,10,1],[3,12,9],[4,7,3],[5,10,5],[6,7,7],[6,11,1],[6,10,3],[7,10,1],[7,12,5],[8,10,5],[10,12,5]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12],"source":11,"target":1}

Model	Answer given
Gemma 4	{"path": [11, 0, 1], "cost": 7}	✓ correct
Llama 3.3	{"path": [11, 6, 0, 1], "cost": 14}	✗ wrong
Qwen · off	{"path": [11, 0, 1], "cost": 7}	✓ correct
Qwen · on	{"path": [11, 0, 1], "cost": 7}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,8,1],[0,12,9],[0,5,8],[0,3,10],[1,9,1],[1,11,2],[1,7,6],[2,7,9],[2,4,1],[2,3,6],[3,8,1],[3,12,9],[3,5,5],[4,14,4],[5,11,4],[5,7,5],[5,10,2],[6,11,3],[7,10,4],[7,14,3],[9,10,4],[10,12,7],[10,14,5],[10,13,9],[12,14,6]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"source":6,"target":4}

Model	Answer given
Gemma 4	{"path": [6, 11, 5, 10, 14, 4], "cost": 18}	✓ correct
Llama 3.3	{"path": [6, 11, 1, 2, 4], "cost": 7}	✗ wrong
Qwen · off	{"path": [6, 11, 1, 9, 10, 5, 0, 8, 3, 2, 4], "cost": 31}	✗ wrong
Qwen · on	{"path": [6, 11, 5, 10, 14, 4], "cost": 18}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,2,2],[0,5,4],[0,3,1],[0,1,3],[1,2,4],[1,5,1],[1,4,4],[2,4,3],[2,3,1],[3,5,2],[3,4,3],[4,5,2]],"nodes":[0,1,2,3,4,5],"source":0,"target":4}

Model	Answer given
Gemma 4	{"path": [0, 3, 5, 4], "cost": 5}	✗ wrong
Llama 3.3	{"path": [0, 3, 4], "cost": 4}	✓ correct
Qwen · off	{"path": [0, 3, 4], "cost": 4}	✓ correct
Qwen · on	{"path": [0, 3, 4], "cost": 4}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,7,1],[0,2,4],[0,6,1],[0,1,3],[0,5,2],[0,4,2],[0,8,2],[1,7,1],[1,2,2],[1,6,1],[1,3,1],[1,4,2],[1,8,3],[2,7,4],[2,6,3],[2,3,4],[2,4,4],[2,8,3],[3,7,4],[3,6,1],[3,5,2],[3,4,1],[3,8,2],[4,7,3],[4,6,1],[4,5,3],[4,8,2],[5,7,4],[5,6,2],[5,8,2],[6,7,3],[6,8,3],[7,8,3]],"nodes":[0,1,2,3,4,5,6,7,8],"source":2,"target":5}

Model	Answer given
Gemma 4	{"path": [2, 1, 3, 5], "cost": 5}	✓ correct
Llama 3.3	{"path": [2, 3, 5], "cost": 6}	✗ wrong
Qwen · off	{"path": [2, 0, 5], "cost": 6}	✗ wrong
Qwen · on	{"path": [2, 1, 3, 5], "cost": 5}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,7,8],[0,2,5],[0,15,8],[1,6,6],[1,7,2],[1,2,9],[1,3,2],[1,11,8],[2,8,9],[2,4,8],[2,15,8],[3,4,7],[3,12,1],[3,10,1],[4,9,8],[4,6,3],[4,14,3],[4,5,5],[5,8,6],[5,6,1],[5,12,9],[5,11,4],[6,15,8],[7,15,1],[7,11,10],[9,13,5],[10,12,6],[10,11,9],[11,14,5],[13,16,9],[13,14,9],[15,16,5]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"source":3,"target":16}

