Let the following game. We have n buttons lined up in the row. Every button has the light in it, and game starts with some lights on and some off. When the button is pushed, it changes state of button pushed and each button right next to it from on to off or vice-versa. You win game by pushing buttons so that all lights are off. Do one of given:
i) Prove that if n=6, you can always win game regardless of state of the lights at the starting of game.
ii) Prove that if n=5, there is initial lighting such that game can't be won.