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## #1 2006-03-06 13:43:27

Math Guy
Member
Registered: 2005-10-12
Posts: 20

### A Thousand DollarsAnd a Bunch of Envelopes

Heres the puzzler. Its very simple.

Im going to hand you one thousand dollars, in one-dollar bills.

Your job is to put some of those dollar bills in the envelopes, in such a manner that no matter what number of dollars I ask you for youll hand me the appropriate combination of envelopes.

TOM: There must be more to it, because I could just use a thousand envelopes.

RAY: There is more. The question is--whats the fewest number of envelopes I can use, and how much money do you put in each one?

*Leave what you think is the right answer here, guessing never hurts!!

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## #2 2006-03-06 14:23:22

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: A Thousand DollarsAnd a Bunch of Envelopes

1, 2, 4, 8, 16, 32, 64, 128, 256, 489

10 envelopes

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #3 2006-03-06 16:29:35

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,812

### Re: A Thousand DollarsAnd a Bunch of Envelopes

Excellent, Ricky!
I remember this question was asked to me about 15 years ago. I managed to say 1,2,4,8,16..etc. But 489 was a little difficult. I did that too! The most satisfying part of it was that I did it without a paper and a pencil. Ever since, this has been one of my favorite questions.
I was able to do it because I was too familiar with the powers of 2, and their sums,  not because of any other reason. (Modest me! )

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #4 2006-03-06 16:39:59

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: A Thousand DollarsAnd a Bunch of Envelopes

Same here.  I figured that you could either give or not give an envelope, and thus, the whole thing is represented as a binary system.  So it just makes sense to do it in base 2.

Being a computer scientist helped a bit too.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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