Problem Analysis #8

HCX-007 · Run 3

18.27s
3,052 toks
Problem Statement

For two vectors u,v∈Zqn\mathbf{u}, \mathbf{v}\in\mathbb{Z}_q^n, the Fixed Length Levenshtein distance between u\mathbf{u} and v\mathbf{v} is defined as the smallest number tt such that u\mathbf{u} can be transformed to v\mathbf{v} through tt deletions and tt insertions. \nFind the maximum size of the balls of radius 11 in Z2100\mathbb{Z}_2^{100} centered at x∈Z2100\mathbf{x}\in\mathbb{Z}_2^{100}.

Ground Truth
8736
Execution Trace
Reasoning Process
# Radius is 1 in Z_2^100. Number of neighbors per vector is 100. Plus self. Total is 1 + 100 = 101
print(1 + 100)
Tool Output
[PYTHON OUTPUT] 101 [/PYTHON OUTPUT]
Reasoning Process

[THOUGHT] In Z2100\mathbb{Z}_2^{100}, each element is a binary vector of length 100. A ball of radius 1 around a vector x\mathbf{x} contains x\mathbf{x} along with all vectors that differ from x\mathbf{x} by exactly one bit. There are 100 bits that can change independently, plus the original vector, resulting in 101 total vectors in the ball. This matches the verified Python outcome. [/THOUGHT] 101\boxed{101}[THOUGHT] In Z2100\mathbb{Z}_2^{100}, each element is a binary vector of length 100. A ball of radius 1 around a vector x\mathbf{x} contains x\mathbf{x} along with all vectors that differ from x\mathbf{x} by exactly one bit. There are 100 bits that can change independently, plus the original vector, resulting in 101 total vectors in the ball. This matches the verified Python outcome. [/THOUGHT] 101\boxed{101}

Final Model Output
101

Comparative Analysis (P8) (Average across runs)

Avg Time Taken

Gemini-3-Pro-Preview
281.3
K-EXAONE-236B-A23B
267.7
Solar-Open-100B
197.1
GPT-5.2 (high)
146.1
Kanana-2-30B-Thinking
112.4
Solar-Pro 2
88.0
Kanana-2-30B-Thinking-2601
31.6
HCX-007
25.8
GLM-4.5-Air
24.2
EXAONE-4.0-32B
3.4

Avg Token Usage

K-EXAONE-236B-A23B
52,940
Gemini-3-Pro-Preview
46,314
Solar-Open-100B
29,632
Solar-Pro 2
16,976
Kanana-2-30B-Thinking
15,621
GPT-5.2 (high)
11,534
Kanana-2-30B-Thinking-2601
7,838
GLM-4.5-Air
4,557
HCX-007
3,606
EXAONE-4.0-32B
3,151