Puzzle 5: Empty the bucket
You are in the desert and you have 3 buckets of water containing a,b,c ounces respectively. Here a,b,c are 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.