# Magic Telephone Number Problem

I received the following email on President's Day - February 16, 2004

O.K. All you brilliant people, let me know how this one is done...

You'll be surprised by the answer. So make sure you do this. Here is a math trick so unbelievable that it will stump you. Personally, I would like to know who came up with this and why that person is not running the country....

- Grab a calculator. (you won't be able to do this one in your head)
- Key in the first three digits of your phone number (
*NOT*the area code). - Multiply by 80.
- Add 1
- Multiply by 250
- Add the last 4 digits of your phone number
- Add the last 4 digits of your phone number again.
- Subtract 250
- Divide number by 2.

Do you recognize the answer?

Yes. It's my number .... FREAK?

Hint: Compare the doing with the undoing. Doing, like adding and multipling and Undoing, like subtracting and dividing.

*Discussion:*

*1 - With algebra and letters ...*

Suppose my phone number was xyz abcd.

If I write it as a seven digit number I would
get x yza bcd

So, with that in mind, lets work the problem.

(((((xyz * 80 ) +1 ) * 250 ) + abcd) + abcd) - 250)
/ 2 simplify with algebra;

because (xyz *( (80 + 1) * 250) + 2(abcd) - 250) / 2 is equal to;

(xyz * (81 * 250) + 2(abcd) - 250) / 2 is equal to;

(xyz * 20 250) + 2(abcd) - 250) / 2 is equal to;

(xyz * 20 250 - 250 ) + 2(abcd) ) / 2 is equal to;

(xyz * 20 000 ) + 2(abcd) ) / 2 is equal to;

((20 000 * xyz) + 2(abcd)) / 2 is equal to;

10 000 * xyz + abcd is equal to;

xyz abcd

*2 - With a phone number... *

Substitute your phone number for xyz and abcd and work through the equations, that might help.

Suppose the your phone number was 123 4567 or 1 234 567

(((((123 * 80) + 1 ) * 250 ) + 4 567) + 4 567) - 250) / 2 solve

(((((9 840 + 1 ) * 250 ) + 4 567 ) + 4 567 ) - 250) / 2

((((9 841 * 250 ) + 4 567) + 4 567) - 250) / 2

(((2 460 250) + 4 567 * 4 567) - 250 ) / 2

((2 460 250 - 250) + (4 567 + 4 567) / 2

((2 460 250 - 250) + (2 * 4 567) / 2

((2 460 000) + (2 * 4 567) / 2

((2 * 1 230 000) + (2 * 4 567) / 2

1 230 000 + 4 567

1 234 567

*Mind boggler*: To prove you should be running the
country make your own.

Like ...

- Grab a calculator. (you won't be able to do this one in your head)
- Key in the first three digits of your phone number (NOT the area code)
- Multiply by 300
- Add 100
- Multiply by 100
- Add the last 4 digits of your phone number
- Add the last 4 digits of your phone number again.
- Add the last 4 digits of your phone number one last time
- Subtract 10 000
- Divide number by 3

Do you recognize the answer?

*Enjoy!*