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# The Telephone Game

You can impress your friends with this calculator game; you can impress them even more if you can explain to them how it works!

Grab a calculator.

Type in the first three numbers of your seven digit telephone number.

Multiply by 80

Add one

Multiply by 250

Add the last four digits of your number

Add them again

Subtract 250

Divide by 2

Type in the first three numbers of your seven digit telephone number.

Multiply by 80

Add one

Multiply by 250

Add the last four digits of your number

Add them again

Subtract 250

Divide by 2

What is the final number?

The result, of course, is your telephone number. Seems bizarre? Not really. If you know some algebra, keep reading to find out why it works!

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.

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