Two ladies each want to buy two quarts of milk.
One lady has a 5-quart pail and the other lady has a 4-quart pail.
Farmer John, the milkman, has two ten-gallon cans full of milk.
How did he measure out exactly 2 quarts of milk for each lady using only
the 2 pails and the 2 full cans and without spilling any milk?
Solution to the Problem:
Call one ten-gallon milk can A and the other B, then proceed as follows:| Can A | Can B | 5-Qt Pail | 4-Qt Pail | |
|---|---|---|---|---|
| Initial Amounts (in quarts) | 40 | 40 | 0 | 0 |
| Fill 5 Pail from Can A | 35 | 40 | 5 | 0 |
| Fill 4 Pail from 5 Pail, leaving 1 quart in 5 pail | 35 | 40 | 1 | 4 |
| Empty 4 Pail into Can A | 39 | 40 | 1 | 0 |
| Pour the quart from 5 pail into 4 pail | 39 | 40 | 0 | 1 |
| Fill 5 Pail from Can A | 34 | 40 | 5 | 1 |
| Fill 4 Pail from 5 Pail, leaving 2 quarts in 5 pail | 34 | 40 | 2 | 4 |
| Empty 4 pail into can A | 38 | 40 | 2 | 0 |
| Fill 4 pail from can B | 38 | 36 | 2 | 4 |
| Pour from 4 pail into can A until A is filled, leaving 2 quarts in 4 pail | 40 | 36 | 2 | 2 |
Click here for Danilo's solution
Here is James Alarie's solution:
Number the cans 0 through 3 that hold 10 gallons, 10 gallons, 4 quarts,
and 5 quarts. Pour thusly:
0 -> 2 : 36 40 4 0
1 -> 3 : 36 35 4 5
2 -> 1 : 36 39 0 5
3 -> 0 : 40 39 0 1
3 -> 2 : 40 39 1 0
0 -> 2 : 37 39 4 0
2 -> 3 : 37 39 0 4
1 -> 3 : 37 38 0 5
3 -> 2 : 37 38 4 1
2 -> 1 : 37 40 2 1
1 -> 3 : 37 36 2 5
3 -> 0 : 40 36 2 2
Correctly solved by:
| 1. Eliza Sheffield and Anna Tetzlaff | Tuscaloosa, Alabama |
| 2. Danilo Calcinaro |
Istituto Tecnico Tecnologico (ITT) "Montani", Fermo, Italy |
| 3. James Alarie | Flint, Michigan |