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 Much shorter solution
Joshua: Your method doesn't work if the great wall is behind you during step 1, or to your left. Plus, all of steps 2 and 3 take place more than a mile from your starting location, which wouldn't be optimal even if it worked.