Problem Analysis #9

GPT-5.1 (high) · Run 1

7.44s
2,707 toks
Problem Statement

Consider the 10×1010\times 10 real symmetric matrix

A=[20101010101010101010102010101010101010101010201010101010101010101020101010101010101010102010101010101010101010201010101010101010101020101010101010101010102010101010101010101010201010101010101010101020].A = \left[ \begin{array}{cccccccccc} 20 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10\\ 10 & 20 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10\\ 10 & 10 & 20 & 10 & 10 & 10 & 10 & 10 & 10 & 10\\ 10 & 10 & 10 & 20 & 10 & 10 & 10 & 10 & 10 & 10\\ 10 & 10 & 10 & 10 & 20 & 10 & 10 & 10 & 10 & 10\\ 10 & 10 & 10 & 10 & 10 & 20 & 10 & 10 & 10 & 10\\ 10 & 10 & 10 & 10 & 10 & 10 & 20 & 10 & 10 & 10\\ 10 & 10 & 10 & 10 & 10 & 10 & 10 & 20 & 10 & 10\\ 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 20 & 10\\ 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 10 & 20 \end{array} \right].

Calculate

N:=det⁡(A).N := \det(A).
Ground Truth
110000000000
Execution Trace
Reasoning Process

[THOUGHT] I will construct the matrix in Python, compute its determinant using sympy, and print the result to verify the determinant. [/THOUGHT] [PYTHON] import sympy as sp

Construct the 10x10 matrix A

n = 10 A = sp.Matrix([[20 if i == j else 10 for j in range(n)] for i in range(n)])

Compute the determinant

detA = A.det() print(detA) [/PYTHON]

Tool Output
[PYTHON OUTPUT] 110000000000 [/PYTHON OUTPUT]
Reasoning Process

[THOUGHT] The determinant computed by Python is 110000000000, and this is the required value of N. [/THOUGHT] 110000000000\boxed{110000000000}

Final Model Output
110000000000

Comparative Analysis (P9) (Average across runs)

Avg Time Taken

EXAONE-4.0.1-32B (high)
1180.7
Solar-Open-100B
211.2
Deepseek-R1-distill-Qwen-32B (high)
114.5
Gemma-3-27B
91.9
Llama-VARCO-8B-Instruct
68.8
Kanana-2-30B-Thinking
30.8
Solar-Pro-2 (31B)(high)
30.2
Gemini-3-Pro-Preview
24.9
Kanana-2-30B-Thinking-2601
19.5
Deepseek-V3.2
19.3
HCX-007(high)
16.9
Grok-4.1-fast
14.3
A.X-4.0 (72B)
13.9
K-EXAONE-236B-A23B
13.4
GPT-oss-20B (high)
11.5
Claude-Opus-4.5
9.4
Qwen3-30B-A3B-2507
8.5
GPT-5.1 (high)
6.9

Avg Token Usage

EXAONE-4.0.1-32B (high)
25,941
Llama-VARCO-8B-Instruct
12,475
K-EXAONE-236B-A23B
8,687
Solar-Pro-2 (31B)(high)
6,433
Kanana-2-30B-Thinking
6,328
Kanana-2-30B-Thinking-2601
5,718
Gemini-3-Pro-Preview
4,874
Gemma-3-27B
4,846
Solar-Open-100B
4,475
Grok-4.1-fast
4,259
Deepseek-R1-distill-Qwen-32B (high)
4,046
A.X-4.0 (72B)
3,685
Deepseek-V3.2
3,590
Claude-Opus-4.5
3,365
GPT-oss-20B (high)
3,078
Qwen3-30B-A3B-2507
2,697
GPT-5.1 (high)
2,695
HCX-007(high)
1,782