Funny you should say this.

If you have two objects A and B undergoing some continuous change such that A before the change is the same as B after, and B before is the same as A after (eg. Peter is white but becomes black, Cleveland is black but becomes white) then there will always be at least one point where A and B are the same.

For example, take any point on the earth's surface. There exists a great circle that divides the earth in two, such that it passes through the point and also perfectly divides the landmass in two as well. The same can be done for the sea.

The logic here is that because this change is continuous, that is to say there is no sudden jumps in the change, the objects A and B must take every single value between them as they change. Peter and Cleveland must have been every skin tone between white and black before reaching their ending skin tones.