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I got asked the cars sold in a year in California question. I answered by saying I would look for a car that was new two years ago, and one that was new this year, and then difference the license plate numbers and divide by 2.

Took the interviewer a while but they finally figured it out.

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What do you mean by 'difference the license plate numbers'?

Chuck is assuming (reasonably) that license plate numbers are assigned in sequential order to all new cars.

So if 1000 cars are sold in a year, maybe he'll see plate #267 from Year 0, and plate #1796 from Year 2. 1800 - 300 / 2 = 750 cars per year, close enough.

Exactly, in California private plates are of the form /[0-9][A-Z]{3}[0-9]{3}/ you can think of it as three digits base 10, and three digits base 26, one digit base 10. There are letter combos they don't use like SUX or FUX etc but each of those only reduce the pool by 1000 vehicles for each banned letter sequence so overall a relatively small hit on the estimate. My wife pointed out you can be more accurate if you include the month of the renewal in the registration (its on the plate as well) to get total months in your sample.

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