COF Mathematics: The Four Numbers Game

Jenya Soprunova will present on "The Four Numbers Game".

A simple game played by one person according to the following rules: Start with four numbers written at the vertices of a square. For each side of the square, compute the positive difference of the two numbers written at the two vertices and write the result at the midpoint of the side. The four midpoints form a square and we have a number written at each of them. Now we can repeat the step for this square. We continue doing this until we arrive at four zeroes. We will analyze this seemingly simple game and explain why each game will eventually terminate. We will then show that for each N>0 there exists a game that takes N steps to terminate. See how long a game you can get by varying j,k,l, and m on the top left.

See here for a game demonstration