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.

This problem is easily solvable, but needs more clarification. For example, does the second person cut and choose, or does the cutting continue until everybody has cut, and then the choosing begins? Also, if cake is chosen before all the cutting is done, is the cake off limits, or can it be cut after it has been taken? For example, if the nth person can redistribute cake that has already been taken, the solution is different, and so on.  

Posted by Eric on 2004-12-27 16:56:50