Henry Ernest Dudeney/Puzzles and Curious Problems/20 - Boys and Girls/Solution

by : $20$

 * Boys and Girls
 * Nine boys and three girls agreed to share equally their pocket-money.
 * every boy gave an equal sum to every girl,
 * and every girl gave another equal sum to every boy.
 * Every child then possessed exactly the same amount.


 * What was the smallest possible amount that each then possessed?

Solution
Let us assume that the smallest unit of money is $1$.

On that basis, each boy possessed $12$ and he gave $1$ to each girl.

Every girl then had $36$, and gave $3$ to each boy.

Everybody then possessed $18$.

's repackaging of this puzzle in was answered on the basis of that unit being $1$ cent.

In England at the time this puzzle was set, the smallest unit of money was $\tfrac 1 4 \oldpence$

On that basis, each boy possessed $3 \oldpence$ and he gave $\tfrac 1 4 \oldpence$ to each girl.

Every girl then had $9 \oldpence$ and gave $\tfrac 3 4 \oldpence$ to each boy.

Everybody then possessed $4 \tfrac 1 2 \oldpence$