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#1 2006-03-07 12:43:27
- Math Guy
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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!!
#2 2006-03-07 13:23:22
- Ricky
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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..."
#3 2006-03-07 15:29:35
- ganesh
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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! 
)
Character is who you are when no one is looking.
#4 2006-03-07 15:39:59
- Ricky
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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..."