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)

The first cook divides the herbs into 12 piles, the second cook then makes 6 piles from the 12 piles, and the third cook makes 3 piles out of the 6. Cook A chooses a pile, then Cook B, then Cook C. Each cook is inclined to make the piles as even as possible because if Cook C makes uneven piles, she will end up with the smallest pile. Cook A's uneven piles would be made more even by Cook B, and Cook B's uneven piles would be made more even by Cook C.

Posted by Chris on 2006-02-10 17:53:58