man gets lost in a large forest,
Source: IV Soros Olympiad 1997-98 R2 10.6 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics
June 1, 2024
geometrycombinatoricscombinatorial geometry
Problem Statement
A man gets lost in a large forest, the boundary of which is a straight line. (We can assume that the forest fills the half-plane.) It is known that the distance from a person to Granina forest does not exceed km. a) Suggest a path along which he will certainly be able to get out of the forest after walking no more than km. (Of course, a person does not know in which direction the border of the forest is, BUT he has the opportunity to move along any pre-selected curve. It is believed that a person left the forest as soon as he reached its border, while the border of the forest is invisible to him, no matter how close he would have approached it.)b) Find a path with the same property and length no more than km.