A box has exactly 100 black balls and 100 white balls. Repeatedly, 3 balls are removed from the box and replaced by other balls that are in a bag as follows:

## BALLS REMOVED  REPLACED BY

3 black $\Longrightarrow 1$ black

2 black and 1 white $\Longrightarrow 1$ black and 1 white

1 black and 2 white $\Longrightarrow 2$ white

3 white $\Longrightarrow 1$ black and 1 white

What can be the content of the box after repeated applications of this procedure?
(a) 2 black
(b) 2 white
(c) 1 black
(d) 1 black and 1 white
(e) 1 white.
Initially observe that after each replacement, the number of white balls either remains the same or decreases by 2. Therefore, the number of white balls remains even. On the other hand, each group of balls removed that contains at least 1 white ball is replaced by another that also contains 1 white ball, so the number of white balls is never zero. Now observe that option (b) is the only one including at least 2 white balls, so it is the correct option. One way to achieve this result is to remove 3 white balls 49 times until you have 149 black and 2 white balls, and then, remove 1 black and 2 white balls 149 times.