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<\|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\": 500, \"parameter\": {\"MAX_N\": 33, \"N\": 29, \"MOD\": 484029, \"reference_answer\": 52740}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 29 vertices labeled from 1 to 29. Every pair of vertices is co...
<\|im_start\|>user Consider a graph with 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\": 501, \"parameter\": {\"MAX_N\": 33, \"N\": 24, \"MOD\": 296545, \"reference_answer\": 209511}, \"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 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\": 502, \"parameter\": {\"MAX_N\": 33, \"N\": 20, \"MOD\": 381125, \"reference_answer\": 80768}, \"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\": 503, \"parameter\": {\"MAX_N\": 33, \"N\": 9, \"MOD\": 159127, \"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 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\": 504, \"parameter\": {\"MAX_N\": 33, \"N\": 18, \"MOD\": 863321, \"reference_answer\": 784894}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 18 vertices labeled from 1 to 18. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 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\": 505, \"parameter\": {\"MAX_N\": 33, \"N\": 8, \"MOD\": 269335, \"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 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\": 506, \"parameter\": {\"MAX_N\": 33, \"N\": 28, \"MOD\": 821775, \"reference_answer\": 664910}, \"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 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\": 507, \"parameter\": {\"MAX_N\": 33, \"N\": 19, \"MOD\": 919913, \"reference_answer\": 697917}, \"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 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\": 508, \"parameter\": {\"MAX_N\": 33, \"N\": 21, \"MOD\": 824511, \"reference_answer\": 147657}, \"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 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\": 509, \"parameter\": {\"MAX_N\": 33, \"N\": 26, \"MOD\": 801011, \"reference_answer\": 173730}, \"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 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\": 510, \"parameter\": {\"MAX_N\": 33, \"N\": 25, \"MOD\": 845527, \"reference_answer\": 455418}, \"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 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\": 511, \"parameter\": {\"MAX_N\": 33, \"N\": 7, \"MOD\": 475465, \"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 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\": 512, \"parameter\": {\"MAX_N\": 33, \"N\": 4, \"MOD\": 854305, \"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 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\": 513, \"parameter\": {\"MAX_N\": 33, \"N\": 4, \"MOD\": 214937, \"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 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\": 514, \"parameter\": {\"MAX_N\": 33, \"N\": 15, \"MOD\": 115153, \"reference_answer\": 30072}, \"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 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\": 515, \"parameter\": {\"MAX_N\": 33, \"N\": 9, \"MOD\": 287197, \"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 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\": 516, \"parameter\": {\"MAX_N\": 33, \"N\": 30, \"MOD\": 767951, \"reference_answer\": 525079}, \"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 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\": 517, \"parameter\": {\"MAX_N\": 33, \"N\": 29, \"MOD\": 452911, \"reference_answer\": 326477}, \"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\": 518, \"parameter\": {\"MAX_N\": 33, \"N\": 30, \"MOD\": 389763, \"reference_answer\": 46134}, \"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 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\": 519, \"parameter\": {\"MAX_N\": 33, \"N\": 23, \"MOD\": 463231, \"reference_answer\": 355193}, \"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\": 520, \"parameter\": {\"MAX_N\": 33, \"N\": 4, \"MOD\": 63343, \"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\": 521, \"parameter\": {\"MAX_N\": 33, \"N\": 7, \"MOD\": 379, \"reference_answer\": 89}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 7 vertices labeled from 1 to 7. Every pair of vertices is connected b...
<\|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\": 522, \"parameter\": {\"MAX_N\": 33, \"N\": 6, \"MOD\": 245571, \"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 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\": 523, \"parameter\": {\"MAX_N\": 33, \"N\": 25, \"MOD\": 714619, \"reference_answer\": 305356}, \"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 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\": 524, \"parameter\": {\"MAX_N\": 33, \"N\": 11, \"MOD\": 11581, \"reference_answer\": 8222}, \"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 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\": 525, \"parameter\": {\"MAX_N\": 33, \"N\": 30, \"MOD\": 572091, \"reference_answer\": 98139}, \"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 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\": 526, \"parameter\": {\"MAX_N\": 33, \"N\": 8, \"MOD\": 223983, \"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 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\": 527, \"parameter\": {\"MAX_N\": 33, \"N\": 33, \"MOD\": 454757, \"reference_answer\": 442913}, \"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 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\": 528, \"parameter\": {\"MAX_N\": 33, \"N\": 29, \"MOD\": 59477, \"reference_answer\": 16312}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 29 vertices labeled from 1 to 29. Every pair of vertices is con...
<\|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\": 529, \"parameter\": {\"MAX_N\": 33, \"N\": 24, \"MOD\": 975613, \"reference_answer\": 59182}, \"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 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\": 530, \"parameter\": {\"MAX_N\": 33, \"N\": 32, \"MOD\": 344809, \"reference_answer\": 293502}, \"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 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\": 531, \"parameter\": {\"MAX_N\": 33, \"N\": 32, \"MOD\": 764985, \"reference_answer\": 24052}, \"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 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\": 532, \"parameter\": {\"MAX_N\": 33, \"N\": 10, \"MOD\": 687837, \"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\": 533, \"parameter\": {\"MAX_N\": 33, \"N\": 16, \"MOD\": 179327, \"reference_answer\": 96117}, \"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 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\": 534, \"parameter\": {\"MAX_N\": 33, \"N\": 17, \"MOD\": 932745, \"reference_answer\": 318731}, \"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 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\": 535, \"parameter\": {\"MAX_N\": 33, \"N\": 8, \"MOD\": 906329, \"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 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\": 536, \"parameter\": {\"MAX_N\": 33, \"N\": 27, \"MOD\": 200519, \"reference_answer\": 192510}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 27 vertices labeled from 1 to 27. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 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\": 537, \"parameter\": {\"MAX_N\": 33, \"N\": 27, \"MOD\": 465797, \"reference_answer\": 106116}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 27 vertices labeled from 1 to 27. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 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\": 538, \"parameter\": {\"MAX_N\": 33, \"N\": 12, \"MOD\": 311117, \"reference_answer\": 97789}, \"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 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\": 539, \"parameter\": {\"MAX_N\": 33, \"N\": 13, \"MOD\": 200879, \"reference_answer\": 30922}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 13 vertices labeled from 1 to 13. Every pair of vertices is co...