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.
(In reply to re: Much shorter solution
by Steve Herman)
You do point out two slight mistakes on my part.
First of all, I meant 90 degree turns, not 45. (I don't know why I put 45?)
Second, if the wall is directly behind you and you were to start out heading left of center, then you would not hit the wall during the three steps.
However, if you add one final right turn of 90 degrees and walked a maximum of another two miles, then you would hit it.
Start out in any direction for one mile.
Turn right 90 degrees and walk another mile.
Turn right 90 degrees and walk two miles.
Turn right 90 degrees and walk two more miles.
So my revised answer would be a minimum of 6 miles not 4.
And, now that I think about it, this forms the golden rectangle, related to the golden spiral, and so is the closest reasonable approximation to the shortest distance that a person could make using dead reckoning.
Edited on September 2, 2011, 3:42 pm
Posted by Joshua
on 2011-09-02 15:41:06