# How To Find Your Way Out of Woods

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

$$2\sqrt{\pi S}$$

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.

For details see this
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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.