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.