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)

Let A divide the herbs into six piles, equal in her eyes.  Let B pick out the smallest pile in his eyes and offer it to C.  If C refuses it, it belongs to A.  Let C, then select the smallest remaining pile and offer it to B.  If B refuses, then it belongs to A.  This back and forth continues until A, B, or C have two of the six piles.  If A has two piles first, then the remaining herbs are recombined and split by B, C gets first choice.  If B or C accept two piles first, the other chooses from the remaining piles for himself until he has two of them, and A accepts what is left behind.

Posted by Mindrod on 2006-01-27 20:30:44