By Tonya C. Brooks

I decided to take a look at what I could do while playing around in Excel Spreadsheet for this investigation, and I found that at a certain point, Excel wasnÕt able to help me much but I will talk about this later in this blip.

I decided to see how long I could get a particular pattern to run.  I wanted to take a set of four numbers and repeat a pattern of taking the absolute value of the differences between one number and the next and then see how long I could go before I get down to zero.

I set up my problem in this way.  At first, I was putting in four numbers.  I set up the Excel sheet to take the absolute value of A - B, B - C, C - D and D – A for the rows below my given numbers.  This way, my sheet was automatically filled for me.

After playing around with little success on what ransom numbers I was choosing, I decided to try some that contained patterns.  For example, I tried numbers like 2, 4, 8 and 16.  I noticed that with certain numbers, this pattern would give me a few more repetitions than I had before.  IÕm a little thick headed, so I tried several other numbers before I decided to try the pattern of exponents.  Once I did this, things went pretty smoothly.  It also helps that we explored this a little in class as a group.

I tried several different patterns of exponents, and I was finally able to end up with a string that lasted 54 rows using the pattern of squaring, cubing and fourth powers of a number, and then tried several whole numbers as well as decimals.  However, at this point, I realized that with my technology I wasnÕt able to continue as easily.  The downside to using Excel is that we are only able to input a string of numbers so long.  After a string of 15 digits, Excel will not accept any more digits and will not work with a longer string.

So, one question is: Will the process always end up giving us a string of zeros?  Well, at first I thought that the answer to this question was yes but after playing around and getting the string I ended up with, I began to think that the answer might be maybe not.  Since I kept getting longer periods before getting that string of zeros by adding certain digits onto the string.  I think that if we had a computer program that was capable of working with longer strings of digits that we would be able to generate longer and longer periods of rows before we ended up with a set of zeros.  I just donÕt think that the average person is able to afford a program that will allow us to delve into this project any farther.