- Pick a number.
- Multiply this number by 200.
- Add 836 to the new number.
- Divide the new number by 2.
- If you have already had your birthday
this year, add 1581. If you haven't, add 1580.
- 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.
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
Let's look at the problem another way.
Let 'n' be your number.
Then add 1580 or 1581 (depending upon if you
have already had your birthday):
Then subtract your birth year:
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.
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