Have you ever had a 10 digit phone number where all 10 numbers, 0-9, appeared once each? I have a part-time job that got me thinking about this, and I realized that I never had such a number.
Well, it would be unlikely in the extreme (we’re talking infinitesimally small odds), so I’m not surprised you haven’t had one.
FTR neither have I.
Well ignoring limitations on types of numbers (can’t start 1 or 0) can’t start n11 or have 555 as digits 4 through 6 and probably others), there are 10! different all digit numbers and 10^10 possible 10 digit numbers so about 0.036% of possible numbers have al ten digits.
There are something like 800 million phone numbers in use so something like 29,000 numbers out there should have all ten digits in them (assuming rndom assignment which isn’t true)
There are some ways to narrow this down. For example, the number 1 can only appear in the last 6 digits, and 0 only in X00-X00-0000 format. And I think the 2nd and 3rd can’t be the same in personal numbers, only 800 numbers and such.
412-867-5309
Why do you think this? There are a **ton **of area codes with the number 1.
Area codes can have a 1 in the 2nd and 3rd position as well. Dallas is 214 for example.
This looks to be a decent list of area codes
https://www.bennetyee.org/ucsd-pages/area.html
Not necessarily infinitesimal. In any given area code there are 7,999,900 numbers you could have, so those are the greatest odds that you could get any specific number. The pool of non-repeating numbers would be larger, but I’m too lazy to calculate.
Assuming numbers are assigned at random (I know they aren’t, but not sure it matters, the odds against are approximately 2755 to 1.
The first number is irrelevant, there are 9 chances in 10 that the second is different, 8 chances in 10 that the third differs from the first two, 7 chances in 10 that the fourth differs from the first three and so on. All in all 9!/10^9. AFAIK, area codes can now be anything, so I see no reason whey this is wrong.
I called that number, and Jenny didn’t answer 
Here’s my calculation.
Area codes cannot start with 0 or 1, and they can’t be of the form X11, so there are only 792 possible area codes, not 1000. For this problem I’m not sure if we should consider only the currently assigned area codes (per Frazzled’s link there are 411 of them) or all 792 so I’ll do it both ways.
Exchange numbers also cannot start with 0 or 1 or be of the form X11 and there are a few other reserved numbers, so the total number of 7 digit numbers in one area code is 7,919,900 (per wikipedia).
So the total number of possible phone numbers using any valid area code is 6,272,560,800, and the total number using the currently assigned area codes is 3,255,078,900.
The number of 10 digit numbers without repeats is 10! or 3,628,800, but this includes invalid numbers (ones where the area code or exchanges start with 0 or 1; obviously it doesn’t include any where either is of the form X11). There are 9! (362,880) where the area code starts with 0, the same number where it starts with 1 and similarly for the exchange, so the total of valid nonrepeating numbers is 10!-4(9!) = 2,177,280.
So I say the probability of a random number being nonrepeating is either 2,177,280 / 6,272,560,800 = 0.035% or 2,177,280 / 3,255,078,900 = 0.067%.
Sorry because typo. 1 is allowed: X11-X11-1111
When they were grafting new area codes onto the Greater Toronto Area, I was hoping they would add area code 234. Then I would have tried to get 234-567-8901*. ������ But 234 went to Cleveland or somewhere.
*Even better in international format: +1 234 567 8901
With how many combinations of numbers you can have (even with the various restrictions) it seems like the odds of this happening are pretty close to the odds of any other specific number coming up.
It’s like going to the grocery store and when the cashier gives you your total and you say ‘wow, 6 dollars even, what are the odds of that’. Well, they’re about the same as the odds of your total being $5.73 or $6.81. Sure, there’s a 1/100 chance that it’s an exact amount over any other number*, but all the other amounts also have a 1/100 chance. It’s just that, like the OPs question, exact dollar amount stand out and therefore appear to be more unusual.
In fact, I recall hearing/reading that when businesses get audited by the IRS, one of the things they’ll look for is the absence of exact dollar amounts. They’re as common as any other number, but because they don’t seem like they are, people fudging the numbers tend to leave them out.
*err, that’d be a 1/100 chance of the cents portion being the same, now that I re-read it.
Interesting. Another thing the IRS will look at is whether you have violated Benford’s law that states that states that a list of numbers taken at random, about 30% (= log 2) of them will start with a 1. The explanation is fairly esoteric, but it starts with the following observations. If asked to choose a random number between 1 and 9, one ninth will start with a 1. If you choose a random number between 1 and 19, more than half (10/19) will start with a 1. Between 1 and 29 more than 1/3 will start with a 1. And so on. It turns out that when all this is taken into account, in a list of numbers chosen at random, about 30% will start with a 1, log 3 - log 2 of them (about 17%) will start with a 2, log 4 - log 3 of them with a 3 and so on. Only about 5% (log 10 - log 9 = 1 - .95) will start with a 9. Unless there is an explanation (all phone numbers are 10 digits), a gross violation of Benford’s law is a red flag. Of course, this is now sufficiently well known that people making up accounting frauds are likely to know it already.
Similarly, businesses tend to have a standard profit margin. It differs depending on their field, but it tends to be pretty close to the same within a given field. For example, if they expect you to have a 30% margin, but yours is 25%, they’re going to look to see if you’re pocketing some of it. But, people (not all) are aware of that, so when they pocket money, they’ll also use some of the that money for day to day business expenses. Essentially running a small business out of their pocket, but more because it keeps the profit margin for the main business in check.
In other words, if you steal a hundred dollars, you’ll use thirty of it to buy stuff for the business.
Wouldn’t it be better ending in “10”?
Back when Google Voice started, you could search for available numbers in a variety of ways, so it might have been easy to get one with all ten digits (although ten sequential digits would be very limited). I got a phone number that’s my first initial followed by my last name (in some random area code).
No, but I currently have a number where 3 digits are used twice.
My own 10-digit number has five instances of a certain digit. I think this has a 1.6% chance if random.
But mine wasn’t a random coincidence. It seemed nifty to have a “special” number, but a phone number with ‘999’ or such cost hundreds of dollars or more. I complained to the young lady who was selling me a phone and she offered to sell me one of her own personal numbers for a small profit. “I can’t take your number!” I said. “No problem,” she replied. “I’ve got lots of numbers.”
For the first few months I got confused calls occasionally, always from a male. 
But Brian would.
