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)

A pours two cones of roughly equal size (height and diameter - as viewed by eye).
B pours out a third cone which is larger than each of these two, and them attempts to make them equal to the third.
C distributes the remaining contents to each of the three piles until all has been used (I am allowing C to add to small amounts from this stock as she feels necessary; this does not need to be as three distinct distributions).

A & B then draw lots for first and second choice of cones.  C gets the remaining one. (If C has been quite fair in her distribution, she can be quite sure that what the others leave her as the smallest will in fact be equal to theirs - otherwise she must pay the price for her poor distribution).

Posted by brianjn on 2006-01-28 07:28:19