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)
My solution may be applicable toward 2, 3, 4 ...actually for any number of cooks, or people dividing shared property.
One of the cooks starts picking up herbs for herself trying to reach what she considers a fair part (1/3 in our case).
The other cooks are allowed to stop this procedure by shouting 'for me".
The one that shouted first gets the part she is satisfied with, A is happy because now there is more than 2/3 to be divided between two persons and ... the rest is easy.
If no one shouted "for me" A gets the part she considers fair and the other two divide what they believe is more than 2/3.
In case of n people , one gets out and the algorythm proceeds with n-1 people.
The only prerequisit to avoid clashes of simultaneous "for me"announcement is to increase the selected part slowly.
It works. I suggested it to some guys trying to divide(without lawyers) some property they inherited.
Edited on January 29, 2006, 9:37 am