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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:
Grab a calculator.
Type in the first three numbers of your seven digit telephone number.
Multiply by 80
Multiply by 250
Add the last four digits of your number
Add them again
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.
Comment by Lawrence K on Nov 17, 2005I remember as a kid a bunch of those little calculator games, and every time I saw one, I thought it was like magic. Showing the algebra behind it is like debunking a myth. It can almost be a bit of a let down, but at the same time, there's great satisfaction in knowing.
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