21. Suppose that Bob is entitled to one-fourth of a cake and Carol is entitled to three-fourths. In a few sentences, explain how divide-and-choose can be used to achieve an allocation in which each party is guaranteed to receive at least as much as he or she is entitled to.
21.
One way is to have Bob divide the cake into four pieces and to let Carol choose any three. Another is to have Bob divide the cake into two pieces and then let Carol choose one. They can do divide-and-choose on the piece that Carol did not choose.