The mangled puzzle: replace identical pairs with single white balls. Replace non-identical pairs with black balls. Number of balls reduces by one after each act

The mangled puzzle: replace identical pairs with single white balls. Replace non-identical pairs with black balls. Number of balls reduces by one after each action resulting in a single ball at the end. I'm not certain of the analogy, but it appears to be something like the white balls are even and the black are odd. Both odd+odd and even+even equal an even (white) number. But odd + even equal an odd number. Since it starts with an odd number of odd numbers, the answer is black.