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)
I name the cooks A, B, and C. A divides the herbs into three piles she deems equal.
The 'two cook method' I refer to is the one in the problem - one cook
divides a pile of herb into two 'equal' piles, the other picks the
'biggest' one, and the other goes to the first cook.
B and C then point to the pile they find the biggest.
a) They point to different piles - they each get that one, A gets the remaining one, everyone is happy.
b) They point to the same one. Then, they divide this pile with
one another in the usual two cook method. After that, they both
point to the remaining pile they find the largest.
1) They point to different piles. Each one
uses the two cook
method to divide their pile of choice with cook A.
2) They point to the same pile. They divide it
with the two cook method, each
taking half. Cook A gets the remaining