A box has exactly one hundred black balls and one hundred white balls. Repeatedly, three balls are taken out of the box and replaced by other balls, which are in a bag, in the following manner.

$$
\begin{aligned} 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 \end{aligned}
$$

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.
The correct option is (b).

Initially observe that, after each substitution, the number of white balls either remains the same or decreases by two. Therefore, the number of white balls remains even. On the other hand, each group of balls removed that contains at least one white ball is replaced by another group that also contains a white ball, so the number of white balls is never zero. Now observe that option (b) is the only one that includes at least two white balls, so it is the correct option. One way to achieve this result is to remove three white balls 49 times until you have 149 black and two white balls, and then remove one black and two white balls 149 times.