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integers 0-n, into unit squares such that sum of integers 2x2 differ

Source: JBMO Shortlist 2015 C1

April 24, 2019
combinatoricsgridtableSquares

Problem Statement

A board n×n n \times n (n≥3n \ge 3) is divided into n2n^2 unit squares. Integers from OO to nn included, are written down: one integer in each unit square, in such a way that the sums of integers in each 2×22\times 2 square of the board are different. Find all nn for which such boards exist.
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