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)
One cook (A) divides the herbs by eye into what she considers 3 equal piles so that she will be happy to accept any pile.
The piles are offered to the other 2 cooks (B and C) If they select different piles then A receives the third and all are happy.
If B and C select the same pile (believing it to be bigger) A is offered either of the other 2 piles ( both of which she believes equal 1/3 total.)
The remaining 2 piles are recombined. Both B and C now believe more than 2/3 of the herbs remain since they have kept the biggest pile.
Either B or C would divide the herbs, by eye, into two piles she considered to be equal. The third cook would then choose the pile she thought was bigger.
Both B and C now believe they have at least half of greater than 2/3 (or greater than 1/3)
As to how to determine who divides and who chooses - well that's another problem.
Edited on January 27, 2006, 7:57 am