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)

The assertion is true for every a,b,c that I try.  But the proof eludes me.  I look forward to seeing the proof.

Edited on May 30, 2017, 10:55 am

Posted by Steve Herman on 2017-05-30 09:37:35