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.

so we have a cake and n persons
we line them (it doesn't mater how)

the first will cut after him a 1/n cut
the next( k person) will come and cut in such a way that it will be almost like the one before him and try to be 1/(n-k)

and so on until the n-1 person
the n person will not cut but he will chose from the n cuts
after him the first will chose from the n-1 cuts and so on until the n-1 person will take the cut that remains

evrybody is logical so that's why everybody will try to cut a fair piece
if not :
-if he cut's a bigger one there will be a person before him who will chose it
-if he cut's it to small the cake that will remain will be bigger and the first will chose it BUT everybody care's about those how have a bigger piece then him so he will try not to cut a verry small one

maybe this is a solution

Posted by Andrei on 2005-01-08 17:24:53