Splitting a cake so nobody feels cheated

Question

Two siblings must split a single cake with no trusted referee and no way to measure it precisely. They disagree about which parts are tastiest, so a straight down-the-middle cut won't satisfy them.

Design a procedure so that each sibling is guaranteed a piece they consider at least half the cake. Then: how would you extend it to three people, each guaranteed at least a third?

Accepted Answer

Two people: "I cut, you choose." One sibling cuts the cake into two pieces; the other sibling picks first. - The cutter, knowing they get the leftover piece, is motivated to cut two pieces they value equally, otherwise the chooser takes the bigger one and the cutter is stuck with the smaller. So the cutter guarantees themselves at least half by their own judgment. - The chooser simply takes whichever piece looks bigger to them, which is at least half by their own judgment. Neither can complain: each ended up with a piece they personally rate at \ge 	frac12. That is envy-free. Three people: t…

Splitting a cake so nobody feels cheated

Your answer

More Brainteasers questions