1. Place any four numbers you choose in the first row of an array.
2. In the second row, in the first three columns write the difference of the two numbers just above and to the right in the first row (the larger minus the smaller). In the fourth column write the difference of the number above and the one in the first column of that row (again the larger minus the smaller). In otherwords, each entry is the absolute value of the difference of the two terms in the previous row.
3. Repeat for each row, in terms of the numbers in the row just above.
4. Will every choice of four number you begin with eventually lead to rows of zeros?
5. Challenge: Find four begining numbers that let you generate more than 10 rows with non-zero values. More than 20?
An Excel Worksheet to Generate Rows
A proof that this always leads to rows of zeros is elusive.
After you have done a few, try this
Some examples with many non-zero rows.