Model	Answer given
Gemma 4	{"path": [3, 4, 6, 15, 16], "cost": 23}	✗ wrong
Llama 3.3	{"path": [3, 12, 10, 11, 14, 13, 16], "cost": 25}	✗ wrong
Qwen · off	{"path": [3, 12, 10, 11, 14, 13, 16], "cost": 35}	✗ wrong
Qwen · on	{"path": [3, 4, 6, 15, 16], "cost": 23}	✗ wrong

test nlgraph-shortest_path-test-48

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,9,6],[0,14,8],[0,5,4],[0,13,5],[1,9,9],[1,6,4],[2,8,10],[2,4,4],[2,3,6],[4,10,6],[4,8,7],[4,6,5],[5,10,8],[5,9,9],[6,8,8],[7,11,4],[8,12,5],[8,9,3],[8,13,10],[9,14,5],[10,12,1],[10,11,4],[10,14,4],[12,14,9]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"source":2,"target":7}

Model	Answer given
Gemma 4	{"path": [2, 4, 10, 11, 7], "cost": 18}	✓ correct
Llama 3.3	{"path": [2, 4, 10, 11, 7], "cost": 18}	✓ correct
Qwen · off	{"path": [2, 4, 10, 11, 7], "cost": 15}	✗ wrong
Qwen · on	{"path": [2, 4, 10, 11, 7], "cost": 18}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,4,8],[0,12,5],[0,2,3],[1,14,7],[1,3,1],[1,16,4],[1,2,5],[2,8,9],[2,15,9],[2,6,4],[3,8,4],[3,6,3],[3,12,8],[4,8,7],[4,15,2],[4,18,7],[4,5,2],[4,10,9],[5,8,8],[5,7,7],[5,6,6],[5,19,6],[5,11,9],[5,13,5],[6,15,6],[6,18,9],[6,13,10],[7,8,1],[7,15,10],[7,11,9],[8,15,2],[8,12,1],[8,17,3],[8,10,4],[9,15,8],[12,19,6],[13,15,4],[13,18,3],[13,17,8],[14,15,7],[15,17,9]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"source":14,"target":5}

Model	Answer given
Gemma 4	{"path": [14, 15, 4, 5], "cost": 11}	✓ correct
Llama 3.3	{"path": [14, 1, 3, 6, 5], "cost": 17}	✗ wrong
Qwen · off	{"path": [14, 15, 4, 5], "cost": 11}	✓ correct
Qwen · on	{"path": [14, 15, 4, 5], "cost": 11}	✓ correct

test nlgraph-shortest_path-test-3

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,7,2],[0,8,3],[0,5,3],[1,5,4],[2,7,2],[2,8,3],[2,4,2],[2,6,1],[3,8,2],[3,6,1],[3,5,4],[4,7,3],[4,8,3],[5,7,3],[5,6,3],[7,8,1]],"nodes":[0,1,2,3,4,5,6,7,8],"source":7,"target":3}

Model	Answer given
Gemma 4	{"path": [7, 8, 3], "cost": 3}	✓ correct
Llama 3.3	{"path": [7, 8, 3], "cost": 3}	✓ correct
Qwen · off	{"path": [7, 8, 3], "cost": 5}	✗ wrong
Qwen · on	{"path": [7, 8, 3], "cost": 3}	✓ correct

test nlgraph-shortest_path-test-38

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,4,3],[0,1,3],[0,2,4],[0,7,4],[1,4,2],[1,6,1],[1,7,3],[1,3,1],[2,6,1],[2,5,2],[2,3,3],[3,4,4],[3,6,4],[3,5,4],[3,7,2],[4,5,2],[4,7,4],[5,6,1],[5,7,2],[6,7,4]],"nodes":[0,1,2,3,4,5,6,7],"source":4,"target":6}

