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 Empty the bucket (Posted on 2017-05-29)
You are in the desert and you have 3 buckets of water containing a,b,c liters respectively (a,b,c - positive integers).
You need an empty bucket for an unspecified purpose. Being in the desert you need the water and cannot just pour it away.
You have to pour the contents of one bucket into another one. But in any pouring, you must double the contents of the bucket which receives the water.
For example the sequence of bucket contents could be:

3 2 1
1 4 1
0 4 2

Now show that no matter what a,b,c are, you can always manage to empty a bucket under this constraint.

You may assume:
a>b>c

&
(capacity of each bucket)>(a+b)

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 the original solution -----p2---spoiler | Comment 11 of 12 |
... the rest of the cases?:
The odd-odd-odd case becomes odd-even-even (solved above) after any move is made.
The other cases are proven by induction.
In the even-even-even case we simply divide all the bucket sizes by 2 and solve the smaller problem.
The even-odd-odd case is solved by first making a move among the two odd buckets, which leads to the (already solved) even-even-even case.    <end>

 Posted by Ady TZIDON on 2017-06-04 14:44:21

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