From the late Martin Gardner comes the following maths/chess problem.
A chessboard has squares that are 5cm on each side. What is the radius of the largest circle that can be drawn on the board in such a way that the circle's circumference is entirely on black squares?
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If you place the centre of the circle in the middle of a white square with the circumference intersecting its corners, the raduis would be one half root 50. But you can get a bigger circle if you place the centre of the circle at the centre of a black square with the circumference intersecting the far corners of the adjacent white squares, in which case the radius is root 72.5.
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