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jgrier3 · Jun 8, 2010, 04:40 PM

A phone number consist of seven digits plus the area code. How many possible phone numbers can have the area code 229?

galactus · Jun 8, 2010, 06:40 PM

That would depend on the restrictions on the number.

i.e. besides the area code, the number rarely begins with 0 and there is most likely no such number as 229-000-0000.

But, that notwithstanding, there are 7 digits to place and 10 choices for each (assuming repetition and no restrictions as aforementioned). So, there are
$10^{7}$ different numbers in said area code.

ebaines · Jun 9, 2010, 06:06 AM

I'm sure that the OP is looking for the answer as Galactus gave it - after all, this is a "math" forum, not a "telephone company" forum. However, in case you're interested: the actual number of usable telephone numbers for any given area code in the US is actually less than $10^7$ . Since the first number of the exchange code is restricted to the digits 2-9 (0 and 1 are not allowed), this reduces it to $8 \times 10^6$ . Then the number of options is further reduced by certain rules such as no phone number is assigned between 555-0100 and 555-0199 (that's why the fictional phone numbers used in movie or TV scripts are always 555-something) - this takes out 100 possibilities. Finally, the second and third digits can't both be 1 (such as 911) - which takes out another 80,000 combinations. After you take these rules into account you end up with a total of 7,919,900 possible numbers within an area code.

Stratmando · Sep 13, 2010, 03:41 PM

I think in the old days, the middle number of an area code was an 0 or a 1.
I see other numbers now.

ebaines · Sep 13, 2010, 03:53 PM

Originally Posted by Stratmando

I think in the old days, the middle number of an area code was an 0 or a 1.
I see other numbers now.

That's right - it changed in the US back in the 80's. The first digit of an area code is still restricted to 2-9. The middle digit used to be only 0 or 1, which let the switching equipment distinguish between an area code being dialed versus the "NNX" exchange code, which at the time didn't alow either a 0 or 1 for the 2nd digits. This enabled 7-digit dialing for local calls to be easily distinguished from a 10- or 11-digit number, even as the dialing was in progress. Now that an area code can "look like" an exchange code most phone systems require you to dial 1 + area code + number, even for local calls in your own area code. Otherwise there would have to be some sort of "time out" mechanism that would guess whether you've finished dialing after 7 digits, and that would lead to more wrong numbers.