Problem Analysis #0

Kanana-2-30B-Thinking · Run 1

92.89s
13,303 toks
Problem Statement

Let X be the group generated by uu and vv, such that

X=\langle u, v \mid u^{46} = 1, v^{40,488,236} = 1, vu = uv^{27,636,633} \rangle $$. What is the order of the group X?
Ground Truth
184
Execution Trace
Reasoning Process

[THOUGHT] We will compute the order of the group X as twice the exponent of v, since the group is a dihedral group of order 2 * 40488236. [/THOUGHT] [PYTHON] print(2 * 40488236) [/PYTHON]

Tool Output
[PYTHON OUTPUT] 80976472 [/PYTHON OUTPUT]
Reasoning Process

[THOUGHT] The Python code executed in the previous step output 80976472, which is the order of the group X. This result is derived from the relation v^{40488236} = 1, and the group is interpreted as having order twice the exponent of v, consistent with the dihedral group structure implied in the initial approach. The final answer is based on the tool's output. [/THOUGHT] 80976472\boxed{80976472}

Final Model Output
80976472

Comparative Analysis (P0) (Average across runs)

Avg Time Taken

Solar-Open-100B
927.7
K-EXAONE-236B-A23B
261.4
Kanana-2-30B-Thinking
94.3
GLM-4.5-Air
89.6
Gemini-3-Pro-Preview
83.6
Kanana-2-30B-Thinking-2601
73.2
Solar-Pro 2
63.9
GPT-5.2 (high)
44.4
HCX-007
31.0
EXAONE-4.0-32B
3.8

Avg Token Usage

Solar-Open-100B
49491.3
K-EXAONE-236B-A23B
19786.0
Kanana-2-30B-Thinking-2601
16432.3
Kanana-2-30B-Thinking
13797.7
Solar-Pro 2
13080.0
Gemini-3-Pro-Preview
11033.7
GLM-4.5-Air
9584.0
GPT-5.2 (high)
4265.7
HCX-007
4078.0
EXAONE-4.0-32B
3113.7