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Posts posted by Sairakan

  1. It took a little to understand the problem, but the key point is that the elevator in essence follows a sinusoidal curve that ranges continuously from 1 to 15. Mr. Smith is trying to stop the elevator on the 13th floor, which is equivalent to finding the intersection of the curve with y=13. I don't know of an easy way to draw this out, but intuitively the only time the elevator will be going down when it reaches the 13th floor is when it is in one of 4 positions:

    14th floor going up (at which it will reach the 15th floor and then turn to go back down and reach Mr. Smith
    15th floor - direction is automatically downward, same as above
    14th floor going down - also same as above
    13th floor going down - right where Mr. Smith wants it

    Meanwhile, there are 24 positions the elevator could be in when it will reach Mr. Smith going up: any time the elevator is at floor 12 or lower, or on the 13th floor going up, it will reach Mr. Smith going up. Thus, the proportion of times when the elevator is going up when it reaches Mr. Smith is 24/28, a quite large ratio.

    I'm not sure at the moment how exactly to tackle the generalization, although I have the feeling it is likely the same answer as for the first part.

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