How come Key A can open Lock A. Key B can open Lock B. But not lock A. And key C can open all the locks? Doesn’t that mean A and B should be able to open each other?
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Instead of thinking about a key “opening” a lock, let’s switch to thinking of a lock as “recognizing” a key. Then we can say that locks are built in such a way that they will “recognize” one or more keys.
If we have your three keys, A, B, and C, and all of them are unique, we can design Lock A to recognize both Key A and Key C, and Lock B to recognize Key B and Key C. Thus neither of the locks will recognize the other’s first key, but they can _both_ recognize Key C.
The way this actually works is by manufacturing the lock to be able to be opened in two separate positons instead of just one. If we then happen to make the second position the same for all locks, we now have the ability to make a “master” key that will fit that second position in every lock.
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