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.
(In reply to
re: Solution by Richard)
Oops, I made a mistake in my reasoning, thinking that disproving 10
sufficed to disprove all values less than 10. When actually
finding the solution, I disproved 9 first before disproving 10, though
I neglected to post the proof for 9 because of the error in my
reasoning. So here it is:
Assume that 9 is possible. Let 84N be the total weight as
before. When dividing among seven people, we see that at least
five people must receive single pieces. So when dividing among
four people, some person gets two 12N pieces, more than his fair share.
re(2): Solution
