[am17an]

This is one of my favourite problems, I still remember that it has a very real edge case even though I solved it more than 10 years ago. Thank you for the problem!

[vhcr]

I'm guessing if you only calculate based on the digits, the probability is going to be slightly different than the real one, because you only have a finite number of plates you can choose from.

[SethTro]

I'm glad you enjoyed! It was a real game I played when driving around.

[JohnLocke4]

Is your real name also Seth? This is wholesome and hilarious

[SethTro]

Yes, the other name in the problem is my sister's name :)

[dpacmittal]

Sounds like the birthday paradox problem. Is it?

[LanceH]

Nearly, but not 8 digits of precision worth.

[knollimar]

Can you reuse a plate with 500?

[hatthew]

The wording seems to strongly imply no; you need two separate plates with 500 on them.