Model	Answer given
Gemma 4	{"path": [4, 1, 6], "cost": 3}	✓ correct
Llama 3.3	{"path": [4, 1, 6], "cost": 3}	✓ correct
Qwen · off	{"path": [4, 1, 6], "cost": 4}	✗ wrong
Qwen · on	{"path": [4, 1, 6], "cost": 3}	✓ correct

test nlgraph-shortest_path-test-9

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,6,4],[0,4,2],[0,3,3],[0,7,1],[0,8,3],[1,6,1],[1,4,2],[1,3,2],[1,9,4],[1,7,1],[1,8,2],[2,6,3],[2,5,3],[2,3,4],[2,9,2],[2,7,4],[2,8,1],[3,4,3],[3,9,3],[3,7,1],[4,9,3],[4,7,4],[5,6,1],[5,9,3],[5,7,2],[6,9,3],[6,7,1],[6,8,4],[7,9,3],[7,8,1],[8,9,2]],"nodes":[0,1,2,3,4,5,6,7,8,9],"source":6,"target":4}

Model	Answer given
Gemma 4	{"path": [6, 1, 4], "cost": 3}	✓ correct
Llama 3.3	{"path": [6, 4], "cost": 2}	✗ wrong
Qwen · off	{"path": [6, 0, 4], "cost": 6}	✗ wrong
Qwen · on	{"path": [6, 1, 4], "cost": 3}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,1,4],[1,8,9],[1,10,6],[2,7,2],[2,8,6],[3,11,4],[3,7,4],[3,8,6],[4,5,1],[4,8,4],[4,6,3],[5,12,4],[5,8,1],[5,10,6],[6,12,2],[7,11,10],[8,9,8],[8,10,5],[9,12,7],[11,12,4]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12],"source":2,"target":5}

Model	Answer given
Gemma 4	{"path": [2, 8, 5], "cost": 7}	✓ correct
Llama 3.3	{"path": [2, 8, 5], "cost": 7}	✓ correct
Qwen · off	{"path": [2, 8, 5], "cost": 7}	✓ correct
Qwen · on	{"path": [2, 8, 5], "cost": 7}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,7,2],[1,4,8],[1,9,5],[2,12,5],[2,9,1],[3,6,8],[4,6,7],[5,7,7],[5,8,4],[6,11,10],[6,10,4],[6,13,2],[7,10,9],[8,10,7],[8,9,1],[9,11,1],[9,10,6]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"source":2,"target":3}

Model	Answer given
Gemma 4	null	✗ wrong
Llama 3.3	InvalidJSON	✗ no usable answer
Qwen · off	{"path": [2, 9, 8, 5, 7, 10, 6, 3], "cost": 32}	✗ wrong
Qwen · on	{"path": [2, 9, 10, 6, 3], "cost": 19}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,9,10],[0,5,5],[0,10,7],[0,12,5],[0,2,10],[1,9,8],[1,5,3],[1,14,4],[2,5,10],[2,10,1],[2,12,3],[2,8,3],[3,7,9],[3,14,6],[4,9,8],[4,5,1],[4,6,3],[4,8,3],[5,15,6],[5,8,4],[5,11,4],[6,10,10],[6,8,1],[6,11,5],[8,10,10],[8,14,4],[8,11,8],[11,13,2],[12,13,2]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"source":13,"target":7}

Model	Answer given
Gemma 4	{"path": [13, 12, 2, 8, 14, 3, 7], "cost": 27}	✓ correct
Llama 3.3	{"path": [13, 11, 5, 4, 3, 7], "cost": 25}	✗ wrong
Qwen · off	{"path": [13, 11, 5, 4, 9, 1, 14, 3, 7], "cost": 30}	✗ wrong
Qwen · on	{"path": [13, 12, 2, 8, 14, 3, 7], "cost": 27}	✓ correct

test nlgraph-shortest_path-test-28

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,2,3],[0,7,2],[0,3,2],[0,5,2],[0,1,2],[0,6,1],[1,2,3],[1,4,3],[1,7,4],[1,3,4],[1,5,4],[2,4,4],[2,7,4],[2,3,2],[2,5,1],[2,6,3],[3,4,3],[3,7,2],[3,5,2],[3,6,3],[4,5,4],[4,6,1],[5,7,4],[5,6,2],[6,7,3]],"nodes":[0,1,2,3,4,5,6,7],"source":4,"target":7}

