Question 66
A group of mathematicians is lost in a forest. The forest has a shape of an infinite strip that is 1 mile wide. Prove that they can choose a path that will guarantee them a way out and that is at most $2 \sqrt{2}$ miles long.
Remark. The mathematicians have no device for orientation and no maps. All they know is that the forest is a region between two parallel lines 1 mile apart from each other. They can't see the end of the forest, unless they are at the edge. However, they can precisely follow any path they design, e.g. they can move along straight line, circle, etc.
Remark. The mathematicians have no device for orientation and no maps. All they know is that the forest is a region between two parallel lines 1 mile apart from each other. They can't see the end of the forest, unless they are at the edge. However, they can precisely follow any path they design, e.g. they can move along straight line, circle, etc.