Making the Cut

The solution

Photograph by John B. Carnett

The minimum cuts required to produce 7, 11, and 16 slices in the 3 cakes are 3, 4, and 5, for a total of 12 cuts and
34 pieces. Each new cut must traverse all the lines already cut, and at least some must avoid the center of the cake.

This can be considered the minimal “best” solution, but there are other solutions that could make greater use of more conventional cuts-where all cuts pass through a single point. For example, the cakes could be cut by 2 conventional, 4 conventional, and 6 unconventional cuts respectively into 4, 8, and 22 slices.

For identical slices, each cake must be cut 6 times, into 12 slices each. “That leaves two extra slices, one for you and one for me,” says Moscovich.

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