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 original parametric-plane problem, one required value is . If this value is in lowest terms, find .
Ground Truth
8
Recorded model response / solution
Reasoning Process
\boxed{8}
Final Model Output
8
Comparative Analysis (P14) (Average across runs)
Averages use reported measurements only. Missing usage is not treated as zero.
Avg Time Taken
K-EXAONE-236B-A23B
24.3
DeepSeek V4 Pro
8.6
GPT-5.5
4.7
Claude Opus 4.8
3.7
Gemini 3.5 Flash
3.6
Solar Pro 3
2.7
KT Mi:dm 2.0 Base Instruct
0.6
Avg Token Usage
KT Mi:dm 2.0 Base Instruct
856.0
K-EXAONE-236B-A23B
681.0
Gemini 3.5 Flash
676.3
Solar Pro 3
573.7
DeepSeek V4 Pro
458.7
GPT-5.5
299.3
Claude Opus 4.8
217.0