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 general Idea is to satisfy A such that the remaining herbs can be pooled back together and divided the normal 2-person way.

A splits herbs into three piles
B and C each points to a pile they want for themselves with their right hand and the pile they want A to have with their left hand

Case 1 -- B and C pick different piles for themselves (problem solved - B and C each get the pile they wanted and A must be happy with the remaining pile since he made all 3 piles)

Case 2 -- B and C pick the same pile for A (problem solved - A must be happy with this pile since he made all 3 piles, B and C are happy for him to have it and they can pool the remaining 2 piles have B divide and C choose)

Case 3 -- B and C both want the same pile and pick different piles for A (problem solved - A must be happy with half of each of the 2 piles where A+B split the pile C chose for A and A+C split the pile B chose for A)

Posted by tanx on 2006-06-29 14:58:11