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Say you have a pizza with a diameter of 1 foot and with 2 straight cuts you cut it into 4 slices of equal shape and size (in the most obvious way, nothing tricky involved here). Can you fit these slices into a square box with sides smaller than 1 foot without overlap? What would such a configuration look like? (I know of two different solutions, one better (and more elegant) than the other)

Erich Friedman is looking at the general case in his Math Magic this month and the best known answers can be found here.