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• Professor Fukanō, the famous eccentric scientist and adventurer,

• has embarked on a new challenge:

• flying around the world nonstop in a plane of his own design.

• Able to travel consistently at the incredible speed of one degree longitude

• around the equator per minute,

• the plane would take six hours to circle the world.

• There's just one problem:

• the plane can only hold 180 kiloliters of fuel,

• only enough for exactly half the journey.

• Let's be honest.

• The professor probably could have designed the plane to hold more fuel,

• but where's the fun in that?

• Instead, he's devised a slightly more elaborate solution:

• building three identical planes for the mission.

• In addition to their speed,

• the professor's equipped them with a few other incredible features.

• Each of the planes can turn on a dime

• and instantly transfer any amount of its fuel to any of the others in midair

• without slowing down,

• provided they're next to each other.

• The professor will pilot the first plane,

• while his two assistants Fugōri and Orokana will pilot each of the others.

• However, only one airport, located on the equator,

• has granted permission for the experiment,

• making it the starting point,

• the finish line,

• and the only spot where the planes can land,

• takeoff,

• or refuel on the ground.

• How should the three planes coordinate

• so the professor can fly continuously for the whole trip and achieve his dream

• without anyone running out of fuel and crashing?

• Pause here if you want to figure it out for yourself.

• According to the professor's calculations,

• they should be able to pull it off by a hair.

• The key is to maximize the support each assistant provides,

• not wasting a single kiloliter of fuel.

• It also helps us to think symmetrically

• so they can make shorter trips in either direction

• while setting the professor up for a long unsupported stretch in the middle.

• Here's his solution.

• All three planes take off at noon flying west,

• each fully loaded with 180 kiloliters.

• After 45 minutes, or one-eighth of the way around,

• each plane has 135 kiloliters left.

• Orokana gives 45 to the professor and 45 to Fugōri,

• fully refueling them both.

• With her remaining 45, Orokana returns to the airport

• and heads to the lounge for a well-deserved break.

• 45 minutes later, with one-quarter of the trip complete,

• the professor and Fugōri are both at 135 kiloliters again.

• Fugōri transfers 45 into the professor's tank,

• leaving himself with the 90 he needs to return.

• Professor Fukanō stretches and puts on his favorite album.

• He'll be alone for a while.

• In the meantime, Orokana has been anxiously awaiting Fugōri's return,

• her plane fully refueled and ready to go.

• As soon as his plane touches the ground, she takes off, this time flying east.

• At this point, exactly 180 minutes have passed

• and the professor is at the halfway point of his journey

• with 90 kiloliters of fuel left.

• For the next 90 minutes,

• the professor and Orokana's planes fly towards each other,

• meeting at the three-quarter mark.

• Just as the professor's fuel is about the run out,

• he sees Orokana's plane.

• She gives him 45 kiloliters of her remaining 90,

• leaving them with 45 each.

• But that's just half of what they need to make it to the airport.

• Fortunately, this is exactly when Fugōri, having refueled, takes off.

• 45 minutes later, just as the other two planes are about to run empty,

• he meets them at the 315 degree point

• and transfers 45 kiloliters of fuel to each, leaving 45 for himself.

• All three planes land at the airport just as their fuel gauges reach zero.

• As the reporters and photographers cheer,

• the professor promises his planes will soon be available for commercial flights,

• just as soon as they figure out how to keep their inflight meals

• from spilling everywhere.

Professor Fukanō, the famous eccentric scientist and adventurer,

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# 【TED-Ed】Can you solve the airplane riddle? - Judd A. Schorr

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Sh, Gang (Aaron) posted on 2016/12/04
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