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)

Don't know if anybody has already posted this one:

Cook 1 divides the herb into 3 piles A, B, C that she considers equal (so she would be happy to take any one of them).

The other two cooks both rank the piles in order of their preference (which pile they like best, second best, and least).

Case 1: cook 2 and cook 3 have different favorites. They each get there preferred pile and cook 1 gets the remaining pile.

Case 2: cook 2 and cook 3 have the same ranking of preference. So they give the pile they both like least to cook 1. Then cook 2 and cook 3 put the other two piles back into one pile and divide it between the two of them in the usual way.

Case 3: cook 2 and cook 3 have the same first preference but differ in the assessment of the other two piles, let's say
Cook 2: 1. A, 2. B, 3. C
Cook 3: 1. A, 2. C, 3. B
In this case cook 2 and cook 3 first share pile A in the usual way. Then cook 2 shares pile B with cook 1 in the usual way.
And cook 3 shares pile C with cook 1 in the usual way.
So they end up with
Cook 2: A1+B1
Cook 3: A2+C1
Cook 1: B2+C2

And everybody should be happy :-)

Posted by katrin on 2006-06-24 08:48:13