Lost in a Forest
Geometry
Level
4
A hiker is lost in a forest, and his only hope is to escape from it.
- He knows that the forest is the shape of an infinite strip with width exactly 1000 meters.
- He has perfect relative bearings, is able to track his position perfectly, and can travel along any line or curve.
- He doesn't know the direction of the strip and cannot see the boundary until he is upon it.
What is the shortest possible walking distance , to the nearest meter, that will ensure he escape from the forest?
The answer is 2278.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
This is one of the classic Bellman problems. The solution for an infinite strip forest (and others) is given here . The shortest distance is 2 2 7 8 . 2 9 2 m, making the answer 2 2 7 8 .