Model	Answer given
Gemma 4	{"path": [4, 6, 7], "cost": 4}	✓ correct
Llama 3.3	{"path": [4, 6, 7], "cost": 4}	✓ correct
Qwen · off	{"path": [4, 6, 0, 7], "cost": 6}	✗ wrong
Qwen · on	{"path": [4, 6, 7], "cost": 4}	✓ correct

test nlgraph-shortest_path-test-52

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,17,3],[0,1,3],[0,6,9],[0,11,4],[0,4,2],[0,18,7],[1,5,6],[1,10,7],[1,8,8],[1,4,4],[1,18,3],[2,14,10],[2,9,10],[3,6,10],[3,8,4],[3,9,9],[3,7,3],[3,16,10],[3,19,7],[3,18,2],[4,13,10],[4,10,9],[4,7,7],[4,19,9],[5,10,4],[5,18,9],[6,17,2],[6,9,6],[6,16,5],[6,12,7],[7,17,2],[7,13,10],[7,14,1],[7,8,4],[8,16,2],[8,12,2],[9,17,3],[9,11,2],[9,19,8],[10,17,6],[10,18,10],[11,14,6],[11,12,2],[12,13,4],[13,14,9],[14,15,9]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"source":15,"target":5}

Model	Answer given
Gemma 4	{"path": [15, 14, 7, 17, 10, 5], "cost": 22}	✓ correct
Llama 3.3	{"path": [15, 14, 7, 3, 1, 5], "cost": 23}	✗ wrong
Qwen · off	{"path": [15, 14, 7, 17, 6, 0, 1, 5], "cost": 24}	✗ wrong
Qwen · on	{"path": [15, 14, 7, 17, 10, 5], "cost": 22}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,2,4],[0,4,2],[0,5,1],[0,3,1],[0,1,2],[1,2,2],[1,5,3],[1,3,2],[2,4,1],[2,5,3],[2,3,3],[3,5,4]],"nodes":[0,1,2,3,4,5],"source":4,"target":5}

Model	Answer given
Gemma 4	{"path": [4, 0, 5], "cost": 3}	✓ correct
Llama 3.3	{"path": [4, 2, 5], "cost": 4}	✗ wrong
Qwen · off	{"path": [4, 0, 5], "cost": 3}	✓ correct
Qwen · on	{"path": [4, 0, 5], "cost": 3}	✓ correct

test nlgraph-shortest_path-test-21

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,1,3],[0,2,2],[1,3,2],[2,5,2],[2,4,2],[3,5,2],[4,5,3]],"nodes":[0,1,2,3,4,5],"source":0,"target":3}

Model	Answer given
Gemma 4	{"path": [0, 1, 3], "cost": 5}	✓ correct
Llama 3.3	{"path": [0, 1, 3], "cost": 5}	✓ correct
Qwen · off	{"path": [0, 1, 3], "cost": 5}	✓ correct
Qwen · on	{"path": [0, 1, 3], "cost": 5}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,5,10],[0,4,10],[1,7,3],[1,5,5],[2,12,3],[2,7,8],[2,4,10],[3,5,5],[3,10,6],[4,7,8],[5,12,3],[5,6,2],[5,9,9],[5,7,1],[6,12,2],[6,9,7],[7,11,6],[8,10,1],[9,11,2],[10,11,6]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12],"source":4,"target":5}

