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. 



I couldn't resist sharing it with the MSE community. Enjoy!
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". $\square$

$\qquad$ 

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.
Lay both pizza's one on top of the other and cut through the whole so that it sliced in half.
Each person get a slice from the pizza with the whole and the remainder of the other pizza.
So the exterior area of the pizzas are equal and the share of the whole is equal.