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Around the world

246 bytes added, 01:25, 25 October 2010
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A group of airplanes is based on a small island. The tank of each plane holds just enough fuel to take it halfway around the world. Any desired amount of fuel can be transferred from the tank of one plane to the tank of another while the planes are in flight. The only source of fuel is on the island, and it is assumed that there is no time lost in refueling either in the air or on the ground. What is the smallest number of planes that will ensure the flight of one plane around the world on a great circle, assuming that the planes have the same constant speed (relative to the ground) and rate of fuel consumption, and that all planes return safely to their island base?
{{Solution | [Update: I (User:Zerrakhi) have since learned that the following solution is wrong. There is a better and simpler solution that uses only three aircraft and relies on a step that I missed. But I don't have the heart to delete all my hard work.] First, let's agree on conventions. The main journey will be westward, and all units will be in degrees. So 360 degrees is a full circle around the earth, 1 unit of fuel is enough fuel to travel one degree, and 1 unit of time is the time taken to travel one degree.
One unassisted aeroplane can travel 180 degrees non-returning, or 90 degrees returning. Let's see how far we can get with two aeroplanes: a main flight and an assisting flight.
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