Henry Ernest Dudeney/Modern Puzzles/11 - The Perplexed Banker/Solution

Modern Puzzles by Henry Ernest Dudeney: $11$

A man went into a bank with $1000$ sovereigns and $10$ bags.

He said,

"Place this money, please, in the bags in such a way that if I call and ask for a certain number of sovereigns

you can hand me over one or more bags, giving me the exact amount called for without opening any of the bags."

How was it to be done?

We are, of course, only concerned with a single application,

but he may ask for any exact number of pounds from $\pounds 1$ to $\pounds 1000$.

For $n = 1$ to $9$, put $2^{n - 1}$ sovereigns in bag $n$.

Put the remaining $489$ in bag $10$.

A thinly-disguised implementation of the Basis Representation Theorem for binary.

$\blacksquare$