A box of candies can be equally divided by weight without cutting pieces between three, four or seven people.
Each piece is an integral number of ounces.
What is the least number of pieces of candy the box could contain? The candies may be of different weights.

If there were only 8 pieces, then, when there were 7 people, one would have to get 2 pieces while the others got 1.  Each of the 6 solo pieces would have 1/7 of the total weight. In order to divide among 4 people, either each person must get 2 pieces or at least one person must get only one.  If the latter, there is no piece large enough to make 1/4 of the weight; if the former, as there are only two pieces that weigh other than 1/7 the total weight, at least two people must get 2/7, which is not 1/4 (of the total weight).

So the new minimum number of pieces that is possible is 9 (no guarantee though that this can be done).

 

Edited on October 8, 2004, 1:11 pm

Posted by Charlie on 2004-10-08 13:07:18