Check out this fun article at Chessbase:
A Mathematical Chessboard Paradox
24.03.2009 – In Germany 2008 was the “Year of Mathematics”, and at the same time there was a Chess World Championship and a Chess Olympiade in the country. Reason enough to take a look at an interesting problem at the interface of these two intellectual activities. It is a fascinating paradox which seems to prove that 64 is equal to 65 simply by cutting up a chessboard. Prof. Christian Hesse explains.
Chess Expeditions
By Prof. Christian Hesse
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