Problem Analysis #18

Gemini 3.5 Flash · Run 1

Correct
2.88s
678 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 sequence (cn)(c_n) satisfy

c2=2,c3=4,c_2=2,\qquad c_3=4,

and for n≥4n\ge4,

cn=cn−1+cn−2.c_n=c_{n-1}+c_{n-2}.

Find c6c_6.

Ground Truth
16
Recorded model response / solution
Reasoning Process

To find c6c_6, we use the given recurrence relation cn=cn−1+cn−2c_n = c_{n-1} + c_{n-2} for n≥4n \ge 4, starting with the given values c2=2c_2 = 2 and c3=4c_3 = 4.

  1. For n=4n = 4:

    c4=c3+c2=4+2=6c_4 = c_3 + c_2 = 4 + 2 = 6

  2. For n=5n = 5:

    c5=c4+c3=6+4=10c_5 = c_4 + c_3 = 6 + 4 = 10

  3. For n=6n = 6:

    c6=c5+c4=10+6=16c_6 = c_5 + c_4 = 10 + 6 = 16

The value of c6c_6 is 16.

\boxed{16}

Final Model Output
16

Comparative Analysis (P18) (Average across runs)

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

Avg Time Taken

DeepSeek V4 Pro
5.0
K-EXAONE-236B-A23B
4.1
GPT-5.5
3.3
Gemini 3.5 Flash
3.0
Solar Pro 3
1.9
Claude Opus 4.8
1.6
KT Mi:dm 2.0 Base Instruct
0.7

Avg Token Usage

KT Mi:dm 2.0 Base Instruct
867.0
K-EXAONE-236B-A23B
706.7
Gemini 3.5 Flash
678.0
Solar Pro 3
439.0
DeepSeek V4 Pro
374.0
Claude Opus 4.8
296.0
GPT-5.5
254.3
    Tokyo · Problem 18 · Gemini 3.5 Flash | EntropyMath