Barney goes to the bank with 1000 - $1 bills and 10 paper bags. His instructions to the teller are to place the bills in the bags in such a way that when he returns later, he can request any amount of money from $1 to $1000 and the teller must be able to give him the money without opening any of the bags. What amount of money goes into each of the 10 bags?

Question

Barney goes to the bank with 1000 - $1 bills and 10 paper bags. His instructions to the teller are to place the bills in the bags in such a way that when he returns later, he can request any amount of money from $1 to $1000 and the teller must be able to give him the money without opening any of the bags. What amount of money goes into each of the 10 bags?

I think (and others) that maybe something to do with scientific notation? But I don't understand completely.

Answer 1

Any number from 1 to 1023 can be written as a combination of

1,2,4,8,16,32,64,128, 256 and 512. These are the powers of 2 from 2^0 to 2^9. Just convert it to binary form and that converted number will tell you how many of each bag is needed.
DECIMAL/BINARY
1 = 0000000001 (1 bag of 1)
2 = 0000000010 (1 bag of 2)
3 = 0000000011 (1 of 1 and 1 of 2)
4 = 0000000100 (1 of 4)
33 = 0000100001 (1 of 32 and 1 of 10
1000 = 1111101000
(1 each of 512,256,128,64,32 and 8)