amazing math trick? or . . . please tell me how this works!

[Bertha Venation]

Got this in email:

1. Grab a calculator

2. Key in the first three digits of your phone number (NOT the areacode)

3. Multiply by 80

4. Add 1

5. Multiply by 250

6. Add the last 4 digits of your phone number

7. Add the last 4 digits of your phone number again.

8. Subtract 250

9. Divide number by 2

Recognize the result?

[gristy]

1. It's just algebra...

If your phone number is XXX-YYYY, then they are asking you to calculate

(((80*XXX)+1)*250+YYYY+YYYY-250)/2

which simplifies to (showing a couple steps)

=(250*80*XXX+250+2*YYYY-250)/2
=(20000*XXX+2*YYYY)/2
=10000*XXX+YYYY

which will be your original phone number, since multiplying the first 3 digits XXX by 10000 will put them in just the right place relative to the last 4 digits.

Fun!

edit: oops! Fixed some errors

[ProudGerman]

2. Cute

I'm also interested in how people come up with these math trick formulas.

[cjbuchanan]

3. Here is your solution

Basically, you a just taking the long way to multiply your phone number by 2. Then you are dividing by 2 at the end.

Let's say your phone number is 242-5656.

For example, take you first three numbers. Let's use 242. If you look at your phone number as a seven digit number, then the first three numbers represent the million, hundred-thousand and ten-thousand spots. So we need to move the 242 to those spots. That's where the multiply by 80 and then 250 come in.

80*250 = 20000

That would make 242*20000= 4840000.

That is twice the number of your first three numbers if you look at you phone number as a seven digit number.

The plus one is canceled out later by step 8. By adding 1 and then multiplying by 250, you are just adding 250 to your total. Step 8 takes that away.

In steps 6&7, you just add the last four numbers twice.

When you divide by 2, you’re got your phone number.

Hope this helps.