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Discussion of Problem 1170. Desert

Question to solvers, authors (warn: spoiler)
Posted by Sirko 3 Mar 2015 06:40
Can you guys provide me with a brief math proof that searched direction always contains at least one rectangles vertex (that is, no need to search for it between those rays made from vertexes coordinates)?
Thanks.
Re: Question to solvers, authors (warn: spoiler)
Posted by ASK 24 Apr 2018 19:30
In a small enough neighborhood of a line that does not pass thru one of the vertices, the distance traveled inside rectangle is smaller on one side and larger on the other, thus the distance on the line is not smaller/larger than in the neighborhood.