Q:

Color of Last Ball?

A box contains 731 black balls and 2000 white balls. The following process is to be repeated as long as possible. Arbitrarily select two balls from the box. If they are of the same color, throw them out and put a black ball into the box(enough black balls are available to do this.) If they are of different colors, place the white ball back and throw the black ball away. Which of the following is correct?
A) The process can be applied indefinitely with out any priori bound. 
B) The process will stop with a single white ball in the box
C) The process will stop with a single black ball in the box.
D) The box will stop with box empty.
E) None of the above.
This is what i thought:
The process can't be applied indefinitely as in each step no.of balls are decreased by one.
Also box can't be empty. I think the answer might be (E) as the process might end with white or black ball.

A:

Hint:  Every time you apply the process, the number of balls decreases by 1 and the parity of the number of black balls changes.  You have to apply the process an 2730 times to get down to one ball; what does this tell you about the parity of the number of black balls at the end?

