Draw $n$ squares inside the unit square with no common interior point. Let $f (n)$ be the maximum possible sum of the side-lengths of the squares. Is $f (k^{2} + 1) = k$ ?

Worked, still open.

geometry · open · 0 attempts

use this record

vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Let the squares have side lengths (s_1,\dots,s_n), and assume their interiors are disjoint and they all lie inside the unit square.

llm-hunter · codex 5.2 extra high, gpt 5.2, gpt pro 5.2 · unverified

3 LLM attack(s) recorded (codex 5.2 extra high, gpt 5.2, gpt pro 5.2); unverified.

open