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Packing dominoes and other shapes

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Suppose we have a chessboard (of the usual 8-by-8 variety), and a supply of 32 dominoes (2-by-1 rectangles). It is a simple task to place the dominoes so that they cover the whole board. But now suppose instead that we have 31 dominoes, and our task is to cover the chessboard with two opposite corners removed. Can this be done?

This is an example of a `packing’ problem. Packings have given rise to some of the most beautiful and visual arguments in mathematics. In this talk we will consider some of the `classical’ theory and then move on to more recent results.

This talk is part of the Cambridge Philosophical Society series.

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