Henry Ernest Dudeney/Modern Puzzles/184 - A Prohibition Poser/Solution 2

by : $184$

 * A Prohibition Poser

Solution
Fill the $7$-quart measure and empty it down the drain a total of $12$ times.

Fill the $5$-quart measure and empty it down the drain a total of $4$ times.

Then you will have thrown away $104$ and have $16$ quarts left in the barrel.

This takes $32$ transactions.

Then perform the transactions according to the following:


 * $\begin {array} {r|c|c|c} & \text {$7$-quart} & \text {$5$-quart} & \text {Barrel} \\ \hline

& 0 & 0 & 16 \\ (1): & 7 & 0 & 9 \\ (2): & 2 & 5 & 9 \\ (3): & 2 & 0 & 9 \\ (4): & 0 & 2 & 9 \\ (5): & 7 & 2 & 2 \\ (6): & 4 & 5 & 2 \\ (7): & 4 & 0 & 2 \\ (8): & 4 & 1 & 1 \\ (9): & 0 & 1 & 1 \\ (10): & 1 & 1 & 0 \\ \end {array}$

This is a total of $42$ transactions.