Question 30
A code lock has 10 keys labeled by digits from 0 to 9. The lock is opened by entering a code of 4 keys that are not necessarily different. It is opened as soon as the correct keys are pressed consequently, no matter what keys have been pressed earlier. For example, if the code happens to be $2002$, the sequence $45677892002$ will open the lock, but the sequence $20202$ will not.
What is the minimal length of a sequence that will guarantee opening the lock regardless of what code is?
What is the minimal length of a sequence that will guarantee opening the lock regardless of what code is?