Problem Analysis #17

GPT-5.5 · Run 1

Correct

10.72s

576 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.

A square number means the square of a nonnegative integer. Let

h(n)=n^2+12n-12.

Find the number of positive integers $n$ for which $h(n)$ is a square number.

Ground Truth

Recorded model response / solution

Reasoning Process

\boxed{3}

Final Model Output

Comparative Analysis (P17) (Average across runs)

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

Avg Time Taken

K-EXAONE-236B-A23B

86.8

DeepSeek V4 Pro

25.3

GPT-5.5

9.9

Gemini 3.5 Flash

8.8

Solar Pro 3

6.2

Claude Opus 4.8

4.6

KT Mi:dm 2.0 Base Instruct

2.9

Avg Token Usage

K-EXAONE-236B-A23B

10194.7

Gemini 3.5 Flash

2192.0

DeepSeek V4 Pro

1626.7

KT Mi:dm 2.0 Base Instruct

1601.0

Solar Pro 3

1105.7

Claude Opus 4.8

575.3

GPT-5.5

557.7