# Using algebra to figure out the trick but I'm stuck!
**URL:** https://boards.straightdope.com/t/using-algebra-to-figure-out-the-trick-but-im-stuck/236511
**Category:** Factual Questions
**Created:** [March 26, 2004, 5:07am UTC](https://boards.straightdope.com/t/using-algebra-to-figure-out-the-trick-but-im-stuck/236511 "2004-03-26T05:07:21Z")
**Posts on this page:** 11
**Page:** 1
### Author:  [@ice1000](https://boards.straightdope.com/u/ice1000)
#### Post date: [March 26, 2004, 5:07am UTC](https://boards.straightdope.com/t/using-algebra-to-figure-out-the-trick-but-im-stuck/236511/1 "2004-03-26T05:07:21Z")
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
---
### Author:  [@Cabbage](https://boards.straightdope.com/u/Cabbage)
#### Post date: [March 26, 2004, 5:18am UTC](https://boards.straightdope.com/t/using-algebra-to-figure-out-the-trick-but-im-stuck/236511/2 "2004-03-26T05:18:44Z")
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.
---
### Author:  [@Cillasi](https://boards.straightdope.com/u/Cillasi)
#### Post date: [March 26, 2004, 5:18am UTC](https://boards.straightdope.com/t/using-algebra-to-figure-out-the-trick-but-im-stuck/236511/3 "2004-03-26T05:18:46Z")
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!
---
### Author:  [@Chookie](https://boards.straightdope.com/u/Chookie)
#### Post date: [March 26, 2004, 5:19am UTC](https://boards.straightdope.com/t/using-algebra-to-figure-out-the-trick-but-im-stuck/236511/4 "2004-03-26T05:19:42Z")
> [@ice1000](#):
>
> 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
((80x+1)250+2y-250)/2
(80x+1)125+y-125
125\*80x+125+y-125
10000x+y
-chookie
---
### Author:  [@don\_t\_ask](https://boards.straightdope.com/u/don_t_ask)
#### Post date: [March 26, 2004, 5:20am UTC](https://boards.straightdope.com/t/using-algebra-to-figure-out-the-trick-but-im-stuck/236511/5 "2004-03-26T05:20:59Z")
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
---
### Author:  [@Bambi\_Hassenpfeffer](https://boards.straightdope.com/u/Bambi_Hassenpfeffer)
#### Post date: [March 26, 2004, 5:26am UTC](https://boards.straightdope.com/t/using-algebra-to-figure-out-the-trick-but-im-stuck/236511/6 "2004-03-26T05:26:51Z")
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 .
---
### Author:  [@Cunctator](https://boards.straightdope.com/u/Cunctator)
#### Post date: [March 26, 2004, 6:53am UTC](https://boards.straightdope.com/t/using-algebra-to-figure-out-the-trick-but-im-stuck/236511/7 "2004-03-26T06:53:50Z")
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.
---
### Author:  [@rayray5884](https://boards.straightdope.com/u/rayray5884)
#### Post date: [March 26, 2004, 7:40am UTC](https://boards.straightdope.com/t/using-algebra-to-figure-out-the-trick-but-im-stuck/236511/8 "2004-03-26T07:40:45Z")
I think the real question here is: Who comes up with this stuff?
---
### Author:  [@ice1000](https://boards.straightdope.com/u/ice1000)
#### Post date: [March 26, 2004, 11:21am UTC](https://boards.straightdope.com/t/using-algebra-to-figure-out-the-trick-but-im-stuck/236511/9 "2004-03-26T11:21:11Z")
ahhh, thank you very much!
And thanks for the clear explanation of the error Bambi!
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### Author:  [@moriah](https://boards.straightdope.com/u/moriah)
#### Post date: [March 26, 2004, 7:12pm UTC](https://boards.straightdope.com/t/using-algebra-to-figure-out-the-trick-but-im-stuck/236511/10 "2004-03-26T19:12:49Z")
> [@rayray5884](#):
>
> I think the real question here is: Who comes up with this stuff?
And… how can we punish them?
---
### Author:  [@sailor](https://boards.straightdope.com/u/sailor)
#### Post date: [March 26, 2004, 7:46pm UTC](https://boards.straightdope.com/t/using-algebra-to-figure-out-the-trick-but-im-stuck/236511/11 "2004-03-26T19:46:25Z")
pretty easy
((80\*A+1)_250+2_B-250)/2 =
(250_80_A +250 -250+2\*B)/2 =
10000\*A + B