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Source labels openChecked July 26, 2026

Erdős ProblemsCombinatorics

Erdős Problem 835

Does there exist a k>2k>2 such that the kk-sized subsets of {1,...,2k} can be coloured with k+1k+1 colours such that for every A{1,,2k}A\subset \{1,\ldots,2k\} with A=k+1\lvert A\rvert=k+1 all k+1k+1 colours appear among the kk-sized subsets of AA?

Mathematical statement

Does there exist a k>2k>2 such that the kk-sized subsets of {1,...,2k} can be coloured with k+1k+1 colours such that for every A{1,,2k}A\subset \{1,\ldots,2k\} with A=k+1\lvert A\rvert=k+1 all k+1k+1 colours appear among the kk-sized subsets of AA?

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_835

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_835 : ( k > 2, Property k)  answer(sorry) := by  sorry
Statement source
Formal Conjectures
Lean version
v4.27.0
Placeholder
Present; no proof artifact
Source evidence
Pinned source index
Fidelity review
Community formulation

References