Henry Ernest Dudeney/Puzzles and Curious Problems/31 - A Queer Settling Up/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $31$
- A Queer Settling Up
- Person 1: "Here is my purse, give me just as much money as you find in it."
- Person 2, having done that: "If you give me as much as I have left of my own, we shall be square."
- After Person 2 has done that, Person 1 find his purse contains three shillings and sixpence,
- while Person 2 has three shillings.
- How much did each possess at the start?
Solution
- Person $1$ started with $2 \shillings 6 \oldpence$
- Person $2$ started with $4 \shillings$
Proof
Before the second transaction:
- person $2$ has half of three shillings, that is, $1 \shillings 6 \oldpence$
- person $1$ has ${3 \shillings 6 \oldpence} + {1 \shillings 6 \oldpence}$, that is, $5 \shillings$
So before the first transaction:
- person $1$ has half of $5 \shillings$, that is, $2 \shillings 6 \oldpence$
- person $2$ has ${1 \shillings 6 \oldpence} + {2 \shillings 6 \oldpence}$, that is, $4 \shillings$
Hence the result.
$\blacksquare$
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $31$. -- A Queer Settling Up
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $28$. A Queer Settling Up