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

September 9, 2019


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.

Only registered users can comment.

  1. So instead of adding a bigger fuel gage which probably would take a couple of days this man was just like imma make 3 extra ones which would take 3x the amount of time🤔

  2. This is great, could solve this one, after like 3 or 4 ridles i coudnt find the answer. Very gratifying.

  3. I figured it out but in a differnt way. Let me explain, also I will use the amount of fuel they have in % instead of using the exact amount like shown in the video to make it easier.

    We know that all of your fuel will take you to just the other side of the planet and you can only land on one spot which is the airport you started from.
    To accomplish this task ive decided to devide the whole trip around the globe into 10 sections. Every section is exactly 36 degree of longitude (One tenth of the whole trip).
    Due to our understanding that half the trip will take up 100% of our fuel we can safely assume that every section will take up 20% of our fuel.
    So basically. 36 deegres of longitude = 1 section = 20% fuel.

    Now to the actual flight we will (just like in the video) fly every plane west. But instead of stopping at 1/8 (or 1.25 sections) of the total flight you will now stop at 1/5 or exactly 2 section. All the planes should now have 60% of their fuel left and has all used 40% of their fuel to get there. Plane 2 and 3 will now transfer 20% of their fuel to plane 1 (each) which will put plane 1 at 100% fuel while the other planes will have 40% each. The second and third plane will now have exactly enough to fly back to the airport to refuel for their next mission. Meanwhile plane 1 will have just enough fuel after the refuel to go 180 degrees of longitude plus the 72 it has already travelled which puts the total at 252 degrees of longitude or in more simple terms, 7 sections.

    Meanwhile, plane 2 and 3 has refueled at the airport and plane 2 has gone 3 sections or 108 defrees longitude and has now reached plane 1. With the remaing 40% they split it even and can now go one more section. Meanwhile plane nr 3 has also gone east and meets up with plane 1 and 2 and they all split the fuel to get 20% each. With this fuel they all aim for the airport and they all crash in the pacific, 18 degrees of longitude from their destination and Fukanōs dreams were crushed and yes I just made you read all that and yes I thought it would work while writing it.

  4. 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.

  5. 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

  6. 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

  7. 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

  8. 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)

  9. 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.

  10. 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

  11. 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.

  12. 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

  13. Solution: hire a tanker plane to refuel mid air whenever fuel is low. This answer is valid since you did not specify a private air tanker cound not be used in the rules.

  14. 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.

  15. 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.

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