How To Find Your Way Out of Woods

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

[tex]2\sqrt{\pi S}[/tex]

It is assumed that the lumberjack can walk along a curve of a given shape.


Caution: This is modified since first published. The originally published riddle was not solvable.

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3 Responses to How To Find Your Way Out of Woods

  1. pp says:

    Unless I’ve missed something, I’m quite confident he can get out by walking at most \sqrt{S/\pi}. :)

  2. 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.

  3. Annika says:

    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.

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