### Brain Teasers

# Mix 'n' Match

I have 18 gallons of water shared unequally between three buckets. Then I:

1. Pour three quarters of the water in bucket 1 into bucket 2.

2. Pour half of the water now in bucket 2 into bucket 3.

3.Pour a third of the water now in bucket 3 into bucket 1.

Now, all of the buckets contain equal amounts of water.

How much water did each bucket start with?

1. Pour three quarters of the water in bucket 1 into bucket 2.

2. Pour half of the water now in bucket 2 into bucket 3.

3.Pour a third of the water now in bucket 3 into bucket 1.

Now, all of the buckets contain equal amounts of water.

How much water did each bucket start with?

### Answer

We can solve this problem by starting at the end and working backwards.Obviously, at the end each bucket will contain 6 gallons of water. Call the buckets B1, B2 and B3.

If pouring a third of the water in B3 at the time into B1 leaves 6 in each, then B3 must have 9 at the time and B1 3.

If pouring half of B2 at the time into B3 at the time leaves 6 in B2 and 9 in B3, then B2 must contain 12 at the time and B3 contain 3. So B3 started with 3 gallons in.

If pouring three quarters of B1 at the time into B2 at the time leaves B1 with 3 and B2 with 12, then B1 had 12 and B2 had 3.

So B1 started with 12 and B2 and B3 both started with 3.

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## Comments

Good puzzle. I would have reworded the question so as to say that not all three buckets have the same amount of water. As is, the question easily leads a reader down the garden path in assuming that all three buckets must contain differing amounts of water, which is clearly not the case.

No, I liked the puzzle too, but don't feel that the phrasing was off. Stating that it was shared unequally means that all 3 do not have the same amount. This does not mean that 2 can't have the same amount as the amount is still unequal in all 3. Good job.

Fun puzzler - so fun I solved it twice! Misread the question initially and thought 1. read "poured three QUARTS"

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