A well-known method of dividing a cake between two people is to have the first person to cut the cake and have the second person to have the first pick. This will guarantee that the first person will cut the cake in half so that the second person cannot leave him with a smaller piece.

Now we want to divide the cake among n people. Let's make the following assumptions:
(a) Each person cannot cut the cake more than once
(b) Everyone is logical
(c) Everyone wishes to get the largest possible piece
(d) Everyone wishes to narrow the gap with those who have a bigger piece than he does
(e) No one cares about anyone who has a smaller piece than themselves.

Can you generalize the strategy to n people? Give your logical steps/proof that this strategy will yield a fair result.

(In reply to Question by Penny)

An Internet search turns up games of various rules.

Would these rules work (e.g. for 5 players) ?

Only vertical cuts are allowed.

Emory divides the cake into two pieces. Franklin divides one of the two pieces. Gibson divides one of the three pieces. Hobson divides one of the four pieces. Ingrams takes the largest of the five pieces. Emory takes the largest of the remaining four pieces. Franklin takes the largest of the remaining three pieces. Gibson takes the largest of the remaining two pieces. Hobson is left with the remaining piece.   

Posted by Penny on 2004-12-27 18:03:59