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 Lost in the woods (Posted on 2016-01-08)
You are driving along a perfectly straight road through the woods and decide the trees look like an inviting hike. After all, you have a GPS that could easily get you back to the road. So you get out and head off in a straight line perpendicular to the road, not paying any attention to your direction because, hey, GPS.

Unfortunately after traveling 1km your GPS crashes. It loses all of its map data as well as any previous journeys. In you panic, you even forgot which direction you were walking.

So here you are: 1 km away from the long straight road (the only one around for many km) in an unknown direction. You have a GPS that can still give your accurate position and path relative to your start.

What is the length of the shortest path (measured from here) that guarantees you will find the road?

Note: the trees are dense enough that you could be very close to the road and not see it.

 Submitted by Jer Rating: 5.0000 (2 votes) Solution: (Hide) Pick a direction and call it North. [1] Turn to 30 degrees East of North and walk 2/√(3)km. [2] Turn to 30 degrees East of South and walk 1/√(3)km. (This brings you to a point 1km from and 60 degrees east of north from the start.) [3] Walk clockwise 7/12 of the way around the circumference of this 1km circle. Distance = 7π/6 km. (This brings you to 1km due West of the start.) [4] Walk 1km due North. Total distance: 1+√3+7π/6 or about 6.3972 km.

 Subject Author Date re: About the problem armando 2016-01-10 13:15:51 About the problem Jer 2016-01-10 12:06:23 re: Graphic? Jer 2016-01-10 11:32:00 Graphic? armando 2016-01-10 10:41:46 Lower armando 2016-01-10 06:27:17 re: Not there yet. Dej Mar 2016-01-09 23:39:14 Not there yet. Jer 2016-01-09 23:25:15 I think lower armando 2016-01-09 11:01:26 re(2): proposed solution Dej Mar 2016-01-09 09:54:33 re: proposed solution Jer 2016-01-08 21:52:48 Unsure solution armando 2016-01-08 18:34:55 proposed solution Charlie 2016-01-08 15:43:08

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