Some of you may have known of the film “X+Y”. This tells about the life of a genius but idiosyncratic boy who represents the English team to participate in the IMO training in Taipei. There is a problem with what the film has stated when Nathan is with his team training in Taipei: 
20 random cards are placed in a row, all face down. A move consists of turning a face-down card face up and turning that immediately to the right. Show that no matter what the choice of cards to turn, this sequence of moves must terminate. 

When solving game problems or some similar kinds, you should “translate” the problem to your “own Math language”. So Nathan, using his math language, solved this problem like below: 

He looked at these cards not as cards but as numbers where facedown cards = 1 and faceup cards = 0. At first, they were all faced down so it was 11111…1. As the move consists of turning a face-down card face up and turning that immediately to the right, a move can either be 11 turning into 01 or 11 turning into 00. Both cases show that our binary is strictly decreasing. So, therefore, the move must terminate.