Privacy Policy + T&C

We use cookies to personalise our content and ads, and for traffic analysis. Information about your use of our site is shared with our advertising and analytics providers. You also agree to our T&C.


Common Answers

Have you entered August's Common Answers?

BB Logo Spacer

Puzzle - Answer

Farmer Stone is quite an eccentric dairy farmer.

He originally had a total 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 in 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?

 [Ref: ZVVT] © Kevin Stone

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. QED!

Back to the puzzles...



This website uses cookies, for more information please view our privacy policy. By using the site you also agree to our terms and conditions.