Here in Maryland, the license plates consist on 3 letters (I and O are not used) and a 3 digit number (we’ll stick with cars only here). So you have 24 letters and 10 numbers to choose from.
Even I can figure out that there are 1000 number combinations, but how do you figure out how many combinations there are with 24 letters to choose from?
So, how many cars have to be on the road until the tag numbers would start to repeat?
Well, there are 242424 = 13824 unique letter combinations. Each unique letter combination has 1000 possible number combinations to be paired with, so you could get a total of 13,824,000 combos.
After that, you start changing the ABC123 format for more unique combinations.
1000=10x10x10, so the letter combinations would be 24x24x24=13,824. This is assuming that the state of Maryland doesn’t eliminate letter combinations that might be perceived as offensive for one reason or another. I doubt if you’ll see FUK 123, for example or even GOD 666. Ignoring that you would have 13,824x1,000 or over 13.8 million possible license plates.
Howdy neighbor.
That would be 24[sup]3[/sup] x 10[sup]3[/sup] = 13,824,000 possible license plates, assuming the stated conditions. Note though that some letter combinations, like those that spell out obscenities, are automatically disqualified. So the true number is slightly less.
And according to this document, there were 4,363,000 cars registered in Maryland as of 2002. So we have a little breathing room yet.
Sorry to keep posting. I really should hold back until I’m ready to make one big post.
A little googling reveals that the state of Ohio forbids some 48 three-letter combinations, whereas the more Victorian state of Kentucky forbids 170 combinations. Some of their choices of what to prohibit are interesting.
I couldn’t find any reference on Maryland’s rules, though I only searched for a few minutes. Assuming for the moment that we’re like Kentucky, you would subtract 170,000 possibilities from the 13.8 million computed above, which still leaves plenty of wiggle room for the time being.
I wonder if by “cars” they mean cars, or vehicles. There are so many special tags out there, from Teamsters to every school in town to Barber Shop Quartet. Not to mention truck, commercial, handicapped, vanity and so on.
[QUOTE=Bytegeist]
Sorry to keep posting
[QUOTE]
Why?
Maybe because it keeps bumping the thread, keeping other more pressing questions off the top page. And maybe it will be seen as meaningless post-count padding. Anyway, while I’m here…
The total combinations for any state is
A[sup]B[/sup] * C[sup]D[/sup]
where
A = total number of allowable letters
B = number of letters on a plate
C = total number of allowable digits
D = total number of digits per plate
In this case, the variables are 24, 3, 10, and 3 respectively, as we know.
In California, they are 26, 3, 10, 4, which gives you 175,760,000
Of course, this doesn’t include vanity plates, obscene exceptions, etc.
We a have the special plates up here in Michigan. They have handicapped plates, of course, but they also have plates for military vets (various wars, plus the generic “Veteran”) as well some plates for local colleges, a plate honoring the auto industry, a plate commemorating lighthouses, one that says “Kid’s: Gotta Love 'Em” in place of the state motto, and probably a few more that I’m forgetting. They all substitute a word or symbol for the first letter of the license plate number. (The kiddie one has a heart.) This raises the number of plate combinations.
Let’s say that there are 15 such special plates in a certain state. They all substitute a word or symbol for the first letter. The number of combinations will be (24+15)2424*1000 = 207,360,000 combinations, minus those that are disqualified for being offensive.