That sounds like a combinatorial problem...alphabets from AAA to ZZZ, numbers from 000 to 999.

That means one of the total sum of possible car plates is 26^3.

Since we want to find pairs (x, y) that x + y = 1000. That means the total sum would also add up sum([1 for x in range(1000) for y in range(1000) if x + y == 1000])/2 since there is a symmetry.

But wait, find the expected number of plates he needs to see for a win. So maybe we need to borrow something from statistics (Possion/chi-squared distribution) or queueing theory...?

Edit: ah I saw the solution, it is a Markov chain.