For example there is a bike lock that rotates the numbers $0$-$9$,on six separate dials, and if multiple dials are adjacent they can be rotated in the same direction for the same number of rotations (i.e., three adjacent dials all moving $2$ places anti-clockwise).
What is the minimum number of rotations needed to get the bike lock to the specific combination to unlock from any possible starting position. So the minimum maximum number of rotations given a specific number of dials and numbers the dials. Also consider that we can assume we want 000000, as the unlock position as it will be the same results no matter what the end position is for the number of turns.
I know how you could find it if there was no adjacent turns allowed, but this complicates the problem. As adjacent turns have to be accounted for.
A general solution is the rounded up value of half the number of dials times half the number of numbers on the dials. However I have not proved this for many case scenarios. And it may be a overestimate with larger values.