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2,625
AlmostCompleteGraphCycleCounting
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 vertices, - Conta...
<think> Okay, let's try to figure out how to find the number of simple cycles in this graph. The graph has 31 vertices, all connected except for the edge between vertex 1 and 31. So, normally, without any missing edges, a complete graph on 31 vertices would have C(31, 2) edges, which is 31*30/2 = 465. But since we're m...
{"environment": "AlmostCompleteGraphCycleCounting", "config": {"seed": 0, "parameter": {"MAX_N": 33, "N": 31, "MOD": 403961, "reference_answer": 290960}, "passing_reward_threshold": 1.0}}
290960
0
0
1
1,249
AlmostCompleteGraphCycleCounting
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 vertices, - Conta...
<think> Okay, let's try to figure out how to find the number of simple cycles in this graph. The graph has 31 vertices, all connected except for the edge between vertex 1 and 31. So, normally, without any missing edges, a complete graph on 31 vertices would have C(31, 2) edges, which is 31*30/2 = 465. But since we're m...
{"environment": "AlmostCompleteGraphCycleCounting", "config": {"seed": 0, "parameter": {"MAX_N": 33, "N": 31, "MOD": 403961, "reference_answer": 290960}, "passing_reward_threshold": 1.0}}
290960
0
0
2
2,811
AlmostCompleteGraphCycleCounting
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 vertices, - Conta...
<think> Okay, let's try to figure out how to find the number of simple cycles in this graph. The graph has 31 vertices, all connected except for the edge between vertex 1 and 31. So, normally, without any missing edges, a complete graph on 31 vertices would have C(31, 2) edges, which is 31*30/2 = 465. But since we're m...
{"environment": "AlmostCompleteGraphCycleCounting", "config": {"seed": 0, "parameter": {"MAX_N": 33, "N": 31, "MOD": 403961, "reference_answer": 290960}, "passing_reward_threshold": 1.0}}
290960
0
0
3
2,568
AlmostCompleteGraphCycleCounting
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 vertices, - Conta...
<think> Okay, let's try to figure out how to find the number of simple cycles in this graph. The graph has 31 vertices, all connected except for the edge between vertex 1 and 31. So, normally, without any missing edges, a complete graph on 31 vertices would have C(31, 2) edges, which is 31*30/2 = 465. But since we're m...
{"environment": "AlmostCompleteGraphCycleCounting", "config": {"seed": 0, "parameter": {"MAX_N": 33, "N": 31, "MOD": 403961, "reference_answer": 290960}, "passing_reward_threshold": 1.0}}
290960
0
0
4
850
AlmostCompleteGraphCycleCounting
"Consider a graph with 31 vertices labeled from 1 to 31. Every pair of vertices is connected by an u(...TRUNCATED)
"<think>\nOkay, let's try to figure out how to find the number of simple cycles in this graph. The g(...TRUNCATED)
"{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 0, \"parameter\": {\(...TRUNCATED)
290960
0
0
5
4,082
AlmostCompleteGraphCycleCounting
"Consider a graph with 31 vertices labeled from 1 to 31. Every pair of vertices is connected by an u(...TRUNCATED)
"<think>\nOkay, let's try to figure out how to find the number of simple cycles in this graph. The g(...TRUNCATED)
"{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 0, \"parameter\": {\(...TRUNCATED)
290960
0
0
6
1,526
AlmostCompleteGraphCycleCounting
"Consider a graph with 31 vertices labeled from 1 to 31. Every pair of vertices is connected by an u(...TRUNCATED)
"<think>\nOkay, let's try to figure out how to find the number of simple cycles in this graph. The g(...TRUNCATED)
"{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 0, \"parameter\": {\(...TRUNCATED)
290960
0
0
7
3,294
AlmostCompleteGraphCycleCounting
"Consider a graph with 31 vertices labeled from 1 to 31. Every pair of vertices is connected by an u(...TRUNCATED)
"<think>\nOkay, let's try to figure out how to find the number of simple cycles in this graph. The g(...TRUNCATED)
"{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 0, \"parameter\": {\(...TRUNCATED)
290960
0
0
8
1,738
AlmostCompleteGraphCycleCounting
"Consider a graph with 31 vertices labeled from 1 to 31. Every pair of vertices is connected by an u(...TRUNCATED)
"<think>\nOkay, let's try to figure out how to find the number of simple cycles in this graph. The g(...TRUNCATED)
"{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 0, \"parameter\": {\(...TRUNCATED)
290960
0
0
9
1,099
AlmostCompleteGraphCycleCounting
"Consider a graph with 31 vertices labeled from 1 to 31. Every pair of vertices is connected by an u(...TRUNCATED)
"<think>\nOkay, let's try to figure out how to find the number of simple cycles in this graph. The g(...TRUNCATED)
"{\"environment\": \"AlmostCompleteGraphCycleCounting\", \"config\": {\"seed\": 0, \"parameter\": {\(...TRUNCATED)
290960
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