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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