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In the past month I've seen two different number plates that are the same as mine except for just one letter or number. This seems pretty chancy to me. So just what are the odds of this happening?

My number plate is of the form "LL NN LL", where "L" is a letter and "N" is a number. Let's say my number plate is "AQ 46 DL". I've seen "AR 46 DL" in the street where I live and today "AQ 41 DL" in the same suburb. As you can see the former differs only at the second letter and is different by only one letter ('R' comes after 'Q'). The latter differs only at the second number and is out by five ('6' vs '1').

There could be up to (26*26) * (10*10) * (26*26) number plates of this form in circulation. This is just over 45.5 million. However, this form has only recently been introduced so the first letter is almost always 'A'. I've seen one or two beginning with B but that's it. Let's assume the full set of those starting with 'A' is out there: that's 1.75 million (1*26 * 10*10 * 26*26).

So how many differ from my plate by just one letter or number?

Consider the letters first. We fix the first letter as 'A' and the two numbers as the same as mine. Then we fix two of the other letters and let the third vary. This can be done for any of the three letters so we multiply the result by three. So we get 3*25 = 75. So there are 75 number plates that differ by one letter from mine.

Now consider the numbers. We fix the first letter as 'A' and the other three letters as the same as mine. Then we fix one of the numbers and and let the other vary. This can be done for either of the two numbers so we multiply the result by two. So we get 2*9 = 18. So there are 18 number plates that differ by one number from mine.

So in total there are 75+18 = 93 number plates that differ by a single letter or number from mine. Out of the 1.75 million that represents about a one in 18,900 chance that I'll see one. Or 0.005%. That's pretty small.

And I've seen two in a month. That's a one in 357 million chance!

I wonder how many cars I see in a month that I take note of the number plate of. If it were 100 a day, that's 3,000. Makes it pretty lucky to spot two.

One factor not considered above is the location of issuing authorities for number plates. I would imagine each RTA office would have a block (or several) or number plates that it can issue. So it's quite possible that if all the cars in a suburb were initially registered at their local RTA office they'd all have similar number plates. This could increase the chances of seeing a similar number plate.

However, I actually bought my car from a dealer in a suburb a long way from home (but still in Sydney). As perhaps many others do. So this might reduce the impact of location. Nonetheless perhaps only a percentage, a significant percentage to be sure, of number plates of this form are in Sydney.