Four Number Problem

We begin by placing four numbers in the first row as follows.

A B C D

Then for each successive we will replace the entries by the absolute value of the difference of the entry just above and the entry just to the right in the previous row. In the fourth position use the absolute value of the difference of the fourth and the first (i.e. cycle)

|A-B| |B-C| |C-D| |D-A|

I began by choosing A=2, B=3, C=5, and D=7

A	B	C	D
2	3	5	7
1	2	2	5
1	0	3	4
1	3	1	3
2	2	2	2
0	0	0	0

Lets choose another set of numbers, say 1, 2, 11, and 23.

A	B	C	D
1	2	11	23
1	9	12	22
8	3	10	21
5	7	11	13
2	4	2	8
2	2	6	6
0	4	0	4
4	4	4	4
0	0	0	0

We can see that we will always get a row of four zeros.

Return to Assignment 12