# The Four Numbers Game

The Four Numbers Game

The Four Numbers Game is played starting with four non-negative integers (not necessarily different) placed at the vertices of a square (shown on orange disks above).

The first step of the game consists in labeling the midpoints of the square (the blue disks) with the absolute value of the difference of the two numbers at its two closest corners; for instance, in between 7 and 5 there is a 2.

Each successive step continues this process of labeling one square inside another following the same rule into a nested chain of squares. When we reach a stage in which a square gets labeled with four zeros, the game ends.

The number of steps needed to end a game is called its length; for instance, the game

is of length 4. By changing the numbers using the sliders, you can experiment to see how the length of a game changes. Can you find numbers that give a game of length 5?

9 | 5 |

7 | 1 |