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Continue reading for the puzzle.
A new type of aviation fuel has been developed and its inventor wants to prove its worth. As with most major aviation advancements since the invention of the airplane, the inventor decides that they will circumnavigate the world non-stop. The plane they will use has been retrofitted to burn the new fuel and it cannot use any other fuels.
Unfortunately, the plane can only carry enough fuel to make it exactly 1/2 of the way around. The company decides that they will retrofit a number of identical planes and refuel in the air. Being paranoid about the secrecy of the fuel’s formula, they keep all of the fuel at their secure headquarters, from which the planes will depart and return. Obviously, they need to have every plane return safely. They do not want to land at any other airport for fear of their competitors stealing their secrets.
What is the minimum number of planes, and what is the strategy required to accomplish this? Assume that the transfer of fuel is done instantly, that the retrofitting does not allow regular jet fuel to be used, and that the fuel used to resupply the main plane is taken from the support plane’s supply; they cannot carry any more than just enough fuel to go 1/2 the total distance around the world. One plane MUST travel all the way around, but the others may return to base from the direction they came, if necessary. Also assume that the world is a sphere, and that main plane is following a great circle (the shortest distance between two points on the surface of a sphere follows a great circle), so there are no shortcuts. Ignore weather, climate, jet stream, winds, etc.