Henry Ernest Dudeney/Modern Puzzles/11 - The Perplexed Banker/Solution
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Modern Puzzles by Henry Ernest Dudeney: $11$
- The Perplexed Banker
- 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 $\pounds 1000$.
Solution
For $n = 1$ to $9$, put $2^{n - 1}$ sovereigns in bag $n$.
Put the remaining $489$ in bag $10$.
Proof
A thinly-disguised implementation of the Basis Representation Theorem for binary.
$\blacksquare$
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $11$. -- The Perplexed Banker
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $7$. The Perplexed Banker