MathDB

There is a safe that can be opened by entering a secret code consisting of

n

digits, each of them is

0

1

. Initially,

n

zeros were entered, and the safe is closed (so, all zeros is not the secret code).
In one attempt, you can enter an arbitrary sequence of

n

digits, each of them is

0

1

. If the entered sequence matches the secret code, the safe will open. If the entered sequence matches the secret code in more positions than the previously entered sequence, you will hear a click. In any other cases the safe will remain locked and there will be no click.
Find the smallest number of attempts that is sufficient to open the safe in all cases.

Problem Statement