Claims

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1975_12_01_graham_selfridge: Erdős reports in his 1975 problem paper that Graham and Selfridge answered the question yes for k = 3; the report gives no argument, and no publication of one is recorded.

2025_10_17_hunter: For every k at least 3, a generic plane projection of the cube [k]^n, with n large by the Hales–Jewett theorem, has in every two-coloring a line holding at least k of its points all of one color; posted in the site's comments.

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