It seems that we could expand this for n people with n choices. So in the first case where there are only 2 people and 2 colours, they assign, say 0 to black a

It seems that we could expand this for n people with n choices. So in the first case where there are only 2 people and 2 colours, they assign, say 0 to black and 1 to red. Then they each sum up the other choices they can see (which happens to be only one other choice in this case) plus their own assigned number (0 or 1) and answer that modulo 2. Er..I think...?