The Hole in One Pizza

In a recent issue of Crux, at the end of the editorial (which is public), it appears the following very nice problem by Peter Liljedahl.

rectangular pizza with a circular hole

I couldn’t resist sharing it with the MSE community. Enjoy!

Answer

Nice riddle! My solution would be to cut along a line through the center of the circle and the center of the rectangle.

Proof.

A cut through the center of a circle divides it into pices of equal size. The same holds for rectangles. Therefore everyone gets the same amount of pizza minus the same “amount of hole”.

It amazed me that this works for pizzas and holes of even stranger shapes as long as they are point-symmetric. In this way one can make the riddle even more interesting, e.g. an elliptic pizza with a hole in the shape of a 6-armed star.

Attribution
Source : Link , Question Author : Robert Z , Answer Author : M. Winter

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