How many unique house keys can possibly exist?

Question

A Yahoo! answers user suggested that there are 5^5 possible unique configurations for a physical key, but the answer wasn't sourced. I wondered if anyone had similar numbers for how many possible key combinations there are. I ask because, it seems impossible that there can be a unique key for every lock in the world, and I'd like to know how many different key configurations a thief would have to try to have a certainty of cracking the lock (if the thief didn't want to force the lock in another way.)

Ankur Dwivedi · Accepted Answer

There's a paper on the subject available to read about unique house keys at jstor.org - https://www.jstor.org/stable/3613451 and the answer isn't quite as simple as {the number of cuts}^{possible cut depths} because there are cases where one cut will remove the possibility of an adjacent depth and so forth. It does get complicated though! There are so many different factors to take into account that it's likely each lock/key combo is pretty unique although some cheap padlocks could have the same shape if the manufacturer is cutting corners.

How many unique house keys can possibly exist?

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