I have a nice mountain bike, which I use on a daily basis. I always lock my bike.
Today, I awoke and to my surprise the bike was stolen. It startled me because it is locked with a really expensive combination lock. I walked around the vicinity and found it lying still locked in a shrubbery. Apparently, someone must have carried it away, tried to break the lock open in a more quieted neighbourhood but failed to do so.
I need to unlock my bike in order to ride it (duh). The trouble is that two of the four wheels with the numbers present on them have been removed. I can still turn the wheels, but I do not know which number I'm "entering" as a combination.
However, I have noticed that there are two cavities in the underlying smooth wheels with no numbers on them. I know for a fact that these cavities are present on the same numbers, but I can't tell them apart and do not know under which number the cavities were initially.
(Note: The two cavities are under the same number, but I don't know whether it is
2 or any other number, I just had to draw the cavities somewhere...)
My combination is
4 2 7 0
I can enter
4 2, but I do not know the other two numbers I'm entering it. I can unlock my lock in $10^2$ trials, but using the additional information I can't help but think that I could need even less trials.
If that is too easy, try and solve the problem for $n$ additional wheels.