Henry Ernest Dudeney/Puzzles and Curious Problems/9 - Pocket-Money/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $9$
- Pocket-Money
- "When I got to the station this morning," said Harold Tompkins, at his club, "I found I was short of cash.
- I spend just one-half of what I had on my railway ticket, and then bought a penny newspaper.
- When I got to the terminus I spent half of what I had left and twopence more on a telegram.
- Then I spent half of the remainder on a bus, and gave threepence to that old match-seller outside the club.
- Consequently I arrive here with this single penny.
- Now, how much did I start out with?"
Solution
- $3 \shillings 6 \oldpence$
Proof
Tompkins ended up with $1 \oldpence$
Before he paid $3 \oldpence$ to the matchseller, he had $4 \oldpence$
Before spending half of what he had on a bus, he had $8 \oldpence$
Before spending $2 \oldpence$ on a telegram he had $10 \oldpence$
Before spending half of what he had left, he had $20 \oldpence$
Before buying a penny newspaper, he had $21 \oldpence$
Before spending half of what he had on a train ticket, he had $42 \oldpence$
That is, he started with $3 \shillings 6 \oldpence$
$\blacksquare$
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $9$. -- Pocket-Money
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $17$. Pocket Money