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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...
<\|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\": 12, \"parameter\": {\"MAX_N\": 33, \"N\": 19, \"MOD\": 282063, \"reference_answer\": 208823}, \"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 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\": 13, \"parameter\": {\"MAX_N\": 33, \"N\": 12, \"MOD\": 304883, \"reference_answer\": 180580}, \"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 7 vertices labeled from 1 to 7. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 7 (so the graph has 7 × (7 - 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\": 14, \"parameter\": {\"MAX_N\": 33, \"N\": 7, \"MOD\": 645797, \"reference_answer\": 847}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 7 vertices labeled from 1 to 7. 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\": 15, \"parameter\": {\"MAX_N\": 33, \"N\": 10, \"MOD\": 12223, \"reference_answer\": 6386}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 10 vertices labeled from 1 to 10. Every pair of vertices is conne...
<\|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\": 16, \"parameter\": {\"MAX_N\": 33, \"N\": 15, \"MOD\": 492017, \"reference_answer\": 132850}, \"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 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\": 17, \"parameter\": {\"MAX_N\": 33, \"N\": 20, \"MOD\": 434289, \"reference_answer\": 331575}, \"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 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\": 18, \"parameter\": {\"MAX_N\": 33, \"N\": 9, \"MOD\": 128783, \"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 connec...
<\|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\": 19, \"parameter\": {\"MAX_N\": 33, \"N\": 25, \"MOD\": 45357, \"reference_answer\": 15184}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 25 vertices labeled from 1 to 25. Every pair of vertices is conn...
<\|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\": 20, \"parameter\": {\"MAX_N\": 33, \"N\": 32, \"MOD\": 757913, \"reference_answer\": 85139}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 32 vertices labeled from 1 to 32. 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\": 21, \"parameter\": {\"MAX_N\": 33, \"N\": 9, \"MOD\": 438301, \"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 connec...
<\|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\": 22, \"parameter\": {\"MAX_N\": 33, \"N\": 33, \"MOD\": 147189, \"reference_answer\": 8224}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 33 vertices labeled from 1 to 33. Every pair of vertices is conn...
<\|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\": 23, \"parameter\": {\"MAX_N\": 33, \"N\": 33, \"MOD\": 817243, \"reference_answer\": 543304}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 33 vertices labeled from 1 to 33. Every pair of vertices is co...
<\|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\": 24, \"parameter\": {\"MAX_N\": 33, \"N\": 26, \"MOD\": 401461, \"reference_answer\": 175660}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 26 vertices labeled from 1 to 26. 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\": 25, \"parameter\": {\"MAX_N\": 33, \"N\": 16, \"MOD\": 805819, \"reference_answer\": 119496}, \"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 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\": 26, \"parameter\": {\"MAX_N\": 33, \"N\": 27, \"MOD\": 950779, \"reference_answer\": 743024}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 27 vertices labeled from 1 to 27. 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\": 27, \"parameter\": {\"MAX_N\": 33, \"N\": 24, \"MOD\": 503195, \"reference_answer\": 134276}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 24 vertices labeled from 1 to 24. Every pair of vertices is co...
<\|im_start\|>user Consider a graph with 7 vertices labeled from 1 to 7. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 7 (so the graph has 7 × (7 - 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\": 28, \"parameter\": {\"MAX_N\": 33, \"N\": 7, \"MOD\": 778417, \"reference_answer\": 847}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 7 vertices labeled from 1 to 7. Every pair of vertices is connecte...
<\|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\": 29, \"parameter\": {\"MAX_N\": 33, \"N\": 21, \"MOD\": 79815, \"reference_answer\": 9429}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 21 vertices labeled from 1 to 21. Every pair of vertices is conne...
<\|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\": 30, \"parameter\": {\"MAX_N\": 33, \"N\": 21, \"MOD\": 847333, \"reference_answer\": 99798}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 21 vertices labeled from 1 to 21. Every pair of vertices is con...
<\|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\": 31, \"parameter\": {\"MAX_N\": 33, \"N\": 4, \"MOD\": 492391, \"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 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\": 32, \"parameter\": {\"MAX_N\": 33, \"N\": 6, \"MOD\": 971505, \"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 connecte...
<\|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\": 33, \"parameter\": {\"MAX_N\": 33, \"N\": 22, \"MOD\": 175381, \"reference_answer\": 135329}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 22 vertices labeled from 1 to 22. 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\": 34, \"parameter\": {\"MAX_N\": 33, \"N\": 20, \"MOD\": 374419, \"reference_answer\": 64782}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 20 vertices labeled from 1 to 20. Every pair of vertices is con...
<\|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\": 35, \"parameter\": {\"MAX_N\": 33, \"N\": 21, \"MOD\": 351663, \"reference_answer\": 278496}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 21 vertices labeled from 1 to 21. Every pair of vertices is co...
<\|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\": 36, \"parameter\": {\"MAX_N\": 33, \"N\": 14, \"MOD\": 61207, \"reference_answer\": 31569}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 14 vertices labeled from 1 to 14. Every pair of vertices is conn...
<\|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\": 37, \"parameter\": {\"MAX_N\": 33, \"N\": 25, \"MOD\": 637281, \"reference_answer\": 372733}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 25 vertices labeled from 1 to 25. 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\": 38, \"parameter\": {\"MAX_N\": 33, \"N\": 24, \"MOD\": 441585, \"reference_answer\": 39541}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 24 vertices labeled from 1 to 24. Every pair of vertices is con...
<\|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\": 39, \"parameter\": {\"MAX_N\": 33, \"N\": 10, \"MOD\": 272279, \"reference_answer\": 174135}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 10 vertices labeled from 1 to 10. Every pair of vertices is co...