So here's the Problem:
Given four numbers placed in a row on a spread sheet (call them A B C D),
we place in the row below the following values:
ABS(A-B) ABS(C-B) ABS(D-C) ABS(A-D)
Now with these new values, do the same formula again in the next row.
Keep repeating this until you get all zeros.
Here's an example:
Here's the questions we want to answer:
a) Will the process always lead to a 0 in all 4 entries?
b) What is the largest number of rows before a zero is generated?
i.What kinds of similarities can we find between different sets of values?
c) How does the pattern change if you increase the number of columns?
i. Do you see any patterns for large set?
d) What other patterns can you generate using different recursive relationships?
What other recursive relationships are there that use 4 values in a row?
I want you to be involved in solving this problem, too, so this problem is set up on an interactive excel spreadsheet that you can download.
Download the File