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<\|im_start\|>user Consider a graph with 12 vertices labeled from 1 to 12. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 12 (so the graph has 12 × (12 - 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\": 600, \"parameter\": {\"MAX_N\": 33, \"N\": 12, \"MOD\": 360719, \"reference_answer\": 97287}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 12 vertices labeled from 1 to 12. Every pair of vertices is co...
<\|im_start\|>user Consider a graph with 10 vertices labeled from 1 to 10. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 10 (so the graph has 10 × (10 - 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\": 601, \"parameter\": {\"MAX_N\": 33, \"N\": 10, \"MOD\": 718675, \"reference_answer\": 446414}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 10 vertices labeled from 1 to 10. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 16 vertices labeled from 1 to 16. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 16 (so the graph has 16 × (16 - 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\": 602, \"parameter\": {\"MAX_N\": 33, \"N\": 16, \"MOD\": 194045, \"reference_answer\": 176107}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 16 vertices labeled from 1 to 16. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 9 vertices labeled from 1 to 9. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 9 (so the graph has 9 × (9 - 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\": 603, \"parameter\": {\"MAX_N\": 33, \"N\": 9, \"MOD\": 577683, \"reference_answer\": 49115}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 9 vertices labeled from 1 to 9. Every pair of vertices is conne...
<\|im_start\|>user Consider a graph with 6 vertices labeled from 1 to 6. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 6 (so the graph has 6 × (6 - 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\": 604, \"parameter\": {\"MAX_N\": 33, \"N\": 6, \"MOD\": 212721, \"reference_answer\": 133}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 6 vertices labeled from 1 to 6. Every pair of vertices is connect...
<\|im_start\|>user Consider a graph with 9 vertices labeled from 1 to 9. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 9 (so the graph has 9 × (9 - 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\": 605, \"parameter\": {\"MAX_N\": 33, \"N\": 9, \"MOD\": 925733, \"reference_answer\": 49115}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 9 vertices labeled from 1 to 9. Every pair of vertices is conne...
<\|im_start\|>user Consider a graph with 27 vertices labeled from 1 to 27. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 27 (so the graph has 27 × (27 - 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\": 606, \"parameter\": {\"MAX_N\": 33, \"N\": 27, \"MOD\": 922265, \"reference_answer\": 197945}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 27 vertices labeled from 1 to 27. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 26 vertices labeled from 1 to 26. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 26 (so the graph has 26 × (26 - 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\": 607, \"parameter\": {\"MAX_N\": 33, \"N\": 26, \"MOD\": 82021, \"reference_answer\": 78351}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 26 vertices labeled from 1 to 26. 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\": 608, \"parameter\": {\"MAX_N\": 33, \"N\": 8, \"MOD\": 696449, \"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 connec...
<\|im_start\|>user Consider a graph with 24 vertices labeled from 1 to 24. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 24 (so the graph has 24 × (24 - 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\": 609, \"parameter\": {\"MAX_N\": 33, \"N\": 24, \"MOD\": 591287, \"reference_answer\": 494908}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 24 vertices labeled from 1 to 24. Every pair of vertices is c...
<\|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\": 610, \"parameter\": {\"MAX_N\": 33, \"N\": 18, \"MOD\": 427333, \"reference_answer\": 159244}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 18 vertices labeled from 1 to 18. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 21 vertices labeled from 1 to 21. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 21 (so the graph has 21 × (21 - 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\": 611, \"parameter\": {\"MAX_N\": 33, \"N\": 21, \"MOD\": 366661, \"reference_answer\": 363765}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 21 vertices labeled from 1 to 21. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 30 vertices labeled from 1 to 30. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 30 (so the graph has 30 × (30 - 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\": 612, \"parameter\": {\"MAX_N\": 33, \"N\": 30, \"MOD\": 888331, \"reference_answer\": 187490}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 30 vertices labeled from 1 to 30. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 12 vertices labeled from 1 to 12. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 12 (so the graph has 12 × (12 - 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\": 613, \"parameter\": {\"MAX_N\": 33, \"N\": 12, \"MOD\": 132209, \"reference_answer\": 33716}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 12 vertices labeled from 1 to 12. Every pair of vertices is co...
