A domino is a 1×2 or 2×1 tile.
Let n≥3 be an integer. Dominoes are placed on an n×n board in such a way that each domino covers exactly two cells of the board, and dominoes do not overlap. The value of a row or column is the number of dominoes that cover at least one cell of this row or column. The configuration is called balanced if there exists some k≥1 such that each row and each column has a value of k. Prove that a balanced configuration exists for every n≥3, and find the minimum number of dominoes needed in such a configuration. combinatoricsdominoescoveringEGMOEGMO 2018