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)

The problem with Vernon's amended solution is that B and C might not agree on which pile is smallest.

Here's my plan:

1) Have A divide the 'erb into three piles.

2) Have B and C each indicate which pile they think is smallest.

3) If B and C agree, then A gets the pile they both think is smallest.  B and C combine and redivide the other two piles between them.

4) If B and C disagree, then:
    a) A and B divide and share the pile that C thinks is smallest
    b) A and C divide and share the pile that B thinks is smallest
    c) B and C divide and share the third pile.
   B and C are happy because they each got at least half of what they think are the two largest piles.

Posted by Steve Herman on 2006-01-27 10:17:15