Hi - if anyone can help me with a particularly puzzling problem, I'd be eternally grateful...thanks...
You are out in a high grass, sparsely-treed, level wilderness, on an overcast summer's day, on a very important quest. Suddenly you startle a momma bear with cubs!!! HOLY MOLEY!!! She immediately attacks you! WHAM!!! WHAM!!!WHAM!!! Using current wisdom, you play dead, praying that it's not a rehearsal for the real thing. After an eternity of her beating and mauling you, she and her cubs disappear.
When you come to, all is quiet except your heart which is pounding like a mad drummer's tattoo. Bleeding profusely, you decide to clear out of there in a HURRY! The only thing you are certain of, is that just before you were attacked, you were beside that tree right there which is EXACTLY 1 kilometer from a perfectly STRAIGHT trail which will lead you to safety. You have no idea in which direction to start off. Fighting the very strong temptation to head off in all directions at once, you force yourself to calm down. You realize that you must get out as soon as possible, or bleed to death. The adrenelin coursing through your body makes your brain work at the speed of light and your thoughts become crystal clear.
You immediately devise an OPTIMAL geometric plan that will guarantee that you find the trail in the SHORTEST travelling distance from that tree compared to ANY other plan, even if you start off using the WORST possible choice of heading. There is no sun, or anything else, to guide you as to direction. You also know you won't see the trail until you are right on top of it.
As it happens, you DO choose the worst initial heading in following the optimal strategy, but your plan works and you manage to get to help just in time to save your life.
A further clue have been supplied:
- The geometry of the optimal path to follow is not an obvious one.The optimal path only requires you to travel along straight lines and along a portion of a circle. For any other plan, if your initial heading is the worst possible choice, then the travel distance to the trail will be greater than for the optimal plan.
Any ideas? Anyone recognize this problem from somewhere (Scientific American, for example), and can provide a link to a solution?