- There is a keypad entry system on a safe door. There is no 'clear' button, but the
safe will open automatically if the last n digits entered match the n digit 'password'
- If there are 10 digits to choose from, what is the fewest number of button presses you would need to type in to guarantee access if the password is 4 digits long?
- What is the length and general solution for a password of n digits?
- What about password length n, with m digits to choose from?
- Can you give an example sequences for (n,m) = (3,2), (3,3), (2,4)?
A combination lock consists of 4 wheels, each numbered sequentially 0 to 9
(with 9 next to both 8 and 0.) How many wheel turns
(changing one digit by one value) are needed to attempt every combination? How
many wheel turns are needed for n wheels of m digits each?
Source: Alan O'Donnell (though I've seen it elsewhere) with original extensions.
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