(related to Problem: The Wassail Bowl)
The division of the twelve pints of ale can be made in eleven manipulations, as below. The six columns show at a glance the quantity of ale in the barrel, the five-pint jug, the three-pint jug, and the tramps $X,$ $Y,$ and $Z$ respectively after each manipulation.
| Barrel | 5-pint | 3-pint | X | Y | Z |
|---|---|---|---|---|---|
| 7 | 5 | 0 | 0 | 0 | 0 |
| 7 | 2 | 3 | 0 | 0 | 0 |
| 7 | 0 | 3 | 2 | 0 | 0 |
| 7 | 3 | 0 | 2 | 0 | 0 |
| 4 | 3 | 3 | 2 | 0 | 0 |
| 0 | 3 | 3 | 2 | 4 | 0 |
| 0 | 5 | 1 | 2 | 4 | 0 |
| 0 | 5 | 0 | 2 | 4 | 1 |
| 0 | 2 | 3 | 2 | 4 | 1 |
| 0 | 0 | 3 | 4 | 4 | 1 |
| 0 | 0 | 0 | 4 | 4 | 4 |
And each man has received his four pints of ale.
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