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.

I can't do better than Federico, but here's an explaination.

To be divisible by 3, 4, and 7, the total weight must be at least 84 since no primes are shared and 3*4*7 = 84.

So combinations of the pieces must be make 7 12's, 4 21's, and 3 28's.

No piece can weigh more than 12, must add 9 to the 12's to get 21, and add 16 to get 28.

A little playing around with those facts turns up weights of 12, 9, 4, and 3.

7 12's: 12, 12, 12, 4+4+4, 9+3, 9+3, 9+3
4 21's: 12+9, 12+9, 12+9, 4+4+4+3+3+3
3 28's: 12+9+4+3, 12+9+4+3, 12+9+4+3

Rajal

Posted by Rajal on 2004-10-08 12:55:26