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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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re(2): But.... | Comment 10 of 11 |
(In reply to re: But.... by armando)

Another interesting thing about the process is how easily it can be reversed.  

Begin at B and walk in some direction a distance 1/N mile
[This is the solution for N=1]
 turn arccos(sqrt(0/1))=90 walk another 1/N mile,
[This is the solution for N=2]
 turn arccos(sqrt(1/2))=45 walk another 1/N mile,
[This is the solution for N=3]
and so on.

The limit as N goes to infinity is the spiral.

  Posted by Jer on 2019-01-16 13:43:17
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