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# Telephone Number Puzzle: A Calculator Game

I suspect calculator games have been around almost as long as calculators. I remember as a child seeing cutesy little games in which you punched numbers in the calculator, performed arithmetic operations, and then flipped the calculator upside-down to see a word spelled out.

There were also puzzles and games which were more clearly mathematical in nature, such as this one, which has been making the rounds again:

Quote
Grab a calculator.
Type in the first three numbers of your seven digit telephone number.
Multiply by 80
Multiply by 250
Subtract 250
Divide by 2

What is the final number?

The result, of course, is your telephone number. When I was a child, this seemed impossibly bizarre and extraordinary. But the truth is, any student with a foundation in algebra can figure this out.

Let X be your first three digits, and Y be your last four digits.

Then the steps are as follows:

Begin with X
Multiply by 80 --> 80X
Add one --> 80X + 1
Multiply by 250 --> 20000X + 250
Add Y (twice) --> 20000X + 250 + 2Y
Subtract 250 --> 20000X + 2Y
Divide by 2 --> 10000X + Y

Which, of course, is your telephone number.

Suggested class plan: Have students try out the puzzle first on their calculators, and then walk through the algebraic process until they see how the result is obtained.