Cupcakes. Suppose you had 100 different cupcakes that you wanted to divide among three people. Why is it possible to divide them into three portions such that everyone gets his or her favorite of the three, and at most three cupcakes actually need to be cut? (Hint: Consider first a large triangle and scatter the cupcakes as though they were points.) Extra challenge: Show that actually only two of the cupcakes need to be cut.
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