You're blindfolded, disoriented, and standing one mile from the Great Wall of China. How far do you have to walk to guarantee that you will run into the wall?

Assume that the wall is infinitely long and straight.

Assuming your disorientation is only in that you do not know the direction of the Great Wall and will have no bearing on walking a straight line or any curve you desire, a distance that can guarantee you will run into the wall is approximately pi + 2 + SQRT(2) miles ~= 6.55581 miles.

Walk SQRT(2) miles straight in any one direction. Turn 3/4*pi radians and travel 1 mile. You should be 1 mile from your starting point. Using your starting point as the center of a circle of one mile radius, walk the arc segment of a semi-circle, then walk 1 mile parallel to the second leg of your hike. Somewhere before the end of that walk you should have encounted the wall.

Edited on August 11, 2010, 9:47 am

Posted by Dej Mar on 2010-07-29 17:34:47