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Difficulty: MediumPuzzle Details

Puzzle IconFarmer 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?

Show Hint Show Answer Print Puzzle
[Ref: ZVVT] © Kevin Stone 

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. QED!


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[Added September 1997]

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