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

Provider / transport error

The request did not complete normally.

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

21,487

Gemini 3.5 Flash

8,356

Solar Pro 3

7,589

DeepSeek V4 Pro

6,235

Claude Opus 4.8

3,554

GPT-5.5

1,173

KT Mi:dm 2.0 Base Instruct

1,150