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Why do the first few steps work in this link? Answered

why does this work to find the third number? what's going on inside the lock?


The lock has a face with numbers up to 50 or so on it, but really its hard to machine mechanical tolerances that tight. (read: its expensive to do). Locks like this are tolerant to being +/- 2 numbers on either side of the actual correct number and still opening, simply because of the shape of the mechanism. In order to be strong, it has to be thick, and if its thick it can't 'fit' that many options in the given surface area of the tumblers and maintain that tolerance. Lastly, ease of manufacture - if they only have 13 different (increments of 4) tumblers for each layer, they can mass produce those components far more simply and assembly becomes a tonne simpler - then they just assign numbers in the 4 digit range to give the illusion of complexity.

Do you know why the rest of the method works. Specifically why does the method for finding the third number in the combo work?

It's just a mathematical certainty that only certain options mechanically work. I don't have a mathematical proof.

shrodinger says I win and lose...in secrecy.

Just a matter of how the lock is manufactured.