For 2^n of such pairs x, y, it happens that x = y. But checking the description of Simon's Problem on Wikipedia, it appears that case is excluded, so that x = y

For 2^n of such pairs x, y, it happens that x = y. But checking the description of Simon's Problem on Wikipedia, it appears that case is excluded, so that x = y ⊕ c doesn't have to hold if x = y.