Henry Ernest Dudeney/Puzzles and Curious Problems/296 - Water Measurement/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $296$

A maid was sent to the brook with two vessels that exactly measured $7$ pints and $11$ pints exactly.

She had to bring back exactly $2$ pints of water.

What is the smallest possible number of transactions necessary?

$14$ transactions are needed.

Let $V_7$ and $V_{11}$ denote the $7$-pint and $11$-pint vessels respectively.

In the below, the successive lines indicate the status of each of $V_7$ and $V_{11}$:

$\begin{array}{c|c} V_7 & V_{11} \\ \hline

7 & 0 \\ 0 & 7 \\ 7 & 7 \\ 3 & 11 \\ 3 & 0 \\ 0 & 3 \\ 7 & 3 \\ 0 & 10 \\ 7 & 10 \\ 6 & 11 \\ 6 & 0 \\ 0 & 6 \\ 7 & 6 \\ 2 & 11 \\ \end{array}$

and it is seen that the required $2$ pints are in the $7$-pint vessel.

$\blacksquare$