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<\|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\": 400, \"parameter\": {\"MAX_N\": 33, \"N\": 13, \"MOD\": 589199, \"reference_answer\": 104786}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 13 vertices labeled from 1 to 13. 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\": 401, \"parameter\": {\"MAX_N\": 33, \"N\": 19, \"MOD\": 106253, \"reference_answer\": 9240}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 19 vertices labeled from 1 to 19. Every pair of vertices is con...
<\|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\": 402, \"parameter\": {\"MAX_N\": 33, \"N\": 30, \"MOD\": 513447, \"reference_answer\": 254265}, \"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 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\": 403, \"parameter\": {\"MAX_N\": 33, \"N\": 11, \"MOD\": 654419, \"reference_answer\": 575136}, \"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 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\": 404, \"parameter\": {\"MAX_N\": 33, \"N\": 6, \"MOD\": 976693, \"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 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\": 405, \"parameter\": {\"MAX_N\": 33, \"N\": 5, \"MOD\": 193543, \"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 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\": 406, \"parameter\": {\"MAX_N\": 33, \"N\": 17, \"MOD\": 973573, \"reference_answer\": 299472}, \"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 25 vertices labeled from 1 to 25. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 25 (so the graph has 25 × (25 - 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\": 407, \"parameter\": {\"MAX_N\": 33, \"N\": 25, \"MOD\": 863795, \"reference_answer\": 157075}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 25 vertices labeled from 1 to 25. 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\": 408, \"parameter\": {\"MAX_N\": 33, \"N\": 29, \"MOD\": 749565, \"reference_answer\": 137898}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 29 vertices labeled from 1 to 29. 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\": 409, \"parameter\": {\"MAX_N\": 33, \"N\": 30, \"MOD\": 541711, \"reference_answer\": 384043}, \"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 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\": 410, \"parameter\": {\"MAX_N\": 33, \"N\": 8, \"MOD\": 718827, \"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 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\": 411, \"parameter\": {\"MAX_N\": 33, \"N\": 10, \"MOD\": 27297, \"reference_answer\": 9662}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 10 vertices labeled from 1 to 10. Every pair of vertices is conn...
<\|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\": 412, \"parameter\": {\"MAX_N\": 33, \"N\": 13, \"MOD\": 906639, \"reference_answer\": 257868}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 13 vertices labeled from 1 to 13. 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\": 413, \"parameter\": {\"MAX_N\": 33, \"N\": 30, \"MOD\": 787355, \"reference_answer\": 351167}, \"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 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\": 414, \"parameter\": {\"MAX_N\": 33, \"N\": 17, \"MOD\": 888281, \"reference_answer\": 873470}, \"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 28 vertices labeled from 1 to 28. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 28 (so the graph has 28 × (28 - 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\": 415, \"parameter\": {\"MAX_N\": 33, \"N\": 28, \"MOD\": 355691, \"reference_answer\": 142977}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 28 vertices labeled from 1 to 28. 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\": 416, \"parameter\": {\"MAX_N\": 33, \"N\": 12, \"MOD\": 878567, \"reference_answer\": 676757}, \"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 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\": 417, \"parameter\": {\"MAX_N\": 33, \"N\": 33, \"MOD\": 626529, \"reference_answer\": 412168}, \"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 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\": 418, \"parameter\": {\"MAX_N\": 33, \"N\": 14, \"MOD\": 371651, \"reference_answer\": 168836}, \"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 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\": 419, \"parameter\": {\"MAX_N\": 33, \"N\": 23, \"MOD\": 715719, \"reference_answer\": 611050}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 23 vertices labeled from 1 to 23. 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\": 420, \"parameter\": {\"MAX_N\": 33, \"N\": 4, \"MOD\": 705817, \"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 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\": 421, \"parameter\": {\"MAX_N\": 33, \"N\": 24, \"MOD\": 643605, \"reference_answer\": 409816}, \"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 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\": 422, \"parameter\": {\"MAX_N\": 33, \"N\": 16, \"MOD\": 306333, \"reference_answer\": 290317}, \"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 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\": 423, \"parameter\": {\"MAX_N\": 33, \"N\": 14, \"MOD\": 171425, \"reference_answer\": 101242}, \"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 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\": 424, \"parameter\": {\"MAX_N\": 33, \"N\": 21, \"MOD\": 487369, \"reference_answer\": 119424}, \"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 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\": 425, \"parameter\": {\"MAX_N\": 33, \"N\": 17, \"MOD\": 93885, \"reference_answer\": 74861}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 17 vertices labeled from 1 to 17. Every pair of vertices is con...
<\|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\": 426, \"parameter\": {\"MAX_N\": 33, \"N\": 9, \"MOD\": 349395, \"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 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\": 427, \"parameter\": {\"MAX_N\": 33, \"N\": 9, \"MOD\": 643081, \"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 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\": 428, \"parameter\": {\"MAX_N\": 33, \"N\": 12, \"MOD\": 889569, \"reference_answer\": 60645}, \"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 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\": 429, \"parameter\": {\"MAX_N\": 33, \"N\": 23, \"MOD\": 919821, \"reference_answer\": 776974}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 23 vertices labeled from 1 to 23. 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\": 430, \"parameter\": {\"MAX_N\": 33, \"N\": 12, \"MOD\": 694113, \"reference_answer\": 594486}, \"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 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\": 431, \"parameter\": {\"MAX_N\": 33, \"N\": 13, \"MOD\": 815043, \"reference_answer\": 764430}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 13 vertices labeled from 1 to 13. Every pair of vertices is c...
<\|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\": 432, \"parameter\": {\"MAX_N\": 33, \"N\": 22, \"MOD\": 678343, \"reference_answer\": 349246}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 22 vertices labeled from 1 to 22. 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\": 433, \"parameter\": {\"MAX_N\": 33, \"N\": 10, \"MOD\": 708713, \"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 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\": 434, \"parameter\": {\"MAX_N\": 33, \"N\": 15, \"MOD\": 72701, \"reference_answer\": 63266}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 15 vertices labeled from 1 to 15. Every pair of vertices is con...
<\|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\": 435, \"parameter\": {\"MAX_N\": 33, \"N\": 30, \"MOD\": 907131, \"reference_answer\": 38496}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 30 vertices labeled from 1 to 30. Every pair of vertices is co...
<\|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\": 436, \"parameter\": {\"MAX_N\": 33, \"N\": 16, \"MOD\": 503937, \"reference_answer\": 97726}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 16 vertices labeled from 1 to 16. Every pair of vertices is co...
<\|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\": 437, \"parameter\": {\"MAX_N\": 33, \"N\": 20, \"MOD\": 297259, \"reference_answer\": 124471}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 20 vertices labeled from 1 to 20. 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\": 438, \"parameter\": {\"MAX_N\": 33, \"N\": 10, \"MOD\": 583817, \"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\": 439, \"parameter\": {\"MAX_N\": 33, \"N\": 16, \"MOD\": 345031, \"reference_answer\": 53813}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 16 vertices labeled from 1 to 16. Every pair of vertices is co...