You are holding a party for some of your fussiest friends. For starters, they are adamant about being treated equally. And they all love cake. For the occasion, you've purchased a frosted cake.
Since you want to make sure that each of your friends gets exactly the same amount of cake and frosting in their slice, you ordered a cake with frosting on the top and sides.
When the time comes to serve dessert, if you have invited N people, how do you cut the square cake into N pieces so that each person gets an equal amount of cake as well as an equal amount of frosting?
If you can solve that, try a more difficult case: what if the cake is rectangular? Say 6 by 12 inches? With N people attending the party, how can you cut the rectangular cake into N pieces so that each person still gets an equal amount of cake as well as an equal amount of frosting?
FYI: Although this problem may appear simple at first, the solution is actually fairly complex.
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