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Gamow's Elevator (Posted on 2020-07-26) Difficulty: 3 of 5
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.

See The Solution Submitted by Charlie    
Rating: 1.5000 (2 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
ccoaboxnovel2020-07-30 22:22:59
soln - w/ logic and computerSteven Lord2020-07-28 21:45:44
re(4): what I have so far... -- HintSteven Lord2020-07-28 07:15:12
re(3): what I have so far... -- HintCharlie2020-07-28 07:03:03
re(2): what I have so far... -- HintSteven Lord2020-07-27 22:53:52
Hints/Tipsre: what I have so far... -- HintCharlie2020-07-27 21:51:43
what I have so far...Steven Lord2020-07-27 19:03:50
clarificationsCharlie2020-07-27 07:03:52
The extreme casebroll2020-07-27 05:09:53
I understand the problem?Steven Lord2020-07-27 01:05:08
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