George Gamow and Marvin Stern occupied offices on the second and sixth floors of a seven-story building, and noted that when either took the elevator to the other's floor, it was going the wrong way. It's apparent why: there were ten segments of the elevator's 12-segment cycle (6 going up and 6 going down in a continuous cycle) where the first elevator arrival would be going the wrong way and only two segments where it would be going the desired direction the next time it passed the boarding floor.
But what if a second elevator were placed in the building. What would the probability be that the next elevator to arrive would be going the wrong way? Ignore stops along the way, as they do not affect the distance that need be traveled and probably have more of them for longer trips. The two elevators move independently of each other.
Gamow himself did not get the correct answer for the two-elevator case, but the correct answer was found by Donald Knuth.
My understanding so far is that the original elevator works like this: its only journey is to go from bottom to top to bottom stopping at all floors each way, right?
There is the question as to whether it just keeps doing this or if it only starts-off from the bottom when someone presses "elevator" somewhere.
(I am trying to understand the statement: when they took... it was going the wrong way.) I imagine _sometimes_ it was going the right way, if another person had started it off earlier. (Or, are we only talking about times when the elevator is stationary on floor #1, and only G or S calls it? Then it _is always_ headed the wrong way.
Otherwise, if no one starts or stops it, and it just keeps going, then it would sometimes be going the right way in its cycle when they wanted to board. True?
Edited on July 27, 2020, 2:08 am