Using algebra to figure out the trick but I'm stuck!

Factual Questions
1

OK, so I get this email:

This is quite impressive, Grab a calculator.

  1. Key in the first three digits of your phone number (NOT the area code)
  2. Multiply by 80
  3. Add 1
  4. Multiply by 250
  5. Add the last 4 digits of your phone number
  6. Add the last 4 digits of your phone number again.
  7. Subtract 250
  8. Divide by 2
    If you do not recognize the answer, you made a mistake!

It’s pretty nice but I’m not that impressed. I get the feeling that things are cancelling out but you can’t see that on a calculator. So I pull out a piece of paper and try to work out the problem. The problem is, I can’t get everything to cancel out! I must be missing something!

x = first 3 numbers of your phone number
y = last 4 numbers of your phone number

I started with the followng formula:
((80x+1)250+2y-250)/2=x+y
I end up with: 500x+y=x+y

Then I removed a paranthesis:
(80x+1*250+2y-250)/2=x+y
and now I end up with: 40x+y=x+y

I can see how the 250’s & the 2y cancel out but that 80 throws me off.
Anyone have ideas?

Frustrated,

Ivan

2

Let:

x = first 3 numbers of your phone number
y = last 4 numbers of your phone number

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

x

  1. Multiply by 80

80x

  1. Add 1

80x + 1

  1. Multiply by 250

20000x + 250

  1. Add the last 4 digits of your phone number

20000x + 250 + y

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

20000x + 250 + 2y

  1. Subtract 250

20000x + 2y

  1. Divide by 2

10000x + y

Since y has four digits, this last expression is x concatenated with y, i.e., your phone number.

3
  1. Key in the first three digits of your phone number (NOT the area code) = x
  2. Multiply by 80 = 80x
  3. Add 1 = 80x + 1
  4. Multiply by 250 = 20,000x + 250
  5. Add the last 4 digits of your phone number= 20,000x + 250 + y
  6. Add the last 4 digits of your phone number again=20,000x + 250 + 2y
  7. Subtract 250= 20,000x + 2y
  8. Divide by 2= 10,000x + y

(10,000x puts the first three digits in the correct position to add the last 4 digits to it and reveal your telephone number.)

If you do not recognize the answer, you made a mistake!

4

((80x+1)250+2y-250)/2
(80x+1)125+y-125
125*80x+125+y-125
10000x+y

-chookie

5
  1. Key in the first three digits of your phone number (NOT the area code)
  2. Multiply by 80

80x

  1. Add 1

80x+1

  1. Multiply by 250

250(80x+1)

  1. Add the last 4 digits of your phone number

250(80x+1) + y

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

250(80x+1) + 2y = 2000x+250+2y

  1. Subtract 250

2000x+2y

  1. Divide by 2

1000x+y

6

What everyone else has said without words is that in your example, using X for your prefix and Y for your extension, inputting X and then Y is not equivalent to X + Y; it is equivalent to 10000x + y.

What I mean is this: Your phone number (123-4567) is not 123+4567, it is (123 * 10000) + 4567. You forgot this when you set up the equation, which should read ( 250 ( 80x + 1 ) + 2y - 250) / 2 = 10000x + y .

7

Of course, it only works if you have a 7 digit phone number. We have 8 digit numbers here in Australia and so the algorithm did not return the correct result.

8

I think the real question here is: Who comes up with this stuff?

9

ahhh, thank you very much!

And thanks for the clear explanation of the error Bambi!

10

And… how can we punish them?

11

pretty easy

((80*A+1)250+2B-250)/2 =

(25080A +250 -250+2*B)/2 =

10000*A + B