A Nice Puzzle

Let us say urns X and Y. Both of them contain same number of balls, Then we can empty both the urns removing same number of balls form each urn.

Else, we remove the same number of balls form each of the urns so that one of the urns contain exactly one ball.

If x and y denote the number of balls is urns, say x > y, there take out y-1 balls from each.

We now double the number of balls of urn Y which contain only one ball and remove one ball form each of the urn. This forcers decreases the number of balls in the other urn x by 1. continuing this way we reach a stage when both the urns contain one ball each, whence we can empty the urns removing one ball from each of the two urns.

http://www.artofproblemsolving.com/Forum/viewtopic.php?p=347816&sid=df687161b1731ca5d30d361de389e421#p347816

1. Let there be x balls in urn 1 and y in the other i.e urn 2.

Now, let k balls be drawn from each such that:

x-k= 2*(y-k)
Thus,
k=(2*y - x)

Now,

Case 1:
If 2*y> x

Then, after performing operation 1, double the no of balls in urn 2 to make it equal to urn 1 and next time draw the remaining balls from each which are equal in both urns by first 2 operations.

Case 2: Otherwise keep doubling the balls in urn 2 until 2*y > x and then follow the procedure as in case 1.

yess