How is this lame math trick possible?

May 6, 2006 12:50 PM

I know this is lame, but how is this lame math trick possible?

1. Grab a calculator
2. Key in the first three digits of your phone number (NOT the area code)
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

The final sum should be your phone number. How in the hell does this work?!

posted by JPowers to Education (5 answers total)

Best answer: First three digits are x, last four digits are y.

Your telephone number is 10,000x + y, agreed?

Ok, take your instructions. You're forming this expression:

((80x+1)250 + 2y -250)/2

Simplify:

(80x+1)125 + y -125

80*125*x+y

10000x + y

There you go!
posted by Wet Spot at 12:56 PM on May 6, 2006

Say 'x' for the number formed from the first three digits and 'y' for the number formed from the last three digits (eg, x=555, y=1212).

Now, your phone number is 10000x+y, agreed?

What you're calculating looks like this, step by step

x
80x
80x+1
250(80x+1)
250(80x+1)+y
250(80x+1)+2y

expanding that just a little, after step 7 you have got
20000x+250+2y

Now, subtract 250 to get
20000x+2y
and divide by 2 to get
10000x+y,
which we agreed up above is your phone number. Yay.
posted by Wolfdog at 12:57 PM on May 6, 2006

On preview, I got beat by 3 minutes...Curses.
posted by SeizeTheDay at 12:59 PM on May 6, 2006

It works because what you're doing is keying in the first three digits, multiplying by 10000 and then adding the last four. The rest is misdirection.

(On preview, I might as well remove my clumsy algebra.)
posted by box at 1:01 PM on May 6, 2006

It's an identity.

Code your phone number as a vector:

x = [1 2 3 4 5 6 7]

so x(1) is the first digit, x(2) is the second, etc...

(*) Then your phone number can be generated from the digits by adding x(7) + 10*x(6) + 100*x(5) ...

So if we took the first three digits of your phone number y = 250*(80*x[1 2 3] + 1) = 2,000,000*x(1) + 200,000*x(2) + 20,000*x(3) + 250 (this gets us to step 6)

Then added digits x(6-10) to this, then getting rid of that extra 250 by subtracting it off, then dividing by 2, gets us into the form I mentioned in (*)
posted by onalark at 1:01 PM on May 6, 2006