Can you solve the airplane riddle? – Judd A. Schorr

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. Answer in: 3 Answer in: 2 Answer in: 1 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.

100 thoughts on “Can you solve the airplane riddle? – Judd A. Schorr

  1. Plot Twist: Fugori and Orokana continue feeding fuel into the professor, who can't do anything except give fuel back, crashlanding them all into the ocean.

  2. Objection: you didn't say that a plane can reful two other planes at the same time.
    You said they can DIME (PAIR)…….
    the planes crashes by A HAIR

  3. Ya'll can dig on Fukano for not being able to make more fuel but this man literally made a plane that can move halfway around the world in 1 hour

  4. There is a much simpler solution.1 and 2 plane goes 1 quarter.2 refill 1 and fly back. 1 goes until 3 quarter. 3 met 1 at 3 quarter and refill and go back. TADAA

  5. Let's be honest. The professor probably could have designed the plane to hold more fuel, but he wants to save as much of his budget as he can so he can pay back his loans to the companies that lent the money to make this possible.
    Edit (CORRECT ME IF I AM WRONG ON ANY BIT): Apparently after doing some math, if the planes can travel one degree longitude per minute (111.3 km), and if 111.3 km ÷ 60 seconds = the speed of 1.855 km per second, this would make the planes 5 times faster than the speed of sound (343 meters per second), therefore Fukano putting on his favorite album won't do anything, since music is sound, and he's going faster than it. Also, a comment by Sarah Mechem stated that the professors would die from massive g-force, and that's true, when Princess Diana died in a car crash, she had a g-force of 70g on her chest and 100g on her head, and, if a 1g acceleration is about 0.00972222… km/s, all of them if they were to turn would suffer a force of 190.8g, which would probably kill them, possibly mutilating them! Basically, the assistants could help fuel the professor for the beginning parts, but they'd both die no matter what would happen, and the task would be rendered impossible unless they were programmed to coordinate and autopilot. At 12:45pm, Orokana's g-force suffrage after turning would send her plummeting towards the sea. The same happens to Fugori at 1:30pm (he could land in one of the Indonesian islands, as shown on the map). The professor would be all alone at this point, and at 4:30pm, he'd plummet towards the Amazon rainforest of Brazil, where he could possibly initiate a crash landing, but even assuming he lives, he'd likely never be heard from again, with the poisonous native wildlife in the area and the vastness of the rainforest, and if unlucky enough, he could be picked off by an uncontacted tribe. In conclusion… pretty much a suicide mission. I smarts! (TL;DR planes go faster than the speed of sound, professor's assistants die of massive g-force, task is rendered impossible as the professor would crash in the amazon rainforest)

  6. I think I got simple solution than this.
    1stly boy assistant and professor will travel 45 then boy assistant gives 90fuel to professor and with remining fuel he goes back.
    So initially professor is having 135 and now 90 is added so he can travel 225 and reaches to 275 degree.
    Then the boy and girl assistant will travel 45 in opposite direction and boy will return giving girl 90 fuel and now girl is having 225.then the girl assistant meet the professor with 180 fuel gives 90 to him and 90 keeps near her and both will come to initial position.

  7. I think I found another way no troll. Prof and another plane travel 80 degrees together, at which point the plane gives the prof 80 fuel, leaving 20 for himself. When he returns back 20 degrees (at the 60 degree mark) the second plane is there to meet him and splits the remaining fuel. The second plane uses 60 to meet him, then they split the remaining 60 each to travel back.

    Meanwhile the prof has enough fuel to get to 260 degrees. This is precisely the same time (100 minutes) the refuel plane will need to meet him on the other side. So they both set out again and one refuels the other at -60 degrees (300) and returns. The other reaches the professor at 260 degrees with 140 of fuel left and splits the remaining fuel (70 each). This is more than enough time for the first refuel plane to come back and meet them at 330 degrees to refuel them both and reach home safely.

    Did I mess up somewhere? I haven't seen this solution anywhere in the comments

  8. Can’t planes 1 and 2 depart together, and then a quarter of the way there 2 gives his fuel to 1, then crashes and dies, and then when 1 is halfway there, 3 takes off, then 3/4 of the way there tree gives here fuel to 1 and crashes and dies.

