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'Triominoes' printed from

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A triomino is a flat L shape made from 3 square tiles.

A chess board is marked into squares the same size as the tiles and just one square, anywhere on the board, is coloured red.

Chess boards for this game are of size 2 k by 2 k where k is any whole number

For example 2 by 2, 4 by 4, 8 by 8 etc.

The aim is to cover the board with triominoes, not overlapping, so that only the red square, wherever it is, is exposed. Is this possible? Investigate. Explain.