Flying around the world with half a tank
An island has an airport and an unlimited supply of fuel. Each plane's tank holds fuel for exactly half the distance around the world. Planes can transfer fuel to each other instantly in mid-air, and can only refuel on the ground at the island. All planes fly at the same speed, and a plane may take off again as soon as it has landed and refuelled.
What is the smallest number of planes needed so that one plane flies all the way round the world (returning to the island) and every plane involved lands safely back at the island? Describe the schedule.
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Measure distance in eighths of the world, so a full tank is 4 units and the trip is 8 units. Send helpers out with the traveller, have them hand over fuel and turn back with just enough to get home, then send them out the other way to meet the traveller on the far side.
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