1000 Dollars

1000 Dollars

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You have 1000 one dollars bills. And you have ten envelopes. Your job, should you decide to accept it is, put different amounts of money in each envelope, so that if I ask for any amount of money between one and one thousand dollars, you could give me any combination of envelopes that would be exactly the amount I asked for, no matter which amount I could ask for.

How much would you put in each envelope?

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Ready for the Answer?
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vv

First of all, I said "You have 1000 one dollars bills" not that I gave you a thousand dollars... Also, I specifically said "Your job, should you decide to accept it..." which leaves it up to you to decide whether to take the task on or not!!!

Thus if you decided not to take the job, you can keep your $1000, but if you decide to take on the task of putting your own $1000 in $1 bills in various quantities in 10 envelopes and give them to me, then I'll gladly take whatever money you put in them!!!

(: (: (: (: (: (: (: Smile :) :) :) :) :) :) :)

But you're not on Candid Camera!!!

If you're still looking for a mathematical solution, the answer would have been "It is done in base2 addition -- binary."

Ten envelopes, thus 10 digits in binary work out as follows:

Env #01: 0000000001(2) = $1(10)
Env #02: 0000000010(2) = $2(10)
Env #03: 0000000100(2) = $4(10)
Env #04: 0000001000(2) = $8(10)
Env #05: 0000010000(2) = $16(10)
Env #06: 0000100000(2) = $32(10)
Env #07: 0001000000(2) = $64(10)
Env #08: 0010000000(2) = $128(10)
Env #09: 0100000000(2) = $256(10)
Env #10: 1000000000(2) = $512(10)

However, when you add them all up, they total $1023 which is $23 more than what you actually have so a little bit of shifting between envelopes would be required unless you wanted to add another $23 of your own money to make things simpler!!!

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