  9. Tell me how Professor Fukano's food was the one to get spilled even though he's the one that went straight the whole time

  10. i have done it bit different way
    all three planes start at 0 time
    we call
    professor as 1
    and lady plane 2
    and other assistant 3
    now at 45 degree 1 and 2 will be fulled by 3 and he will return to base at time 90
    while 1 and 2 will be at 90 degree
    at 110 degree 1 and 2 tank will have 115 liters of fuel each. 2 will full the tank of 1 and will have 50 liter left in her tank. time is 110 at time 100 3 has already taken off from base with full tank and will meet at 60 degree with number 2 and will give her half of the fuel both will have 60 liters at 60 degree and they both will reach base at 220 mins while plane 1 will be on 220 degree mark with 70 liters left now at 220 min 2 will take off base with full tank while 3 will take off after 35 mins, 2 will meet 1 at 290 when 1 has 0 fuel 2 will give 35 liters of fuel to 1 and he will have 75 liters of enough to reach base. at 325 degree plane 3 will meet 1 and he will provide 35 liters of fuel to 1 to reach base. all 3 plane will land at safely at base kudos.

  11. Better way is that
    the professor design enough long Pipe which is connected to the fuel tank and the plane at all time, it just keeps continues fuel to the plane but the pipe has to be long enough to go around the world.

  12. There's another strategy for each assistant going in opposite directions when the professor is getting to the 25% and 75%

  13. Sacrifice the assistants for the professor, it’s for a good cause!
    Wait, everyone else is saying that, and I’m not original… oh


  15. Wait I got a better and easy solution.suppose, professor and his one student flew and at 90° student fill the tank of professor reaching again the full capacity of plane and student goes back. And when professor reaches 180° another student flew from the airport in opposite direction and the both student and professor met at 270° and both of them are left with 90° and 90°kmpl fuel left with them.

  16. This solution doesn’t consider the fact that earth is spinning while they are flying. If it calculated too, the solution will be more simple
    If you agree plz like this

  17. They didn't account for drafting, drag, or the earth's rotation. That's like deducing how high one needs to jump to dunk a ball without accounting for gravity.

  18. get the other two two to refuel the professor when needed and have them declare emergency for low fuel accordingly

  19. I have a different solution: All three Planes start simultaniously, heading west. After 30 Minutes, Assistent 2 gives each other 30 kl and heads home again. At 60 Minutes, A2 reaches home, refuels (has to be as fast as transferring fuel between planes, else this doesn't work) and heads off west again. At 90 Minutes, A1 transfers 60 kl to the professor and heads home. At 120 Minutes, A1 and A2 meat, A2 transfers 30 kl to A2, they both head home. At 180 Minutes, they reach home and refuel, heading east afterwards. At 210 Minutes, A2 transfers 30 kl to A1 and heads home. At 240, A2 reaches home, refuels and heads east. At 270, A1 reaches the Professor and transfers 60 kl. At 300, all meet, A2 transfers 30 kl each to everyone, so everyone has 60 kl left to head home

  20. Aaaand I solved this one backwards LOL….I did the trips in reverse order starting from the first trip….idek how I did it….

  21. Alt Solution 1: beg and bribe another airport for permission.
    Alt Solution 2: stop being so ambitious and make a larger fuel tank.

  22. Dang! Mah calculates are just half right, about the halfway where Fikano are travel alone for 180 degrees and his two partner that flying west first then east

  23. An ingenious solution

    Ted Ed Aeroplane riddle – 10 Steps

    1) All three set off from equator. Let A be the professor, B & C be his workers.

    A: 180L , B: 180L , C: 180L

    2) At 45 degrees, B gives A 45L and C gives B 90L.

    A: 180L, B: 180L, C: 45L

    3) C goes back to base and refill. B travels another 45 degrees with A.

    A:135L, B: 135L, C: 180L

    4) At 90 degree mark, B gives A 45L and heads back to equator.

    A:180L, B:90L, C: 180L

    5) B goes back base and refills. A travels till 270L mark.

    A:0L, B: 180L, C: 180L

    6) B and C come to rescue. At 315 degree mark C gives B 45L of petrol.

    A:0L, B:180L, C:90L

    7) C goes back base & refills while B reaches 270 degree

    A:0L, B:135L, C:180L

    8) B gives A 45L and move together to 315 degree mark.

