Question 57413: You are given exactly one thousand dollars in in one-dollar bills. You are also given exactly ten envelopes. Your task is to place the dollar bills in the envelopes so that you can dispense any amount of money from $1 to $1,000 by using a combination of the envelopes.
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! Try an easier problem first.
What if I had 5 envelopes to put $31 dollar bills in so I could
come up with any amount?
I could fill the enveolpes like this
$1, $2, $4, $8, $16
Check and see if there's any amount that you can't get with combinations
of envelopes. There isn't.
What if I had $27 instead of $31?
I'd fill them like this
$1, $2, $4, $8, $12
It still works
Now how to fill 10 envelopes with $1 bills so I can get any amount up to
$1000
Well, If I fill them this way,
$1, $2, $4, $8, $16, $32, $64, $128, $256, $512
Each number is double the previous one, but I use up more than my $1000
1+ 2+ 4+ 8+ 16+ 32+ 64+ 128+ 256+ 512 = 1023
So I need to subtract $23 from the $512. That makes $489 that I
need to put in the last envelope.
$1, $2, $4, $8, $16, $32, $64, $128, $256, $489 is the answer
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