Model	Answer given
Gemma 4	{"path": [4, 7, 5], "cost": 9}	✓ correct
Llama 3.3	{"path": [4, 7, 5], "cost": 9}	✓ correct
Qwen · off	{"path": [4, 0, 5], "cost": 20}	✗ wrong
Qwen · on	{"path": [4, 7, 5], "cost": 9}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,2,4],[0,1,4],[0,4,2],[0,3,2],[1,2,3],[1,4,4],[1,5,3],[2,4,3],[2,3,2],[2,5,1],[3,4,1],[3,5,2],[4,5,3]],"nodes":[0,1,2,3,4,5],"source":1,"target":3}

Model	Answer given
Gemma 4	{"path": [1, 5, 3], "cost": 5}	✓ correct
Llama 3.3	{"path": [1, 2, 3], "cost": 5}	✓ correct
Qwen · off	{"path": [1, 2, 3], "cost": 5}	✓ correct
Qwen · on	{"path": [1, 2, 3], "cost": 5}	✓ correct

test nlgraph-shortest_path-test-4

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,8,4],[0,2,1],[0,1,2],[1,3,4],[1,8,2],[1,7,4],[1,5,1],[2,3,1],[2,4,1],[2,6,2],[3,5,3],[3,9,4],[4,8,4],[4,5,4],[4,9,2],[5,8,1],[5,9,4],[6,7,1],[8,9,1]],"nodes":[0,1,2,3,4,5,6,7,8,9],"source":3,"target":8}

Model	Answer given
Gemma 4	{"path": [3, 5, 8], "cost": 4}	✓ correct
Llama 3.3	{"path": [3, 5, 8], "cost": 4}	✓ correct
Qwen · off	{"path": [3, 2, 0, 1, 8], "cost": 8}	✗ wrong
Qwen · on	{"path": [3, 5, 8], "cost": 4}	✓ correct

test nlgraph-shortest_path-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,1,2],[0,4,4],[1,2,4],[1,3,2],[1,4,4],[3,4,3]],"nodes":[0,1,2,3,4],"source":2,"target":3}

Model	Answer given
Gemma 4	{"path": [2, 1, 3], "cost": 6}	✓ correct
Llama 3.3	{"path": [2, 1, 3], "cost": 6}	✓ correct
Qwen · off	{"path": [2, 1, 3], "cost": 6}	✓ correct
Qwen · on	{"path": [2, 1, 3], "cost": 6}	✓ correct

development nlgraph-shortest_path-train-12

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,4,1],[0,5,2],[0,3,3],[0,2,3],[1,4,3],[1,5,1],[1,3,3],[1,2,2],[2,4,3],[2,5,1],[2,3,3],[3,4,2],[3,5,3],[4,5,2]],"nodes":[0,1,2,3,4,5],"source":0,"target":1}

development nlgraph-shortest_path-train-190

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,3,4],[0,1,1],[0,4,4],[0,2,4],[1,3,2],[2,3,4],[3,4,4]],"nodes":[0,1,2,3,4],"source":1,"target":4}

development nlgraph-shortest_path-train-106

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,5,10],[0,13,3],[1,2,5],[2,14,9],[2,9,2],[3,6,4],[3,5,7],[3,10,7],[3,11,10],[4,15,5],[4,8,7],[4,12,5],[5,10,7],[6,8,3],[6,7,9],[8,11,10],[8,13,2],[9,11,9],[10,11,5],[11,15,3],[12,13,9],[14,15,5]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"source":7,"target":1}

development nlgraph-shortest_path-train-232

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,4,1],[0,6,4],[1,5,3],[1,7,1],[1,4,3],[1,6,3],[1,2,2],[2,7,1],[2,4,2],[2,6,4],[3,4,3],[3,6,2],[4,5,3],[4,6,2],[5,7,4],[5,6,1],[6,7,4]],"nodes":[0,1,2,3,4,5,6,7],"source":5,"target":3}