    A: 0L, B:45L, C:180L

    9) C reaches 315 degree mark and gives A 45L,

    A:45L, B:45L, C:90L

    10) All of them come back to equator safely.

  24. Found a different solution for the plane riddle:

    A = Professor Fukano, B = Fugori, C = Orokana. A full tank is 180kl of fuel.

    A and B start together. At the 60degree mark, B gives A 60kl of Fuel, B returns with 60kl of fuel. A now has 180kl of fuel and continues towards the 240degree mark. Then, B and C fly out together the opposite way. At the 300degree mark, B gives C 60kl of fuel then returns with 60kl. C now has 180kl of fuel. C meets A at the 240degree mark and shares 60kl of fuel. Both A and C now have only 60kl of fuel left. B flies out and meets A and C at the 300degree mark, giving them each 60kl. Everyone now has 60kl of fuel to travel the final 60degrees home.

  25. Hey TED-Ed. Nice riddle! Only comment: 2:38 point in video ("one-quarter of the trip complete"). 12:00 takeoff + 45 minutes = 12:45. + 45 more minutes = 13:30 (one-quarter, or 90 minutes of the 360-minute trip by the Professor), not 14:15 as shown in large font. Someone added 45 minutes to Orokana's landing time rather than to the time they split up at first fuel transfer point. Sorry if one of the other 3.990 Comments already pointed this out. See ya!

  26. My plan is this each plane has 180 fuel and each plane can give fuel so this id what I would do I would have them be put together in a triangle shape so in the very beginning the plane on the left side gives 120 fuel to the right so then the right gives 240 fuel to the plane at the top where the scientist resides and since I said at the very beginning of the flight the assistants can then go back to the port for refuel

  27. “The professor probably could have designed the plane to hold more fuel, but where’s the fun in that?”

  28. I have an alternate solution that I think would work. Someone correct this if it is wrong.
    At time 0 (in hours): All three planes start to fly west.
    At time 1.2: The three planes each have 108 kl of fuel. Fugori and Orokano both give 36 kl to the professor, leaving the professor with 180 and Fugori and Orokano with 72. Fugori and Orokano turn around.
    At time 2.4: The professor is now 2.4/6 of the way around the world with 108 kl of fuel while Fugori and Orokano arrive at the station just as their planes were about to run out of fuel. Fugori and Orokano refuel and fly to the east.
    At time 3.4: Both Fugori and Orokano now have 120 kl of fuel. Orokano gives 60 kl of fuel to Fugori, leaving Fugori with 180 kl and Orokano with 60 kl. Orokano turns around while Fugori keeps going. The professor is now 3.4/6 of the way around the world with 48 kl.
    At time 4.2: The professor and Fugori meet. The professor has 0 kl of fuel while Fugori has 132 kl. Fugori now gives 66 kl to the professor, leaving both the professor and Fugori with 66 kl. The professor continues while Fugori turns around, following the professor.
    At time 4.4: Orokano arrives at the station and refuels to 180 kl. The professor and Fugori are now 4.4/6 of the way around the world with 54 kl.
    At time 5.2: Orokano meets the professor and Fugori. Orokano now has 132 kl, the professor and Fugori each have 6 kl. Orokano gives 42 kl to both the professor and Fugori so now, all three planes have 48 kl, just enough to make it back. All three planes now approach the station.
    At time 6: all three planes safely arrive at the station, just as all three are about to run out of fuel.

  29. Or because i dont remembre the names ,Lets assume they r: A B C, A Nd B go from west both of them once they got 90 km B will give A 90 kiloletres Nd then comeback to the aeoroport .. After 180 of A + 90 given by B only 90 left to finish the circle … C will fly east give A 90 Nd they both comeback

  30. I just realized. In order for the professor to travel around the globe at 1 degree longitude per minute, he'd be travelling roughly 4,150 miles per hour!

  31. You didnt freaking consider the earth's rotation!
    By the time the professor reaches the half way mark the earth would be rotated 180 degree below him!….. No refuelling or his assistants are needed the entire time

  32. I thought the answer was that the professor and plane number 2 come to 1/4 of the way and number 2 would give fukano all his fuel and on the other side when fukano runs out of fuel on 3/4 of the way number 3 would be there and give all their fuel and the guy would make it and then I realized that the other guys had to be alive too… wow

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