Please comment your solutions, questions and remarks..
A lumberjack got lost in a forest. He knows that the area of the forest is S and that there are no meadows in the forest. Show that he can get out from the forest after walking at most
It is assumed that the lumberjack can walk along a curve of a given shape.
2/5
Caution: This is modified since first published. The originally published riddle was not solvable.
Unless I’ve missed something, I’m quite confident he can get out by walking at most \sqrt{S/\pi}. :)
You definitely miss something. For instance if he walks along a straight line for \sqrt{S/\pi}, then provided the forest is a rectangle with sides 2\sqrt{S/\pi} and \sqrt{S\pi}/2, he might still be in the forest. In fact if he walks along a path of *any* shape for \sqrt{S/\pi}, he might still be in the forest, provided the forest has a nasty shape.
If he just walks along the curve of a circle with the radius sqrt(S/pi) so that the starting point is a point in the circle he will sooner or later get out.