Question 115
Let $n$ cards are placed in a circle. Each card has a white side and a black side. On each move, you pick one card with black side up, flip it over, and also flip over the two neighbouring cards. Suppose initially, there are only one black-side-up card.
(a) If $n = 2015$, can you make all cards white-side-up through a finite number of moves?
(b) If $n = 2016$, can you make all cards white-side-up through a finite number of moves?
Prove your claim for both cases.
(a) If $n = 2015$, can you make all cards white-side-up through a finite number of moves?
(b) If $n = 2016$, can you make all cards white-side-up through a finite number of moves?
Prove your claim for both cases.