Henry Ernest Dudeney/Puzzles and Curious Problems/31 - A Queer Settling Up/Solution

by : $31$

 * A Queer Settling Up

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.