Problem Analysis #28

DeepSeek V4 Pro · Run 1

Correct
125.70s
8,757 toks

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

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.

Let a=3/5a=3/5, and define

f(x)=a8(x−1)2+2a−3.f(x)=\frac{a}{8}(x-1)^2+\frac{2}{a}-3.

For every integer nn, define the periodic triangular-wave function gg by

g(x)={x−2n,2n≤x<2n+1,−x+2n+2,2n+1≤x<2n+2.g(x)= \begin{cases} x-2n,&2n\le x<2n+1,\\ -x+2n+2,&2n+1\le x<2n+2. \end{cases}

Find the number of intersection points of y=f(x)y=f(x) and y=g(x)y=g(x) in the range x≥0x\ge0.

Ground Truth
4
Recorded model response / solution
Reasoning Process

4\boxed{4}

Final Model Output
4

Comparative Analysis (P28) (Average across runs)

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

Avg Time Taken

K-EXAONE-236B-A23B
154.8
DeepSeek V4 Pro
110.5
Solar Pro 3
41.0
Gemini 3.5 Flash
24.8
GPT-5.5
24.4
Claude Opus 4.8
21.8
KT Mi:dm 2.0 Base Instruct
3.3

Avg Token Usage

K-EXAONE-236B-A23B
18,781
DeepSeek V4 Pro
7,326
Solar Pro 3
6,956
Gemini 3.5 Flash
6,012
Claude Opus 4.8
2,484
KT Mi:dm 2.0 Base Instruct
1,793
GPT-5.5
1,457
    Tokyo · Problem 28 · DeepSeek V4 Pro | EntropyMath