Jan 04, 2020
RAY: We're going to play a little card game. I'm going to deal out 21 cards from an ordinary deck of cards to a pile in front of us. We're going to alternate taking cards from the pile.
Here are the rules:
When it's your turn, you can take as many as three cards, but you must take at least one. So, you can take one, two, or three cards from the pile. The winner of the game is whoever picks up the last card, or cards, from the table.
For example, if there are six cards left and I pick up three, you will pick up the last three, because we're alternating turns, and you would win. So, clearly, if there were six cards left, I wouldn't take three.
The question is, is there a strategy you could use that would guarantee you would win?
RAY: You would want to make sure that when you had made your next to last play, there would be four cards left. So no matter what I did, whether I took one, two or three cards you would win.
To extrapolate from that, we want to make sure that in order to get to that point where there are four cards left, you have to do that every time it's your move. That is, you have to make sure that there is a multiple of four cards left every time.
So for example, when there are 21 cards on the table --
And if you just took one that would be a multiple of four.
And then no matter what I did you could make a move that would then leave 16, another multiple of four. Etcetera, etcetera, until it finally got down to four, and when I'm faced with four cards no matter what I do, I lose.