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Boltyanski's Cake Problem

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Cut a cake into two pieces to put into a box:
2α = 3β: first way
2α = 3β: second way
α = 90°
​
α = 3β
​
α = 2β < 90°
α = 2β > 90°
Cut a cake into three pieces.
time
V. G. Boltyansky's problem (1977) states: given a cake in the form of a triangle and a box that fits the mirror image of the cake, cut the cake into a minimal number of pieces so that it can be put into the box. The cake has icing on top, so we are not allowed to put it into the box upside down. Examples of cakes that can be cut into two to put into the box are given in this Demonstration. Any cake can be cut into three pieces to put into the box.
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