prefix stringlengths 9.11k 16.4k | data_source stringclasses 1
value | response stringclasses 5
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<|im_start|>user
Consider a graph with 31 vertices labeled from 1 to 31. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 31 (so the graph has 31 × (31 - 1) / 2 - 1 edges).
What's the number of **simple cycles** in this graph? A simple cycle must:
- Have at least 3 ... | AlmostCompleteGraphCycleCounting | {"metadata": "{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 0, \"parameter\": {\"MAX_N\": 33, \"N\": 31, \"MOD\": 403961, \"reference_answer\": 290960}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 31 vertices labeled from 1 to 31. Every pair of vertices is con... | |
<|im_start|>user
Consider a graph with 8 vertices labeled from 1 to 8. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 8 (so the graph has 8 × (8 - 1) / 2 - 1 edges).
What's the number of **simple cycles** in this graph? A simple cycle must:
- Have at least 3 verti... | AlmostCompleteGraphCycleCounting | {"metadata": "{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 1, \"parameter\": {\"MAX_N\": 33, \"N\": 8, \"MOD\": 596855, \"reference_answer\": 6062}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 8 vertices labeled from 1 to 8. Every pair of vertices is connecte... | |
<|im_start|>user
Consider a graph with 31 vertices labeled from 1 to 31. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 31 (so the graph has 31 × (31 - 1) / 2 - 1 edges).
What's the number of **simple cycles** in this graph? A simple cycle must:
- Have at least 3 ... | AlmostCompleteGraphCycleCounting | {"metadata": "{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 2, \"parameter\": {\"MAX_N\": 33, \"N\": 31, \"MOD\": 993871, \"reference_answer\": 1176}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 31 vertices labeled from 1 to 31. Every pair of vertices is conne... | |
<|im_start|>user
Consider a graph with 11 vertices labeled from 1 to 11. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 11 (so the graph has 11 × (11 - 1) / 2 - 1 edges).
What's the number of **simple cycles** in this graph? A simple cycle must:
- Have at least 3 ... | AlmostCompleteGraphCycleCounting | {"metadata": "{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 3, \"parameter\": {\"MAX_N\": 33, \"N\": 11, \"MOD\": 621431, \"reference_answer\": 151633}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 11 vertices labeled from 1 to 11. Every pair of vertices is con... | |
<|im_start|>user
Consider a graph with 11 vertices labeled from 1 to 11. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 11 (so the graph has 11 × (11 - 1) / 2 - 1 edges).
What's the number of **simple cycles** in this graph? A simple cycle must:
- Have at least 3 ... | AlmostCompleteGraphCycleCounting | {"metadata": "{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 4, \"parameter\": {\"MAX_N\": 33, \"N\": 11, \"MOD\": 318033, \"reference_answer\": 49188}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 11 vertices labeled from 1 to 11. Every pair of vertices is conn... | |
<|im_start|>user
Consider a graph with 23 vertices labeled from 1 to 23. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 23 (so the graph has 23 × (23 - 1) / 2 - 1 edges).
What's the number of **simple cycles** in this graph? A simple cycle must:
- Have at least 3 ... | AlmostCompleteGraphCycleCounting | {"metadata": "{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 5, \"parameter\": {\"MAX_N\": 33, \"N\": 23, \"MOD\": 267855, \"reference_answer\": 257938}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 23 vertices labeled from 1 to 23. Every pair of vertices is con... | |
<|im_start|>user
Consider a graph with 29 vertices labeled from 1 to 29. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 29 (so the graph has 29 × (29 - 1) / 2 - 1 edges).
What's the number of **simple cycles** in this graph? A simple cycle must:
- Have at least 3 ... | AlmostCompleteGraphCycleCounting | {"metadata": "{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 6, \"parameter\": {\"MAX_N\": 33, \"N\": 29, \"MOD\": 601695, \"reference_answer\": 11268}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 29 vertices labeled from 1 to 29. Every pair of vertices is conn... | |
<|im_start|>user
Consider a graph with 14 vertices labeled from 1 to 14. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 14 (so the graph has 14 × (14 - 1) / 2 - 1 edges).
What's the number of **simple cycles** in this graph? A simple cycle must:
- Have at least 3 ... | AlmostCompleteGraphCycleCounting | {"metadata": "{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 7, \"parameter\": {\"MAX_N\": 33, \"N\": 14, \"MOD\": 993911, \"reference_answer\": 333547}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 14 vertices labeled from 1 to 14. Every pair of vertices is con... | |
<|im_start|>user
Consider a graph with 11 vertices labeled from 1 to 11. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 11 (so the graph has 11 × (11 - 1) / 2 - 1 edges).
What's the number of **simple cycles** in this graph? A simple cycle must:
- Have at least 3 ... | AlmostCompleteGraphCycleCounting | {"metadata": "{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 8, \"parameter\": {\"MAX_N\": 33, \"N\": 11, \"MOD\": 388407, \"reference_answer\": 229173}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 11 vertices labeled from 1 to 11. Every pair of vertices is con... | |
<|im_start|>user
Consider a graph with 18 vertices labeled from 1 to 18. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 18 (so the graph has 18 × (18 - 1) / 2 - 1 edges).
What's the number of **simple cycles** in this graph? A simple cycle must:
- Have at least 3 ... | AlmostCompleteGraphCycleCounting | {"metadata": "{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 9, \"parameter\": {\"MAX_N\": 33, \"N\": 18, \"MOD\": 643005, \"reference_answer\": 415706}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 18 vertices labeled from 1 to 18. Every pair of vertices is con... | |
<|im_start|>user
Consider a graph with 22 vertices labeled from 1 to 22. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 22 (so the graph has 22 × (22 - 1) / 2 - 1 edges).
What's the number of **simple cycles** in this graph? A simple cycle must:
- Have at least 3 ... | AlmostCompleteGraphCycleCounting | {"metadata": "{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 10, \"parameter\": {\"MAX_N\": 33, \"N\": 22, \"MOD\": 34169, \"reference_answer\": 16790}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 22 vertices labeled from 1 to 22. Every pair of vertices is conn... | |
<|im_start|>user
Consider a graph with 18 vertices labeled from 1 to 18. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 18 (so the graph has 18 × (18 - 1) / 2 - 1 edges).
What's the number of **simple cycles** in this graph? A simple cycle must:
- Have at least 3 ... | AlmostCompleteGraphCycleCounting | {"metadata": "{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 11, \"parameter\": {\"MAX_N\": 33, \"N\": 18, \"MOD\": 907799, \"reference_answer\": 865019}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 18 vertices labeled from 1 to 18. Every pair of vertices is co... |
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