1000 $1 Bills in 10 EnvelopesDate: 12/11/2002 at 04:10:54 From: Kendel Subject: Word problem You are given 1000 one dollar bills and 10 envelopes. Put the bills into the envelopes in such a way that someone can ask you for any amount of money from $1 to $1000 (examples - $532, $619, $88, etc.) and you can give it to them through a combination of the envelopes. I am NOT a math person by any means and I'm sure that the answer to this problem is painfully obvious; however, I can't get it! I can do it with 12 envelopes like this - 400, 300, 100, 100, 40, 30, 20, 10, 5, 2, 2, 1, but I can't get it down to ten. I'd appreciate a response as soon as you have time. Thank you, Kendel Date: 12/11/2002 at 10:19:20 From: Doctor Ian Subject: Re: Word problem Hi Kendel, If you can add 23 dollars of your own, then it's easy, since you can then use each envelope to represent one place value in a binary expansion: 512 256 128 64 32 16 8 4 2 1 Now you can get any number between 1 and 1023, e.g., 9 8 7 6 5 4 3 2 1 0 2 2 2 2 2 2 2 2 2 2 512 256 128 64 32 16 8 4 2 1 $1 = x $5 = x x $143 = x x x x x $1023 = x x x x x x x x x x But if you only have $1000, you can only get 489 into the final envelope. Does this make a difference? Well, you can still use the first 9 envelopes to return any amount up to $511. So with the final envelope you can get anything between $489 + $1 = $490 and $489 + 511 = $1000 So it works fine. Does this make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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