1. Four Numbers Game

2. How to Play Start by drawing a large square on your paper
Label the corners with four whole numbers
Pay attention to the order and placement of the numbers. 5 3 7 2

3. Find the midpoint of each side of the square and connect them to form a smaller square.5 3 7 2 5 3 7 2

4. Label each vertex in the new square with the difference between the numbers on the ends of the original edge.
To be precise, we are labeling the vertex with the absolute value of the difference. 5 3 7 2 1

5. Now find the midpoints of the smallest square and connect them to form an even smaller square.
Label each vertex in the new square with the difference between the numbers on the ends of the original edge. 1 4 3

6. So… Keep repeating this process until the four numbers are all zeros.
Keep track of your steps.
A step is each new square drawn after the original square.
This square shows 2 steps.

7. This game: 5 steps 1 2 2 3 3 2 2 1

8. Each Group will examine three cases:
Case 1: A > B > C > D
Case 2: A > B > D > C
Case 3: A > C > B > D A B C D

9. Make a poster of your cases:
Are there any similarities between cases?
How are the cases different?

10. Compare Posters: Are there any similarities between cases?
How are the cases different?

11. Questions Will all games end in zeros? How do you know?
Does initial order of numbers matter?
What is the shortest game?
What is the longest game for single digit numbers?
How does even/odd numbers affect the game?
How does rotational and reflection symmetry affect the game?