Henry Ernest Dudeney/Modern Puzzles/80 - The Flocks of Sheep/Solution

by : $80$

 * The Flocks of Sheep

Solution
Adam had $60$ sheep.

Ben had $50$ sheep.

Claude had $40$ sheep.

Dan had $30$ sheep.

Proof
Let $A$, $B$, $C$ and $D$ be the number of sheep owned by Adam, Ben, Claude and Dan respectively.

Let $B_1$ and $C_1$ be the number of sheep owned by Ben and Claude respectively after Claude gives Ben a quarter of his.

Let $B_2$ and $A_2$ be the number of sheep owned by Ben and Adam respectively after Adam gives Ben a third of his.

Let $B_3$ and $C_3$ be the number of sheep owned by Ben and Claude respectively after Ben gives Claude a quarter of his.

Let $C_4$ and $D_4$ be the number of sheep owned by Claude and Dan respectively after Claude gives Dan a fifth of his.

Let $A_5$, $B_5$, $C_5$ and $D_5$ be the number of sheep owned by Adam, Ben, Claude and Dan respectively at the end of the series of exchanges.

We have:

and so on.