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)

c1 divides to 3 parts a,b and c.

1. c2 c3 chose what they want. if they are different then everybody is happy, prob solved.

2. otherwise, lets say they both chose part a. we put it back in a bag. and ask them to choose between b and c.
    2.1 if they choose the same lets say b. then c1 takes c and go away. and c2 and c3 put a and b togather and divide usual way.
    2.2 otherwise lets say c2 chose b and c3 chose c. then c1 divides them both to two parts. c2 takes the half he wants and put in the bag with a. c3 makes the same with part c. c1 takes the left parts of b and c. and the others divides the bag the usual way.

Posted by ludwig on 2006-04-13 07:01:56