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 and you can give it to them through a combination of the envelopes.

Fill the envelopes with $1, $2, $4, $8, $16, $32, $64, $128, $256 and $489.

This involves binary maths. Let’s try an easier problem – $31 with 5 envelopes.

The envelopes have to be filled with $1, $2, $4, $8 and $16 . Note that the numbers are in powers of two:

2^{0} = $1

2^{1} = $2

2^{2} = $4

2^{3} = $8

2^{4} = $16

Using this logic, for $1000, the envelopes need to be filled with: $1, $2, $4, $8, $16, $32, $64, $128, $256 and $512. But this adds up to $1023. So, the last envelope will only have $512 – $23 or $489.