August 2016
Problem of the Month

The Milkman's Puzzle
by Sam Loyd

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

Send any comments or questions to: David Pleacher