API · no tools. This is the prompt and response recorded for this attempt; a full solution may not have been returned.
Problem Statement
Return a single integer only. The problem has been revised so that no final answer is an irrational number, a parameterized expression, a range, a proof, a drawing, a graph, a locus equation, or a region description.
In the setting of the original midpoint-angle problem, the condition leads to a positive value satisfying
Instead of giving this irrational value, compute the integer
Ground Truth
6
Recorded model response / solution
Reasoning Process
\boxed{6}
Final Model Output
6
Comparative Analysis (P2) (Average across runs)
Averages use reported measurements only. Missing usage is not treated as zero.
Avg Time Taken
DeepSeek V4 Pro
10.2
K-EXAONE-236B-A23B
8.7
Gemini 3.5 Flash
4.3
GPT-5.5
4.0
Solar Pro 3
2.5
Claude Opus 4.8
2.4
KT Mi:dm 2.0 Base Instruct
1.0
Avg Token Usage
K-EXAONE-236B-A23B
1484.7
KT Mi:dm 2.0 Base Instruct
969.0
Gemini 3.5 Flash
892.3
Solar Pro 3
511.7
DeepSeek V4 Pro
400.0
Claude Opus 4.8
348.0
GPT-5.5
294.7