Farmer Stone is quite an eccentric dairy farmer.

He originally had a total of 54 gallons of milk in three churns and he wanted to make sure each churn contained 18 gallons of milk.

In order to do this, he did the following:

First, he poured 1/4 of the first churn into the second churn.

He then poured 1/2 of the second churn into the third churn.

Finally, he poured 1/3 of the third churn into the first churn.

How many gallons did each churn contain before Farmer Stone started pouring?

Puzzle Copyright © Kevin Stone

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Hint

Try working backwards with each churn containing 18 gallons.

Answer

12, 33, and 9 gallons respectively for churns 1, 2, and 3.

The solution may require more than one read!

Before After Therefore

Pour 1 C1 = 12 C1 = 9 C2 = +3

Pour 1 C2 = 33 C2 = 36

Pour 2 C2 = 36 C2 = 18 C3 = +18

Pour 3 C3 = 27 C3 = 18 C1 = +9

Pour 3 C1 = 9 C1 = 18

To explain a little further. After pour 3, C3 must have contained 18 gallons, so it must have contained 27 before the pour.

Similarly, after pour 2, C2 must have contained 18 gallons, so must have contained 36 before the pour.

After pour 3, C1 must have contained 18 gallons, and it received 9 gallons from pour 3, so must have had 9 before the pour.

So pour 1 left 9 gallons in C1, which means C1 contained 12 before the pour and C2 received 3 gallons.

We know that C2 had 36 gallons before pour 2, so must have started with 33 gallons.