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<\|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\": 100, \"parameter\": {\"MAX_N\": 33, \"N\": 8, \"MOD\": 481853, \"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 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\": 101, \"parameter\": {\"MAX_N\": 33, \"N\": 22, \"MOD\": 888269, \"reference_answer\": 496802}, \"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 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\": 102, \"parameter\": {\"MAX_N\": 33, \"N\": 8, \"MOD\": 709147, \"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 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\": 103, \"parameter\": {\"MAX_N\": 33, \"N\": 26, \"MOD\": 478465, \"reference_answer\": 473511}, \"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 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\": 104, \"parameter\": {\"MAX_N\": 33, \"N\": 4, \"MOD\": 914217, \"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 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\": 105, \"parameter\": {\"MAX_N\": 33, \"N\": 32, \"MOD\": 620051, \"reference_answer\": 271986}, \"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 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\": 106, \"parameter\": {\"MAX_N\": 33, \"N\": 26, \"MOD\": 944881, \"reference_answer\": 943694}, \"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 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\": 107, \"parameter\": {\"MAX_N\": 33, \"N\": 11, \"MOD\": 649919, \"reference_answer\": 602136}, \"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 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\": 108, \"parameter\": {\"MAX_N\": 33, \"N\": 8, \"MOD\": 750055, \"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 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\": 109, \"parameter\": {\"MAX_N\": 33, \"N\": 12, \"MOD\": 240143, \"reference_answer\": 166908}, \"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\": 110, \"parameter\": {\"MAX_N\": 33, \"N\": 33, \"MOD\": 406885, \"reference_answer\": 103802}, \"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 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\": 111, \"parameter\": {\"MAX_N\": 33, \"N\": 30, \"MOD\": 994809, \"reference_answer\": 338904}, \"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 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\": 112, \"parameter\": {\"MAX_N\": 33, \"N\": 19, \"MOD\": 873431, \"reference_answer\": 629274}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 19 vertices labeled from 1 to 19. 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\": 113, \"parameter\": {\"MAX_N\": 33, \"N\": 4, \"MOD\": 685625, \"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 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\": 114, \"parameter\": {\"MAX_N\": 33, \"N\": 11, \"MOD\": 590055, \"reference_answer\": 371265}, \"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 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\": 115, \"parameter\": {\"MAX_N\": 33, \"N\": 32, \"MOD\": 297007, \"reference_answer\": 45614}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 32 vertices labeled from 1 to 32. Every pair of vertices is co...
<\|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\": 116, \"parameter\": {\"MAX_N\": 33, \"N\": 30, \"MOD\": 781727, \"reference_answer\": 178132}, \"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\": 117, \"parameter\": {\"MAX_N\": 33, \"N\": 11, \"MOD\": 190223, \"reference_answer\": 126521}, \"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 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\": 118, \"parameter\": {\"MAX_N\": 33, \"N\": 26, \"MOD\": 662603, \"reference_answer\": 140004}, \"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 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\": 119, \"parameter\": {\"MAX_N\": 33, \"N\": 33, \"MOD\": 299891, \"reference_answer\": 261903}, \"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 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\": 120, \"parameter\": {\"MAX_N\": 33, \"N\": 20, \"MOD\": 259933, \"reference_answer\": 239236}, \"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 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\": 121, \"parameter\": {\"MAX_N\": 33, \"N\": 6, \"MOD\": 228751, \"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 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\": 122, \"parameter\": {\"MAX_N\": 33, \"N\": 20, \"MOD\": 223415, \"reference_answer\": 36373}, \"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 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\": 123, \"parameter\": {\"MAX_N\": 33, \"N\": 5, \"MOD\": 280681, \"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 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\": 124, \"parameter\": {\"MAX_N\": 33, \"N\": 12, \"MOD\": 574889, \"reference_answer\": 436055}, \"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 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\": 125, \"parameter\": {\"MAX_N\": 33, \"N\": 32, \"MOD\": 254595, \"reference_answer\": 130372}, \"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 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\": 126, \"parameter\": {\"MAX_N\": 33, \"N\": 22, \"MOD\": 63145, \"reference_answer\": 56573}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 22 vertices labeled from 1 to 22. 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\": 127, \"parameter\": {\"MAX_N\": 33, \"N\": 5, \"MOD\": 956685, \"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 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\": 128, \"parameter\": {\"MAX_N\": 33, \"N\": 31, \"MOD\": 248145, \"reference_answer\": 234633}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 31 vertices labeled from 1 to 31. 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\": 129, \"parameter\": {\"MAX_N\": 33, \"N\": 22, \"MOD\": 910197, \"reference_answer\": 894978}, \"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 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\": 130, \"parameter\": {\"MAX_N\": 33, \"N\": 20, \"MOD\": 446133, \"reference_answer\": 248337}, \"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 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\": 131, \"parameter\": {\"MAX_N\": 33, \"N\": 14, \"MOD\": 390543, \"reference_answer\": 323959}, \"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 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\": 132, \"parameter\": {\"MAX_N\": 33, \"N\": 17, \"MOD\": 163343, \"reference_answer\": 131963}, \"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 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\": 133, \"parameter\": {\"MAX_N\": 33, \"N\": 19, \"MOD\": 371707, \"reference_answer\": 242718}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 19 vertices labeled from 1 to 19. 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\": 134, \"parameter\": {\"MAX_N\": 33, \"N\": 19, \"MOD\": 548543, \"reference_answer\": 518840}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 19 vertices labeled from 1 to 19. 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\": 135, \"parameter\": {\"MAX_N\": 33, \"N\": 25, \"MOD\": 391733, \"reference_answer\": 304835}, \"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 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\": 136, \"parameter\": {\"MAX_N\": 33, \"N\": 22, \"MOD\": 449681, \"reference_answer\": 249151}, \"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 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\": 137, \"parameter\": {\"MAX_N\": 33, \"N\": 6, \"MOD\": 190415, \"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 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\": 138, \"parameter\": {\"MAX_N\": 33, \"N\": 10, \"MOD\": 400457, \"reference_answer\": 45957}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 10 vertices labeled from 1 to 10. Every pair of vertices is co...
<\|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\": 139, \"parameter\": {\"MAX_N\": 33, \"N\": 4, \"MOD\": 728749, \"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...