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<\|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\": 700, \"parameter\": {\"MAX_N\": 33, \"N\": 9, \"MOD\": 946431, \"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\": 701, \"parameter\": {\"MAX_N\": 33, \"N\": 27, \"MOD\": 293165, \"reference_answer\": 42655}, \"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 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\": 702, \"parameter\": {\"MAX_N\": 33, \"N\": 28, \"MOD\": 792315, \"reference_answer\": 540020}, \"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 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\": 703, \"parameter\": {\"MAX_N\": 33, \"N\": 5, \"MOD\": 333563, \"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 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\": 704, \"parameter\": {\"MAX_N\": 33, \"N\": 30, \"MOD\": 652875, \"reference_answer\": 25632}, \"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 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\": 705, \"parameter\": {\"MAX_N\": 33, \"N\": 28, \"MOD\": 272039, \"reference_answer\": 72211}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 28 vertices labeled from 1 to 28. 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\": 706, \"parameter\": {\"MAX_N\": 33, \"N\": 23, \"MOD\": 937417, \"reference_answer\": 258999}, \"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\": 707, \"parameter\": {\"MAX_N\": 33, \"N\": 4, \"MOD\": 635329, \"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 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\": 708, \"parameter\": {\"MAX_N\": 33, \"N\": 7, \"MOD\": 903515, \"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 connect...
<\|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\": 709, \"parameter\": {\"MAX_N\": 33, \"N\": 21, \"MOD\": 726665, \"reference_answer\": 676169}, \"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 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\": 710, \"parameter\": {\"MAX_N\": 33, \"N\": 16, \"MOD\": 719151, \"reference_answer\": 55930}, \"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 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\": 711, \"parameter\": {\"MAX_N\": 33, \"N\": 23, \"MOD\": 508781, \"reference_answer\": 450879}, \"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 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\": 712, \"parameter\": {\"MAX_N\": 33, \"N\": 13, \"MOD\": 652789, \"reference_answer\": 394706}, \"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 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\": 713, \"parameter\": {\"MAX_N\": 33, \"N\": 16, \"MOD\": 667837, \"reference_answer\": 614877}, \"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 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\": 714, \"parameter\": {\"MAX_N\": 33, \"N\": 28, \"MOD\": 122785, \"reference_answer\": 28950}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 28 vertices labeled from 1 to 28. 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\": 715, \"parameter\": {\"MAX_N\": 33, \"N\": 20, \"MOD\": 77853, \"reference_answer\": 25764}, \"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 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\": 716, \"parameter\": {\"MAX_N\": 33, \"N\": 9, \"MOD\": 489823, \"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 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\": 717, \"parameter\": {\"MAX_N\": 33, \"N\": 11, \"MOD\": 710879, \"reference_answer\": 236376}, \"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 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\": 718, \"parameter\": {\"MAX_N\": 33, \"N\": 12, \"MOD\": 790121, \"reference_answer\": 98886}, \"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\": 719, \"parameter\": {\"MAX_N\": 33, \"N\": 12, \"MOD\": 732387, \"reference_answer\": 74193}, \"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 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\": 720, \"parameter\": {\"MAX_N\": 33, \"N\": 27, \"MOD\": 162985, \"reference_answer\": 60745}, \"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 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\": 721, \"parameter\": {\"MAX_N\": 33, \"N\": 8, \"MOD\": 764645, \"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 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\": 722, \"parameter\": {\"MAX_N\": 33, \"N\": 23, \"MOD\": 730407, \"reference_answer\": 593161}, \"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 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\": 723, \"parameter\": {\"MAX_N\": 33, \"N\": 21, \"MOD\": 184009, \"reference_answer\": 13677}, \"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 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\": 724, \"parameter\": {\"MAX_N\": 33, \"N\": 32, \"MOD\": 764605, \"reference_answer\": 506132}, \"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 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\": 725, \"parameter\": {\"MAX_N\": 33, \"N\": 6, \"MOD\": 521989, \"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 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\": 726, \"parameter\": {\"MAX_N\": 33, \"N\": 12, \"MOD\": 790351, \"reference_answer\": 84396}, \"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 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\": 727, \"parameter\": {\"MAX_N\": 33, \"N\": 32, \"MOD\": 553575, \"reference_answer\": 497332}, \"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 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\": 728, \"parameter\": {\"MAX_N\": 33, \"N\": 33, \"MOD\": 42587, \"reference_answer\": 27722}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 33 vertices labeled from 1 to 33. Every pair of vertices is con...
<\|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\": 729, \"parameter\": {\"MAX_N\": 33, \"N\": 26, \"MOD\": 343177, \"reference_answer\": 200324}, \"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 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\": 730, \"parameter\": {\"MAX_N\": 33, \"N\": 13, \"MOD\": 128245, \"reference_answer\": 27644}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 13 vertices labeled from 1 to 13. 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\": 731, \"parameter\": {\"MAX_N\": 33, \"N\": 27, \"MOD\": 72777, \"reference_answer\": 42842}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 27 vertices labeled from 1 to 27. Every pair of vertices is con...
<\|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\": 732, \"parameter\": {\"MAX_N\": 33, \"N\": 25, \"MOD\": 126631, \"reference_answer\": 14097}, \"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 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\": 733, \"parameter\": {\"MAX_N\": 33, \"N\": 17, \"MOD\": 952153, \"reference_answer\": 884204}, \"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\": 734, \"parameter\": {\"MAX_N\": 33, \"N\": 25, \"MOD\": 357245, \"reference_answer\": 170700}, \"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 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\": 735, \"parameter\": {\"MAX_N\": 33, \"N\": 17, \"MOD\": 836775, \"reference_answer\": 161486}, \"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 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\": 736, \"parameter\": {\"MAX_N\": 33, \"N\": 12, \"MOD\": 73131, \"reference_answer\": 1167}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 12 vertices labeled from 1 to 12. Every pair of vertices is conn...
<\|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\": 737, \"parameter\": {\"MAX_N\": 33, \"N\": 4, \"MOD\": 599743, \"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 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\": 738, \"parameter\": {\"MAX_N\": 33, \"N\": 31, \"MOD\": 171749, \"reference_answer\": 97177}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 31 vertices labeled from 1 to 31. 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\": 739, \"parameter\": {\"MAX_N\": 33, \"N\": 10, \"MOD\": 780113, \"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...