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Professor Fukanō, the famous eccentric scientist and adventurer,
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has embarked on a new challenge:
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flying around the world nonstop in a plane of his own design.
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Able to travel consistently at the incredible speed of one degree longitude
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around the equator per minute,
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the plane would take six hours to circle the world.
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There's just one problem:
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the plane can only hold 180 kiloliters of fuel,
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only enough for exactly half the journey.
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Let's be honest.
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The professor probably could have designed the plane to hold more fuel,
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but where's the fun in that?
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Instead, he's devised a slightly more elaborate solution:
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building three identical planes for the mission.
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In addition to their speed,
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the professor's equipped them with a few other incredible features.
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Each of the planes can turn on a dime
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and instantly transfer any amount of its fuel to any of the others in midair
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without slowing down,
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provided they're next to each other.
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The professor will pilot the first plane,
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while his two assistants Fugōri and Orokana will pilot each of the others.
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However, only one airport, located on the equator,
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has granted permission for the experiment,
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making it the starting point,
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the finish line,
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and the only spot where the planes can land,
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takeoff,
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or refuel on the ground.
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How should the three planes coordinate
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so the professor can fly continuously for the whole trip and achieve his dream
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without anyone running out of fuel and crashing?
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Pause here if you want to figure it out for yourself.
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Answer in: 3
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Answer in: 2
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Answer in: 1
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According to the professor's calculations,
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they should be able to pull it off by a hair.
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The key is to maximize the support each assistant provides,
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not wasting a single kiloliter of fuel.
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It also helps us to think symmetrically
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so they can make shorter trips in either direction
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while setting the professor up for a long unsupported stretch in the middle.
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Here's his solution.
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All three planes take off at noon flying west,
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each fully loaded with 180 kiloliters.
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After 45 minutes, or one-eighth of the way around,
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each plane has 135 kiloliters left.
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Orokana gives 45 to the professor and 45 to Fugōri,
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fully refueling them both.
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With her remaining 45, Orokana returns to the airport
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and heads to the lounge for a well-deserved break.
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45 minutes later, with one-quarter of the trip complete,
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the professor and Fugōri are both at 135 kiloliters again.
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Fugōri transfers 45 into the professor's tank,
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leaving himself with the 90 he needs to return.
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Professor Fukanō stretches and puts on his favorite album.
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He'll be alone for a while.
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In the meantime, Orokana has been anxiously awaiting Fugōri's return,
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her plane fully refueled and ready to go.
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As soon as his plane touches the ground, she takes off, this time flying east.
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At this point, exactly 180 minutes have passed
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and the professor is at the halfway point of his journey
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with 90 kiloliters of fuel left.
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For the next 90 minutes,
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the professor and Orokana's planes fly towards each other,
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meeting at the three-quarter mark.
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Just as the professor's fuel is about the run out,
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he sees Orokana's plane.
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She gives him 45 kiloliters of her remaining 90,
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leaving them with 45 each.
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But that's just half of what they need to make it to the airport.
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Fortunately, this is exactly when Fugōri, having refueled, takes off.
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45 minutes later, just as the other two planes are about to run empty,
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he meets them at the 315 degree point
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and transfers 45 kiloliters of fuel to each, leaving 45 for himself.
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All three planes land at the airport just as their fuel gauges reach zero.
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As the reporters and photographers cheer,
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the professor promises his planes will soon be available for commercial flights,
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just as soon as they figure out how to keep their inflight meals
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from spilling everywhere.