Work backwards?

No fuckin clue.

250(80x+1)->
20,000x +250->
20,000x +250 +y ->
20,000x +250 +2y ->
20,000x + 250 +2y -250 ->
10,000x +y ->

basically a lot of math to multiply the first three digits by 10,000 and then add the last four digits

(((80x + 1) * 250 + 2y) - 250) * 0.5

where x is the first three digits of your phone number and y is the last four digits.

We can reduce this as follows:

0.5 * ((80x + 1) * 250 + 2y) - 125

(80x + 1) * 125 + y - 125

125 * 80x + 125 + y - 125

125 * 80x + y

10000x + y

Note that the effect of multiplying by 10000 is to shift the first three digits of your phone number left by four digits, effectively "making room" for the last four digits.

So really someone just did the simple thing (multiply by 10000) then factored in a bunch of silly ways to obfuscate what they were doing. That's pretty much the standard operating procedure for stuff like this.

2. Multiply by 10,000.

3. Add the last 4 digits of your phone number...

look familiar?

amazing!!! how can math possible do such amazing things???

Formula [(80A + 1) x 250 +B +B -250]/2

= [20000A +250 +2B -250]/2

=[20000A +2B]/2

= 10000A +B

Plug in A say 323 and it becomes 3230000 and B 7101 add them together and you get

3237101

It's like a psychic telling you exactly what you've told them and making it sound like they already knew.

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

2. Multiply by 10,000.

3. Add the last 4 digits of your phone number...

look familiar?

amazing!!! how can math possible do such amazing things???

[/condescension]

In other words: (abc x 10000) + defg = abcdefg.

I've broken it down into three parts where the puzzle maker tried to confound what's actually happening. Here they are:

1)80x250=20000
20000/2 = 10000
10000x(abc)= abc0000

2)80+1=81
81x250=20250
20250-250 = 20000
20000/2 = 10000
10000x(abc) = abc0000

3)(defg)+(defg) = 2d2e2f2g
2d2e2f2g = 2(defg)
2(defg)/2 = defg
abc0000+defg = abcdefg

I know that's not a very mathematically correct way to show how this works, but it makes sense to me.

You will also note that the rule about not using the area code is pure stagecraft. But isn't that the whole point?

Won't some enterprising soul come up with a version that also incorporates the area code? Then it will look even more convoluted and impressive!

You've just given over your phone number to The Man.

Three businessmen need a hotel room (this is an old riddle) and the clerk gave them a room for $30 - after they went up he realized that he had overcharged for the room, it was really only twenty-five dollars. He called the bellhop over and sent him up with 5 one dollar bills to give the men a refund. The bellhop couldn't figure out how to divide the five among three so he gave them each one dollar and kept two for himself. So each of the men paid $9 dollars or a total of $27 and the bellhop has $2 for a total of $29 - what happened to the missing dollar?

Now give Dan some time.

Grab a calculator.

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

2. Multiply by LXXX

3. Add I

4. Multiply by CCL

5. Add the last IV digits of your phone number

6. Add the last IV digits of your phone number again

7. Subtract CCL

8. Divide by II

Recognize the answer?

1. Key in your area code

2. Add your area code again

3. Multiply by 500

4. Add the first three digits of your phone number (NOT the area code)

5. Multiply by 80

6. Add 1

7. Multiply by 250

8. Add the last 4 digits of your phone number

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

10. Subtract 250

11. Divide by 2

From the businessmen's perspective, they paid the hotel $10 each and each received a $1 back. So the hotel got $27 and they have the remaining $3. (3x9)+(3x1)=27+3=30

From the bellboy's perspective, the hotel got $25, he skimmed $2 and the remaining $3 went to the business men. 25+2+3=30