Problem Analysis #21

GPT-5.5 · Run 1

Correct
13.32s
705 toks

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.

From the 1515 lattice points

{(x,y):x,y∈Z, 1≤x≤3,1≤y≤5},\{(x,y):x,y\in\mathbb Z,\ 1\le x\le3, 1\le y\le5\},

choose three distinct points uniformly at random. Let p5p_5 be the probability that the three chosen points are the vertices of a triangle. If p5=p/qp_5=p/q in lowest terms, find p+qp+q.

Ground Truth
867
Recorded model response / solution
Reasoning Process

\boxed{867}

Final Model Output
867

Comparative Analysis (P21) (Average across runs)

Averages use reported measurements only. Missing usage is not treated as zero.

Avg Time Taken

K-EXAONE-236B-A23B
122.0
DeepSeek V4 Pro
93.8
Solar Pro 3
61.7
Gemini 3.5 Flash
19.0
Claude Opus 4.8
14.5
GPT-5.5
13.5
KT Mi:dm 2.0 Base Instruct
2.7

Avg Token Usage

K-EXAONE-236B-A23B
17431.0
Solar Pro 3
9212.3
DeepSeek V4 Pro
5621.7
Gemini 3.5 Flash
4505.0
KT Mi:dm 2.0 Base Instruct
1601.7
Claude Opus 4.8
1420.7
GPT-5.5
714.7
    Tokyo · Problem 21 · GPT-5.5 | EntropyMath