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.

No way to prove this is minimum but here goes:

I got a 13 piece solution.

The total number of ounces should be 3x4x7 = 84

Which is 7 divisions of 12 oz., 4 divisions of 21 oz., and 3 divisions of 28 oz.

The pieces should be 12, 12, 9, 9, 9, 9, 4, 4, 4, 3, 3, 3, 3.

28 = 12 + 9 + 4 + 3 = 9 + 9 + 4 + 3 + 3

21 = 12 + 9 = 9 + 3 + 3 + 3 +3 = 9 + 4 + 4 + 4

12 = 12 = 9 + 3 = 4 + 4 + 4 + 4

(I hope I'm right!)

-Jer

[I'm not]

Edited on October 8, 2004, 1:00 pm

Posted by Jer on 2004-10-08 12:58:18