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<\|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\": 900, \"parameter\": {\"MAX_N\": 33, \"N\": 33, \"MOD\": 654403, \"reference_answer\": 530692}, \"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 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\": 901, \"parameter\": {\"MAX_N\": 33, \"N\": 17, \"MOD\": 691869, \"reference_answer\": 356099}, \"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\": 902, \"parameter\": {\"MAX_N\": 33, \"N\": 12, \"MOD\": 678363, \"reference_answer\": 356010}, \"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 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\": 903, \"parameter\": {\"MAX_N\": 33, \"N\": 5, \"MOD\": 704877, \"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 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\": 904, \"parameter\": {\"MAX_N\": 33, \"N\": 26, \"MOD\": 948011, \"reference_answer\": 578544}, \"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\": 905, \"parameter\": {\"MAX_N\": 33, \"N\": 25, \"MOD\": 362563, \"reference_answer\": 346805}, \"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 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\": 906, \"parameter\": {\"MAX_N\": 33, \"N\": 4, \"MOD\": 281765, \"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 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\": 907, \"parameter\": {\"MAX_N\": 33, \"N\": 26, \"MOD\": 422393, \"reference_answer\": 109697}, \"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 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\": 908, \"parameter\": {\"MAX_N\": 33, \"N\": 24, \"MOD\": 36641, \"reference_answer\": 11571}, \"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\": 909, \"parameter\": {\"MAX_N\": 33, \"N\": 10, \"MOD\": 696235, \"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 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\": 910, \"parameter\": {\"MAX_N\": 33, \"N\": 23, \"MOD\": 643969, \"reference_answer\": 330472}, \"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 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\": 911, \"parameter\": {\"MAX_N\": 33, \"N\": 18, \"MOD\": 409019, \"reference_answer\": 242556}, \"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 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\": 912, \"parameter\": {\"MAX_N\": 33, \"N\": 20, \"MOD\": 777305, \"reference_answer\": 349818}, \"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 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\": 913, \"parameter\": {\"MAX_N\": 33, \"N\": 7, \"MOD\": 16943, \"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 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\": 914, \"parameter\": {\"MAX_N\": 33, \"N\": 5, \"MOD\": 314867, \"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 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\": 915, \"parameter\": {\"MAX_N\": 33, \"N\": 9, \"MOD\": 327015, \"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 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\": 916, \"parameter\": {\"MAX_N\": 33, \"N\": 25, \"MOD\": 613131, \"reference_answer\": 428044}, \"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 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\": 917, \"parameter\": {\"MAX_N\": 33, \"N\": 31, \"MOD\": 788455, \"reference_answer\": 55003}, \"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 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\": 918, \"parameter\": {\"MAX_N\": 33, \"N\": 31, \"MOD\": 748905, \"reference_answer\": 729813}, \"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 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\": 919, \"parameter\": {\"MAX_N\": 33, \"N\": 25, \"MOD\": 545101, \"reference_answer\": 425993}, \"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 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\": 920, \"parameter\": {\"MAX_N\": 33, \"N\": 23, \"MOD\": 331971, \"reference_answer\": 50509}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 23 vertices labeled from 1 to 23. Every pair of vertices is co...
<\|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\": 921, \"parameter\": {\"MAX_N\": 33, \"N\": 33, \"MOD\": 364135, \"reference_answer\": 30367}, \"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 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\": 922, \"parameter\": {\"MAX_N\": 33, \"N\": 5, \"MOD\": 530959, \"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\": 923, \"parameter\": {\"MAX_N\": 33, \"N\": 30, \"MOD\": 501705, \"reference_answer\": 129762}, \"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 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\": 924, \"parameter\": {\"MAX_N\": 33, \"N\": 22, \"MOD\": 795377, \"reference_answer\": 437980}, \"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 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\": 925, \"parameter\": {\"MAX_N\": 33, \"N\": 32, \"MOD\": 97789, \"reference_answer\": 75493}, \"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 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\": 926, \"parameter\": {\"MAX_N\": 33, \"N\": 24, \"MOD\": 441119, \"reference_answer\": 361181}, \"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 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\": 927, \"parameter\": {\"MAX_N\": 33, \"N\": 24, \"MOD\": 982169, \"reference_answer\": 385772}, \"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 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\": 928, \"parameter\": {\"MAX_N\": 33, \"N\": 13, \"MOD\": 426815, \"reference_answer\": 30199}, \"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 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\": 929, \"parameter\": {\"MAX_N\": 33, \"N\": 10, \"MOD\": 556543, \"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 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\": 930, \"parameter\": {\"MAX_N\": 33, \"N\": 20, \"MOD\": 836493, \"reference_answer\": 729609}, \"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 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\": 931, \"parameter\": {\"MAX_N\": 33, \"N\": 29, \"MOD\": 444579, \"reference_answer\": 46695}, \"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 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\": 932, \"parameter\": {\"MAX_N\": 33, \"N\": 20, \"MOD\": 859593, \"reference_answer\": 280461}, \"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 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\": 933, \"parameter\": {\"MAX_N\": 33, \"N\": 20, \"MOD\": 596241, \"reference_answer\": 513663}, \"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 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\": 934, \"parameter\": {\"MAX_N\": 33, \"N\": 18, \"MOD\": 260431, \"reference_answer\": 98347}, \"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 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\": 935, \"parameter\": {\"MAX_N\": 33, \"N\": 30, \"MOD\": 718969, \"reference_answer\": 573890}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 30 vertices labeled from 1 to 30. Every pair of vertices is c...
<\|im_start\|>user Consider a graph with 8 vertices labeled from 1 to 8. Every pair of vertices is connected by an undirected edge, except for the edge between vertices 1 and 8 (so the graph has 8 × (8 - 1) / 2 - 1 edges). What's the number of simple cycles in this graph? A simple cycle must: - Have at least 3 verti...	AlmostCompleteGraphCycleCounting	{"metadata": "{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 936, \"parameter\": {\"MAX_N\": 33, \"N\": 8, \"MOD\": 981521, \"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 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\": 937, \"parameter\": {\"MAX_N\": 33, \"N\": 21, \"MOD\": 140163, \"reference_answer\": 137493}, \"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 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\": 938, \"parameter\": {\"MAX_N\": 33, \"N\": 18, \"MOD\": 523613, \"reference_answer\": 379784}, \"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 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\": 939, \"parameter\": {\"MAX_N\": 33, \"N\": 33, \"MOD\": 102207, \"reference_answer\": 57427}, \"passing_reward_threshold\": 1.0}}", "prompt": "Consider a graph with 33 vertices labeled from 1 to 33. Every pair of vertices is co...