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Candy Box (Posted on 2004-10-08) Difficulty: 3 of 5
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.

See The Solution Submitted by Brian Smith    
Rating: 3.5000 (4 votes)

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re(2): Solution | Comment 9 of 18 |
(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.

  Posted by David Shin on 2004-10-08 15:54:49

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