Suppose you have N people and one cake. How can you cut the cake such that each person is satisfied that the pieces have been distributed fairly? This is an old problem that Martin Gardner wrote up in his column for Scientific American and in the case of two people it is quite simple: One person gets to cut the cake into two and the other person gets to select the piece they want. (But see later for a problem with this.)
But what if there are more than two people? Below the fold, I give Gardner’s explanation on how to do it, starting with the case where N=3, quoted by Walter Stromquist in an issue of The American Mathematical Monthly.