It does seem odd to me, because phone numbers aren’t random. There are just over 300 area codes in the US, and I suspect that most of the people in your address book share just a few of those. But I may be overestimating the chances, but I’m not skilled enough to do the math.
It’s a hijack and I’m not sure it’s proper to post it in GQ. Perhaps Spoiler tags will prevent rebuke.[SPOILER]
While searching for that, I found another coincidence I posted in MPSIMS.
https://boards.straightdope.com/sdmb/showpost.php?p=13660126&postcount=1[/SPOILER]
Thanks for the link. I’m for sure going to have to watch it a bunch more times to wrap my head around it.
OK, i just whipped up a python script (boy am I rusty!) to generate a string from 000 0000 to 999 9999, representing a 7-digit number. As said above, obviously, many of these numbers are not legitimate phone numbers, but this will create an upper bound.
The script can compare strings for an exact match, or any n-character match you want. After doing a sanity check with known numbers (like we should expect on average 23 numbers for a 3-digit match out of 365 on the birthday problem) and being convinced that the output at least looked correct, I ran 1000 trials for a (at least) 6-digit match on a 7-digit phone number, with an output also showing me the two numbers that matched.
On 1000 trials, it gave me an average of 502 numbers needed to be generated before 6 out of any 7 digits matched in a previous number generated. For all 7 to match (which couldn’t happen with phone numbers in the same area code, of course), I just ran 100 trials (my code is a bit slow), and that gave me a result of 3906, where the expected average should be around 3724, using the equation above, so it looks like my code is in the right ballpark.
From the facts given, we know that there are about 775 exchanges (3 digit prefix) and the coincidence is that the friend’s number and the mother’s number only differ by one digit in the exchange. So the first question is how many of the 775 exchanges are there that differ by one digit, and then how many possible 4 digit suffixes exist for all exchanges. From this, analogous to the shared birthday problem, we could calculate the probability of this coincidence as 1 minus the probability of it not happening. Without an accurate list of the exchanges, the best we could do, as pulkyamell suggests, is estimate an upper limit but with the restriction that we are limited to only 775 3 digit prefixes, not the 1000 that his(?) approach uses.
Actually, quick nit-pick: the expected average of 3724 is not as precise as it seems. I neglected to take into account that because of the gigantic numbers used in the equation, that Wolfram Alpha uses estimated values at some points. So my empircal result is probably closer to the true expectation of how many random numbers from 0000000 to 9999999 you’d need to pick before two are expected to match in the group. I’ll keep it running in the background for shits & giggles and report back after a larger sample size. (It’s kind of tangential to the problem at hand, but it’s interesting to see that if you got about 4000-ish people together to write down a number from one to ten million, you’re likely to have a match somewhere in that group.)
ETA: (And, yes, “he” is the correct pronoun for me.)
OK, to keep it simple, if we just do 775 exchanges * 10000 numbers per exchange, that makes 7 750 000 possible numbers. With those plugged in, I’m now getting an average of needing about 448 numbers on average for there to be a group of two six-digit matches.
I saw a few of the latest comments, I’m working thru understanding them.
I’ll also add that I double checked my list, and the next, most similar numbers, have all but two numbers in the suffix different, the rest of the numbers exactly the same otherwise.
1st story, in the orchard, that would’ve freaked me out a little bit as well. 2nd story I guess I’d have to know more.
thanks for sharing.
I’m not sure if I should share this as it’s kinda off topic, kinda on topic, but the craziest coincidence I’ve probably had occur was when I was at a friend’s folks house eating Christmas dinner. One of his uncles was joking around and said something about how he thought he was getting taller (when really he just had some high waters on). I mentioned a My Three Sons episode I remembered where they were messing with Uncle Charlie, trying to make him think he was getting taller by sawing off a little of his cane, hemming his pants, and maybe even messing with his chair at the dinner table.
My buddy said it sounded like an episode of MASH where the two laid back surgeon guys were messing with the bald headed uptight guy that dated Hotlips, trying to fool him into thinking the same thing. I said I’d never seen the episode, no doubt because I’d only watched MASH a few times in my life, and that was forever ago.
Anyway, fast forward a few hours, I go home from dinner, turn on the tv, look at the channel guide and on it I see theres an episode of MASH listed on one of the channels. Entirely because we’d just talked about the show, I switched to it. It was just coming back from a commercial break. I’ll be gadamn’ed if it was not only the episode he’d told me about, but it was the exact scene he’d told me about that was just starting.
there’s probably no way to ever quantify what a coincidence that was, so I won’t dare ask.