# Nice puzzle: 100 bread rings and two bags

You have two empty bags and 100 bread rings. The goal is to put all your rings into the bags in such a way that one of the bags will contain exactly twice as many rings then the other.

You can't eat, break and lose the rings. All of them should go into the bags.

Let me know if my explanation is not clear.

Actually, I know the answer but I'd like to share it with you. IMHO, it is pretty nice.

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I like this one, too –  Ross Millikan Dec 3 '10 at 19:31
The solution to this puzzle doesn't appear to be mathematical. –  Qiaochu Yuan Dec 3 '10 at 19:33
@Qiaochu : Venn diagrams aren't mathematical ? :-) –  Djaian Dec 3 '10 at 20:05
@Djaian: in my opinion, a puzzle carries with it an implicit mathematical problem, and a solution which violates one or more of the assumptions that go into the implicit mathematical problem is not mathematical. It's "lateral thinking." –  Qiaochu Yuan Dec 3 '10 at 20:07
Ah, that old ugly double-bagger trick. I agree with Qiaochu. It's a trick that has no math content - analogous to the recent trick of turning 8 sideways to get $\infty$ in this recently closed thread. –  Bill Dubuque Dec 3 '10 at 20:30

## 1 Answer

Put half in one bag, and put half in the other bag. Then put one bag inside the other.

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+1: You beat me to it. 100 not divisible by 3 implies we need to resort to such trickery :-) –  Aryabhata Dec 3 '10 at 19:33
+1: Same here... –  user17762 Dec 3 '10 at 19:44
Exactly. I've been surprised that most people spent a lot of time solving it :-) –  Stas Dec 3 '10 at 19:47
I had never seen the puzzle before. But it's a bit silly, and I agree with Qiaochu that it is not mathematical (except in so far as math shows that you cannot do it as a union of disjoint sets). –  Arturo Magidin Dec 3 '10 at 20:05
(+1) I think its a bit mathematical. The question could be restated as: Let $S$ be a set of 100 elements. Find two sets $A,B\subseteq S$ such that $S=A\cup B$. The difficulty comes from avoiding the assumption that $A,B$ are disjoint. Not hard as a math question, but a bit mathematical. –  Amr Feb 5 '13 at 10:37