An urn contains 75 white balls and 150 black ones. A pile of black ones is also available.

The following two-step operation occurs repeatedly. First we withdraw two balls at random from the urn, then:

- If both are black, we put one of them back in the urn and throw the other away.
- If one is black and the other white, we put the white one back and throw the black one away.
- If both are white, we throw both away and put a black ball from the pile into the urn.

This is another nice problem I found at Futility Closet. Really an entertaining blog. Greg cites this as from the 1983 Australian Mathematical Olympiad, via Ross Honsberger,

*From Erdös to Kiev*, 1996. Another nice problem for teachers to add to their files.

If you can't figure it out,Alexander Bogomolny has a solution for the problem at his "Cut-the-knot" web site... a great source for students (and teachers) to explore.