X Y Clip Nathan solves math problem Pinnacle Films

20 random cards are placed in row, all faced down. move consists of turning face-down card face up and turning over the card immediately to the right. Show that no matter what that the choice of cards to turn this sequence of moves must terminate. Nathan! Hiding in the back won't help you. Would you like to come up and show us? Go on, Nathan. Ok, so we need to look at the cards not as cards but as, as numbers. We can call face-down cards... one. face-up cards zero. And initally there would be sequence of ones as the cards are all face down, but after while it would look something like that. As we can see that's binary number. And move that consists of turning face-down card face-up and the card immediately to the right of it could be that one followed by one will turn into zero followed by zero. That would look like that, or it can be one followed by zero turning into zero followed by one. In either case we can see that the number in binary is strictly decreasing. And that means? Which means that the sequence must terminate. Because? Because you can't keep taking away from positive integer without it turning negative. No You can't. You definitely can't. Good work. Everyone, good work!