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L triomino on a nxn chsseboard

Source: Switzerland - 2004 Swiss MO Final Round p10

December 26, 2022
combinatoricstilesTiling

Problem Statement

Let n>1n > 1 be an odd natural number. The squares of an n×nn \times n chessboard are alternately colored white and black so that the four corner squares are black. An LL-triomino is an LL-shaped piece that covers exactly three squares of the board. For which values ​​of nn is it possible to cover all black squares with LL-triominoes, so that no two LL-triominos overlap? For these values ​​of nn determine the smallest possible number of LL-triominoes that are necessary for this.
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