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Mechanical combination locks

My new "home" has an idiotic mechanical combination lock at the entrance. One lucky evening I had to spend a few hours outside due to a pure mechanical failure of the lock shown below.

Such primitive and low-reliability mechanical locking systems seem to be used everywhere in England. This made me think how fast can one possibly crack such a lock, provided that he needs very strong fingers and about 5 seconds to type the code in.

For a long time I was thinking that the combinations of a standard mechanical 4-digit lock are not that many because no consecutive digits can be used due to a limitation of the mechanical mechanism. Writing out this trivial solution:

1. The first digit can be from 0 to 9 so we have 10 possibilities.

2. The latter digits until the fourth can be from 0 to 9 but should not repeat with the previous digit, so we have 9 possibilities for all the rest.

We therefore end up with all possible combinations being: $$10\times 9\times 9\times 9 = 7290$$ An intuitive engineering thinking this times did not fail dramatically as after calming down I was imagining about $\frac{2}{3}$ of all the possible combinations which are 10000. If one masters a good code punching technique then $$7290\times 5 \text{sec} = 607 \text{h} = 25 \text{days}$$

At the end of the day, maybe electronic locks are more vulnerable to elegant cracking techniques as compared to their mechanical siblings.

Date:Tue Oct 05 22:11:17 CEST 2014