Three cooks have each paid one third to purchase a bag of herbs. In the past, two of the cooks have divided their purchases in the following manner:
First one cook would divide the herb, by eye, into two piles she considered to be equal. The second cook would then choose the pile she thought was bigger.
By what process may the three cooks divide their herbs in such a way that each was content that she had recieved at least one third of the total?
(No scales or other devices are available to assist the division)
After reading the problem, this is what first came into my mind in case I was in a situation like this.
1. The cooks divide the piles in an unequal manner. It doesn't matter at this stage. Let's say for convenience that the herbs are divided into piles of 2/10, 3/10 an 5/10.
2. They assign each of these piles to each cook.
3. Every cook has to divide her pile in what she perceives are 3 equal shares.
4. Then each one of the cooks picks up one of the 3 equal perceived shares of the other cook's piles. They are able to choose fisrt from one cook and second from the other.
To make it clearer. Let's say that cook A had to divide the pile with 2/10 of the original bag of herbs, cook B the 3/10 and cook C the 5/10.
Then cook A can choose first one share from cook B pile and second from cook C pile. Cook B can choose first from cook C pile and second from cook A pile. Cook C can choose first from cook A and second from cook B.
In the end the 2 shares that every cook have chosen will add up with the one that remained to her, in order to be a somewhat fair 1/3 of the bag.

Posted by Magda
on 20060220 10:43:38 