<\|im_start\|>user Consider a graph with 12 vertices labeled from 1 to 12. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 12 (so the graph has 12 × (12 - 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\": 614, \"parameter\": {\"MAX_N\": 33, \"N\": 12, \"MOD\": 242431, \"reference_answer\": 178154}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 12 vertices labeled from 1 to 12. Every pair of vertices is c...
<\|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\": 615, \"parameter\": {\"MAX_N\": 33, \"N\": 11, \"MOD\": 395949, \"reference_answer\": 146211}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 11 vertices labeled from 1 to 11. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 4 vertices labeled from 1 to 4. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 4 (so the graph has 4 × (4 - 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\": 616, \"parameter\": {\"MAX_N\": 33, \"N\": 4, \"MOD\": 722135, \"reference_answer\": 3}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 4 vertices labeled from 1 to 4. Every pair of vertices is connected...
<\|im_start\|>user Consider a graph with 26 vertices labeled from 1 to 26. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 26 (so the graph has 26 × (26 - 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\": 617, \"parameter\": {\"MAX_N\": 33, \"N\": 26, \"MOD\": 496639, \"reference_answer\": 345149}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 26 vertices labeled from 1 to 26. Every pair of vertices is c...
<\|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\": 618, \"parameter\": {\"MAX_N\": 33, \"N\": 18, \"MOD\": 704297, \"reference_answer\": 645012}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 18 vertices labeled from 1 to 18. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 20 vertices labeled from 1 to 20. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 20 (so the graph has 20 × (20 - 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\": 619, \"parameter\": {\"MAX_N\": 33, \"N\": 20, \"MOD\": 958335, \"reference_answer\": 65463}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 20 vertices labeled from 1 to 20. Every pair of vertices is co...
<\|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\": 620, \"parameter\": {\"MAX_N\": 33, \"N\": 11, \"MOD\": 455713, \"reference_answer\": 400233}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 11 vertices labeled from 1 to 11. Every pair of vertices is c...
<\|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\": 621, \"parameter\": {\"MAX_N\": 33, \"N\": 14, \"MOD\": 646445, \"reference_answer\": 347902}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 14 vertices labeled from 1 to 14. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 13 vertices labeled from 1 to 13. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 13 (so the graph has 13 × (13 - 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\": 622, \"parameter\": {\"MAX_N\": 33, \"N\": 13, \"MOD\": 62541, \"reference_answer\": 58875}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 13 vertices labeled from 1 to 13. Every pair of vertices is con...
<\|im_start\|>user Consider a graph with 5 vertices labeled from 1 to 5. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 5 (so the graph has 5 × (5 - 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\": 623, \"parameter\": {\"MAX_N\": 33, \"N\": 5, \"MOD\": 395775, \"reference_answer\": 22}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 5 vertices labeled from 1 to 5. Every pair of vertices is connecte...
<\|im_start\|>user Consider a graph with 10 vertices labeled from 1 to 10. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 10 (so the graph has 10 × (10 - 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\": 624, \"parameter\": {\"MAX_N\": 33, \"N\": 10, \"MOD\": 944649, \"reference_answer\": 446414}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 10 vertices labeled from 1 to 10. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 17 vertices labeled from 1 to 17. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 17 (so the graph has 17 × (17 - 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\": 625, \"parameter\": {\"MAX_N\": 33, \"N\": 17, \"MOD\": 266299, \"reference_answer\": 134580}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 17 vertices labeled from 1 to 17. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 15 vertices labeled from 1 to 15. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 15 (so the graph has 15 × (15 - 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\": 626, \"parameter\": {\"MAX_N\": 33, \"N\": 15, \"MOD\": 811863, \"reference_answer\": 89173}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 15 vertices labeled from 1 to 15. Every pair of vertices is co...
