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# Where is the F@\$%(\$* Road?

## Question

After parachuting into the woods at night, you land right next to a sign that says : "Road: One Mile." But it has fallen over, and there's no way to know what direction the road is. Describe the shortest path you might take that will guarantee reaching (touching) the road. (You can't see the road until you reach it!) What's the maximum distance you might walk on your path?

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First try.

Walk a mile in any direction.
Turn right and walk a one-mile-radius circle.
That could be (1+2pi) miles of walking
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Walk 1mile 12o 'clock, then track the perimeter (1m radius) clockwise until 9'oclock, then straight 12'oclock again.

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Is the road a straight line?

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Is the road a straight line?

You have no way of knowing since this is a new location for you

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Is the road a straight line?

You have no way of knowing since this is a new location for you

since it can be a circular road the maximum can be 1mile

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I Do not understand

Is the road a straight line?

You have no way of knowing since this is a new location for you

since it can be a circular road the maximum can be 1mile

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I Do not understand

Is the road a straight line?

You have no way of knowing since this is a new location for you

since it can be a circular road the maximum can be 1mile

opps..i mean the minimum, but since you are asking for maximum..many miles should be the answer.

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I disagree. If you take the shortest path possible the maximum distance until you find the road, would not simply be many many miles.

I Do not understand

Is the road a straight line?

You have no way of knowing since this is a new location for you

since it can be a circular road the maximum can be 1mile

opps..i mean the minimum, but since you are asking for maximum..many miles should be the answer.

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I disagree. If you take the shortest path possible the maximum distance until you find the road, would not simply be many many miles.

I Do not understand

Is the road a straight line?

You have no way of knowing since this is a new location for you

since it can be a circular road the maximum can be 1mile

opps..i mean the minimum, but since you are asking for maximum..many miles should be the answer.

Okey i will get it..

What's the maximum distance you might walk on your path . The shortest path that guarantee reaching the road has minimum and maximum. Maximum ..without walking back.

As I understand the question : What is the shortest or minimum possible distance to ensure reaching the road? Since the road is possible to be circular that maximum is also minimum.

To make it maximum we take the road to be a none straight end of the road.

So even it is a straight one if it is the " end of the road" (non tangential) the answer is still 1+2pi..

Edited by TimeSpaceLightForce
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yes. And the solution changes if the road is straight as in the other problem

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yes. And the solution changes if the road is straight as in the other problem

the default assumption on pt.2 is full tangential.. could be radial or half tangential

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Yes but full tangential is what leads to the max shortest path possible, right?

yes. And the solution changes if the road is straight as in the other problem

the default assumption on pt.2 is full tangential.. could be radial or half tangential

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