Henry Ernest Dudeney/Puzzles and Curious Problems/302 - Delivering the Milk/Solution

by : $302$

 * Delivering the Milk

Solution
To simplify understanding, let us convert all measurements to pints.

Let $C_1$ and $C_2$ denote the two $10$-gallon cans, each of which hold $80$ pints.

Let $J_5$ and $J_4$ denote the $5$ pint and $4$ pint jugs repectively.

Proceed as follows:


 * $(1): \quad$ Fill $J_5$ from $C_1$.
 * $(2): \quad$ Fill $J_4$ from $J_5$.
 * $(3): \quad$ Empty $J_4$ back into $C_1$.
 * $(4): \quad$ Empty $J_5$ into $J_4$.
 * $(5): \quad$ Fill $J_5$ from $C_1$.
 * $(6): \quad$ Fill $J_4$ from $J_5$.
 * $(7): \quad$ Empty $J_4$ back into $C_1$.

At this stage, $J_5$ contains the first required quart, $C_2$ is still full, $J_4$ is empty, and $C_1$ is $1$ quart short of full.


 * $(8): \quad$ Fill $J_4$ from $C_2$.
 * $(9): \quad$ Fill $C_1$ from $J_4$.

As $C_1$ was $1$ quart, that is $2$ pints, short of full, $J_4$ now holds the second required $2$ quarts.