Does there exist a $k > 2$ such that the $k$ -sized subsets of ${1, \dots, 2 k}$ can be coloured with $k + 1$ colours such that for every $A \subset {1, \dots, 2 k}$ with $∣ A ∣ = k + 1$ all $k + 1$ colours appear among the $k$ -sized subsets of $A$ ?

Worked, still open.

graph theory · open · formalized (Lean) · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

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

This is (as of **31 Dec 2025 / 18 Jan 2026**) an **open problem** for general (k>2), with substantial partial results.

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

AMS 5 · open (literature)

theorem erdos_835 : (∃ k > 2, Property k) ↔ answer(sorry)

open