Problem Analysis #4

DeepSeek V4 Pro · Run 1

Error · counted as incorrect

Time not reported

Tokens not reported

API · no tools. This is the prompt and response recorded for this attempt; a full solution may not have been returned.

This attempt timed out or failed at the API. It counts as incorrect.

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.

In three-dimensional space, take $A(0,1,1)$ and $O(0,0,0)$ . Let $P$ be a point on the $xy$ -plane satisfying

OP=2,\qquad \angle AOP\ge \frac{2\pi}{3},\qquad \angle OAP\le \frac{\pi}{3}.

Let $L$ be the total arc length of the set of all possible points $P$ . If $L=p\pi/q$ in lowest terms, find $p+q$ .

Ground Truth

Recorded model response / solution

No model response was recorded for this attempt.

Final Model Output

No final answer recorded

Comparative Analysis (P4) (Average across runs)

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

Avg Time Taken

K-EXAONE-236B-A23B

163.3

DeepSeek V4 Pro

97.8

Solar Pro 3

49.5

Gemini 3.5 Flash

33.8

Claude Opus 4.8

33.0

GPT-5.5

21.3

KT Mi:dm 2.0 Base Instruct

1.5

Avg Token Usage

K-EXAONE-236B-A23B

21487.0

Gemini 3.5 Flash

8355.7

Solar Pro 3

7589.0

DeepSeek V4 Pro

6235.0

Claude Opus 4.8

3554.3

GPT-5.5

1173.0

KT Mi:dm 2.0 Base Instruct

1150.0