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IMO ShortList 2002, combinatorics problem 2

Source: IMO ShortList 2002, combinatorics problem 2

September 28, 2004
combinatoricsTilingdissectionIMO Shortlist

Problem Statement

For nn an odd positive integer, the unit squares of an n×nn\times n chessboard are coloured alternately black and white, with the four corners coloured black. A it tromino is an LL-shape formed by three connected unit squares. For which values of nn is it possible to cover all the black squares with non-overlapping trominos? When it is possible, what is the minimum number of trominos needed?
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