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Puzzle #7
Lösung \ solution

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Prim oder?

You are caught in a small empty storage room (no windows, one closed door, weekend, no other people there to help you) and the door can only be opened form outside. In your hands you hold a remote control for your model car (or little test robot) - you have access to the car, but the car's batteries are almost "dead". The model car is placed somewhere in a large empty warehouse - next to your storage room - and you know the car (or the cars antenna) is placed exactly 10 yards away from a beam of a light barrier - which is part of a alarm system and in the cars (or the antennas) height - but you don't know in which direction your car has to move, to hit this light beam. Try to find the "shortest" way to "turn on the alarm" (by hitting the light beam with your model car) ...
your "special" remote control has the 2 (remote) programable "autopilot" functions
   a) forward distance f ... f<0 is backward movement
   b) circle with radius r>=0 and angle a ... a<0 is left turn; a>0 is right turn
your cars batteries are good for a remaining distance of 65 to 85 yards with
p(<=65yards)=100%; p(75yards)=20%; p(>=85yards)<1%


find:
shortest (worst case) distance for your model car = ? yards
p(worst case distance moved to hit the light beam) = ? %