Problem Statement
Consider the 10$$\times$$ 10 real symmetric matrix
Calculate
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] \boxed{110000000000}
Final Model Output
110000000000
Comparative Analysis (P9) (Average across runs)
Avg Time Taken
EXAONE-4.0.1-32B (high)
1180.7
Deepseek-R1-distill-Qwen-32B (high)
114.5
Gemma-3-27B
91.9
Llama-VARCO-8B-Instruct
68.8
Solar-Pro-2 (31B)(high)
30.2
Gemini-3-Pro-Preview
24.9
Deepseek-V3.2
19.3
HCX-007(high)
16.9
Grok-4.1-fast
14.3
A.X-4.0 (72B)
13.9
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)
25940.7
Llama-VARCO-8B-Instruct
12475.0
Solar-Pro-2 (31B)(high)
6433.3
Gemini-3-Pro-Preview
4874.3
Gemma-3-27B
4846.0
Grok-4.1-fast
4259.3
Deepseek-R1-distill-Qwen-32B (high)
4045.7
A.X-4.0 (72B)
3684.7
Deepseek-V3.2
3590.0
Claude-Opus-4.5
3365.3
GPT-oss-20B (high)
3077.7
Qwen3-30B-A3B-2507
2697.0
GPT-5.1 (high)
2694.7
HCX-007(high)
1782.3