development nlgraph-shortest_path-train-165

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,5,10],[0,9,9],[1,10,5],[1,8,5],[1,11,9],[1,6,2],[1,5,9],[2,3,2],[2,11,8],[3,10,5],[3,13,6],[3,5,6],[4,8,9],[4,9,6],[5,12,9],[5,8,4],[6,12,5],[6,7,8],[7,12,10],[7,9,3],[8,10,1],[8,11,1],[9,10,10],[9,12,2],[11,12,4],[12,13,9]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"source":13,"target":8}

development nlgraph-shortest_path-train-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,6,2],[0,3,4],[0,5,4],[0,1,3],[1,6,1],[1,2,2],[1,3,2],[1,4,3],[1,7,4],[2,6,1],[2,4,3],[2,5,4],[3,7,2],[4,6,1],[4,8,1],[5,6,4],[5,8,2],[7,8,3]],"nodes":[0,1,2,3,4,5,6,7,8],"source":6,"target":3}

development nlgraph-shortest_path-train-4

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,16,2],[0,12,5],[0,2,7],[1,3,9],[1,8,9],[1,13,5],[2,3,6],[2,12,2],[2,15,10],[2,4,9],[3,6,2],[3,17,2],[3,10,7],[3,15,6],[3,13,7],[4,6,4],[4,13,3],[5,6,9],[5,14,8],[7,11,10],[8,12,6],[8,15,3],[8,13,10],[9,14,9],[10,15,6],[11,12,5],[11,17,9],[12,13,5],[15,17,7]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"source":11,"target":9}

development nlgraph-shortest_path-train-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,1,8],[0,11,8],[0,8,3],[0,16,8],[0,5,4],[0,19,6],[0,13,2],[0,18,7],[0,4,7],[1,9,2],[1,3,7],[1,11,9],[1,8,9],[1,15,5],[1,5,2],[1,19,5],[1,13,5],[1,7,9],[1,2,4],[2,12,10],[3,16,7],[3,10,3],[3,7,2],[4,9,3],[4,8,7],[4,15,3],[4,17,6],[4,13,1],[5,16,6],[5,18,5],[5,6,1],[6,17,1],[6,10,10],[7,9,9],[7,11,9],[7,16,7],[7,17,6],[7,19,7],[7,13,9],[7,18,9],[8,11,9],[9,16,5],[9,12,3],[10,15,6],[11,16,9],[11,17,6],[11,13,9],[12,14,6],[13,18,5],[16,19,3]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"source":9,"target":10}

development nlgraph-shortest_path-train-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,1,9],[0,3,6],[1,2,9],[2,7,9],[2,6,3],[3,6,3],[4,8,3],[4,7,4],[5,11,8],[5,10,5],[8,9,7],[9,10,2]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11],"source":10,"target":6}

development nlgraph-shortest_path-train-192

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,2,3],[0,4,3],[1,3,4],[1,4,3],[2,3,4],[2,4,3],[3,4,3]],"nodes":[0,1,2,3,4],"source":2,"target":1}

development nlgraph-shortest_path-train-153

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,9,2],[0,7,1],[0,6,1],[0,2,2],[0,4,3],[0,8,4],[0,3,4],[1,9,4],[1,7,4],[1,6,2],[1,2,4],[1,4,3],[1,5,3],[2,9,3],[2,7,2],[2,6,3],[2,4,1],[2,3,4],[3,9,4],[3,7,1],[3,4,2],[3,5,1],[4,9,3],[4,7,4],[4,6,2],[5,7,1],[6,7,2],[6,8,1],[7,9,2],[8,9,3]],"nodes":[0,1,2,3,4,5,6,7,8,9],"source":9,"target":6}

development nlgraph-shortest_path-train-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,7,6],[0,16,7],[1,2,5],[1,5,2],[1,12,8],[2,6,6],[2,5,10],[2,11,1],[2,14,6],[3,13,6],[3,14,7],[3,8,1],[4,6,3],[4,7,8],[4,11,10],[4,14,9],[4,8,8],[5,11,4],[6,10,6],[6,13,8],[7,10,1],[7,8,8],[9,13,8],[10,11,5],[10,14,4],[12,15,3],[12,16,6],[15,16,8]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"source":15,"target":7}

