Recursion and the four numbers game

Recursion means doing a process again and again.

In the lesson portion of this meeting, we introduced the idea of recursion with the Pass the Candy game. In this game everyone starts with a pile of candy, and passes half of it to the left. When you repeat the process, everyone eventually ends up with the same amount of candy. If you can write down the recursive equation that simulate the game, then you can use math or spreadsheets to explain why this happens.

In the investigation portion of this meeting, we explored the Four Numbers Game. In this game one starts with four numbers on the corners of a square. One then forms a new square inside by finding the difference between each pair of adjacent numbers. When this is repeated, one eventually comes to the four numbers 0,0,0,0. Does it always work this way? If so, why?

Check out our handout:
Four Numbers Game Handout