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Trominoes on a white and black chessboard

Source: Italy TST 2003

November 9, 2010
analytic geometryinductioncombinatorics proposedcombinatoricsHi

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 tromino is an LL-shape formed by three connected unit squares. (a)(a) For which values of nn is it possible to cover all the black squares with non-overlapping trominoes lying entirely on the chessboard? (b)(b) When it is possible, find the minimum number of trominoes needed.
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