development nlgraph-shortest_path-train-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,9,10],[0,2,8],[0,5,5],[1,10,6],[1,8,5],[1,2,9],[2,11,5],[3,12,8],[3,4,1],[3,5,3],[6,12,4],[6,9,7],[7,11,1],[8,9,3]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12],"source":12,"target":8}

development nlgraph-shortest_path-train-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,4,4],[0,3,3],[0,1,3],[1,4,4],[2,4,2],[2,3,1],[3,4,1]],"nodes":[0,1,2,3,4],"source":0,"target":2}

development nlgraph-shortest_path-train-245

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,3,3],[0,4,3],[0,6,1],[0,5,4],[0,2,1],[0,1,1],[1,4,2],[1,6,2],[1,2,3],[2,3,2],[2,4,4],[2,6,3],[2,5,1],[3,4,3],[4,6,3],[4,5,1]],"nodes":[0,1,2,3,4,5,6],"source":3,"target":6}

development nlgraph-shortest_path-train-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,4,3],[0,9,1],[0,5,3],[0,8,1],[0,1,3],[1,7,4],[1,4,2],[1,9,1],[1,6,4],[1,8,1],[1,2,2],[2,4,2],[2,3,4],[2,6,2],[2,5,2],[2,8,2],[3,7,2],[3,4,2],[3,5,2],[3,8,4],[4,9,1],[4,6,4],[4,5,1],[4,8,1],[5,7,3],[5,9,1],[6,7,2],[6,9,2],[6,8,4],[7,9,2],[8,9,1]],"nodes":[0,1,2,3,4,5,6,7,8,9],"source":7,"target":4}

development nlgraph-shortest_path-train-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,12,6],[0,3,3],[0,11,4],[1,9,8],[1,8,1],[1,4,5],[2,7,9],[2,5,10],[2,14,10],[2,10,2],[3,12,1],[3,14,1],[3,11,7],[4,7,6],[4,14,8],[5,14,4],[5,16,4],[6,8,10],[6,13,2],[7,14,5],[7,15,7],[8,10,8],[12,14,9],[13,16,1],[14,15,10]],"nodes":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"source":0,"target":13}

development nlgraph-shortest_path-train-300

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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,10,7],[0,3,8],[1,10,1],[1,5,2],[1,2,3],[1,3,6],[1,7,4],[2,9,3],[2,5,1],[4,6,2],[6,8,5],[8,10,5]],"nodes":[0,1,2,3,4,5,6,7,8,9,10],"source":9,"target":4}

development nlgraph-shortest_path-train-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,8,1],[0,5,4],[0,6,1],[0,2,3],[0,1,2],[1,4,4],[1,7,3],[1,8,3],[1,3,4],[1,2,2],[2,4,3],[2,7,3],[2,8,3],[2,3,1],[2,5,4],[2,6,3],[3,7,2],[3,5,3],[3,6,1],[4,7,3],[4,8,4],[4,5,4],[4,6,3],[5,7,1],[5,8,2],[5,6,3],[6,8,3],[7,8,2]],"nodes":[0,1,2,3,4,5,6,7,8],"source":0,"target":4}

development nlgraph-shortest_path-train-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 and each third number is a positive travel time in minutes. Return a minimum-time route from source to target as a JSON object with exactly "path" (list of node IDs) and "cost" (total minutes). Any optimal route is accepted. If no route exists return null.
Network: {"directed":false,"edges":[[0,1,4],[0,5,1],[0,4,3],[0,3,2],[1,5,3],[1,4,4],[1,2,2],[1,3,1],[2,5,1],[2,4,4],[2,3,2],[3,5,2],[3,4,2],[4,5,2]],"nodes":[0,1,2,3,4,5],"source":0,"target":2}