Intermath | Workshop Support
Write-up


Title
Composite Numbers


Problem Statement

  1. Pick a number.
  2. Multiply this number by 200.
  3. Add 836 to the new number.
  4. Divide the new number by 2.
  5. If you have already had your birthday this year, add 1581. If you haven't, add 1580.
  6. Last step: Subtract the four digit year that you were born.

Try the process a few times with different initial numbers. Why are the results significant? Explain why the process produces this pattern.
 

Plans to Solve/Investigate the Problem

Use an Excel spreadsheet to follow steps 1-6.  While exploring this problem I first tested the results using my birth year and then I tested the results using a different birth year.  As expected, the ending results were different, but the pattern that was developed was true for both birth years.

 

Investigation/Exploration of the Problem

Using an Excel spreadsheet I was able to test the results and I found that the first digit(s) of the solution were the same as the number I picked in step one.  I also found that the remaining numbers do not change.

 

Click here to see the spreadsheet.  Try it for yourself.  Fill in any number in the A1 cell and watch what happens.

 

Why does this produce this pattern?

Let's look at the problem another way.  Let 'n' be your number.

200n+836

       2

 

Gives you:

100n+418

 

Then add 1580 or 1581 (depending upon if you have already had your birthday):

100n+418+1580(1)

100n+1998

 

Then subtract your birth year:

100n +1998-1973

 

Gives you:

100n + 25

 

The number 25 is significant because this becomes the last two digits of your solution.  This number will change depending upon the result from the subtraction of your birth year, but the solution will become the last digit(s) of your solution.  The 100n produces the first digit(s) for your solution. 

 

Author & Contact
Teresa Johnson
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