I am an orthodox Jew who lives in an apartment building with a Sabbath elevator. I usually takes the stairs on the Sabbath, but use the elevator occasionally. While in it, I always contemplate other possible strategies the elevator could use to speed up the runtime. All Sabbath elevators I've seen follow the route `1,2,3,...,N,1,2,...` which can take up to `2N - 1` steps (open/close cycles) in the worst case (you just miss the elevator on the ground floor and are going up to `N`). What if they went `1,2,4,6,...,N,1,3,5,7,...,N`? Worst case is still `2N -1` but if you relax the goal to only care about getting within one floor of your target (go one away from your floor and take the stairs for the last flight) worst case drops to `N`. (Each step would take a little longer due to having to travel 2 flights, but most of the time is spent waiting for the doors anyways.) Has anyone seen a Sabbath elevator that doesn't follow the standard route?