Given a positive integer n≥3, colour each cell of an n×n square array with one of ⌊(n+2)2/3⌋ colours, each colour being used at least once. Prove that there is some 1×3 or 3×1 rectangular subarray whose three cells are coloured with three different colours.(Russia) Ilya Bogdanov, Grigory Chelnokov, Dmitry Khramtsov floor functionceiling functiongeometryrectanglecombinatorics proposedcombinatoricsdouble counting