<\|im_start\|>user Consider a graph with 33 vertices labeled from 1 to 33. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 33 (so the graph has 33 × (33 - 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\": 627, \"parameter\": {\"MAX_N\": 33, \"N\": 33, \"MOD\": 263071, \"reference_answer\": 159456}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 33 vertices labeled from 1 to 33. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 32 vertices labeled from 1 to 32. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 32 (so the graph has 32 × (32 - 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\": 628, \"parameter\": {\"MAX_N\": 33, \"N\": 32, \"MOD\": 416711, \"reference_answer\": 174532}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 32 vertices labeled from 1 to 32. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 5 vertices labeled from 1 to 5. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 5 (so the graph has 5 × (5 - 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\": 629, \"parameter\": {\"MAX_N\": 33, \"N\": 5, \"MOD\": 328341, \"reference_answer\": 22}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 5 vertices labeled from 1 to 5. Every pair of vertices is connecte...
<\|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\": 630, \"parameter\": {\"MAX_N\": 33, \"N\": 18, \"MOD\": 162371, \"reference_answer\": 121093}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 18 vertices labeled from 1 to 18. Every pair of vertices is c...
<\|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\": 631, \"parameter\": {\"MAX_N\": 33, \"N\": 29, \"MOD\": 296963, \"reference_answer\": 61388}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 29 vertices labeled from 1 to 29. Every pair of vertices is co...
<\|im_start\|>user Consider a graph with 15 vertices labeled from 1 to 15. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 15 (so the graph has 15 × (15 - 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\": 632, \"parameter\": {\"MAX_N\": 33, \"N\": 15, \"MOD\": 243731, \"reference_answer\": 162229}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 15 vertices labeled from 1 to 15. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 5 vertices labeled from 1 to 5. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 5 (so the graph has 5 × (5 - 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\": 633, \"parameter\": {\"MAX_N\": 33, \"N\": 5, \"MOD\": 388499, \"reference_answer\": 22}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 5 vertices labeled from 1 to 5. Every pair of vertices is connecte...
<\|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\": 634, \"parameter\": {\"MAX_N\": 33, \"N\": 8, \"MOD\": 230161, \"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 connec...
<\|im_start\|>user Consider a graph with 15 vertices labeled from 1 to 15. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 15 (so the graph has 15 × (15 - 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\": 635, \"parameter\": {\"MAX_N\": 33, \"N\": 15, \"MOD\": 361065, \"reference_answer\": 291136}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 15 vertices labeled from 1 to 15. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 10 vertices labeled from 1 to 10. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 10 (so the graph has 10 × (10 - 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\": 636, \"parameter\": {\"MAX_N\": 33, \"N\": 10, \"MOD\": 966525, \"reference_answer\": 446414}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 10 vertices labeled from 1 to 10. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 19 vertices labeled from 1 to 19. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 19 (so the graph has 19 × (19 - 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\": 637, \"parameter\": {\"MAX_N\": 33, \"N\": 19, \"MOD\": 208559, \"reference_answer\": 95208}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 19 vertices labeled from 1 to 19. Every pair of vertices is co...
<\|im_start\|>user Consider a graph with 24 vertices labeled from 1 to 24. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 24 (so the graph has 24 × (24 - 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\": 638, \"parameter\": {\"MAX_N\": 33, \"N\": 24, \"MOD\": 243873, \"reference_answer\": 103252}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 24 vertices labeled from 1 to 24. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 26 vertices labeled from 1 to 26. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 26 (so the graph has 26 × (26 - 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\": 639, \"parameter\": {\"MAX_N\": 33, \"N\": 26, \"MOD\": 838639, \"reference_answer\": 508592}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 26 vertices labeled from 1 to 26. Every pair of vertices is c...