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Reach home (Posted on 2019-01-14) Difficulty: 3 of 5
Points A and B are on a plane surface, 1 mile apart. Suppose you must walk in a path consisting of N straight lines from point A to point B, such that at all times your (Euclidean) distance to point B is decreasing. What is the longest possible route length (as a function of N)?

No Solution Yet Submitted by Danish Ahmed Khan    
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Some Thoughts conjecture | Comment 2 of 11 |
When N is 2, it seems certain that the longest route while constantly decreasing the distance to B, would be the two legs of an isosceles right triangle with AB as the hypotenuse.

The conjecture is that the maximum distance would be achieved by inscribing equal-length chords in a semicircle with A and B as endpoints.  

That would come out to a path length of N * sin(pi/(2*N)).

Edited on January 14, 2019, 4:32 pm
  Posted by Charlie on 2019-01-14 16:26:06

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