Can You Solve the Airplane Fuel Riddle?

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Here's a fun riddle: Professor Fukanō plans to circumnavigate the world in his new airplane. But the plane's fuel tank doesn't hold enough for the trip—in fact, it holds only enough for half the trip. But with the help of two identical support planes (which can refuel him in mid-air) piloted by his assistants Fugori and Orokana, the professor thinks he can make it in one trip. But since all three planes have the same problem of limited fuel, how can they work together to achieve the professor's goal without anyone running out of fuel?

This TED-Ed riddle is very much like a Popular Mechanics riddle written in 2016. It's a tricky one, and it helps to have a piece of paper handy.

It's explained in the video below (along with a "pause now" bit so you can solve it yourself). If you're not a fan of video, here are the starting rules:

1. The professor's plane must make a single continuous trip around the world without landing or turning around.

2. Each plane can travel exactly 1 degree of longitude in 1 minute for every kiloliter of fuel. Each can hold a maximum of 180 kiloliters of fuel.

3. Any plane can refuel any of the others in mid-air by meeting at the same point and instantly transferring any amount of fuel.

4. Fugori and Orokana's planes can turn around instantaneously without burning fuel.

5. Only one airport is available for any of the planes to land, take off, or refuel.

6. All three planes must survive the experiment, and none may run of fuel in mid-air.

As the video explains, the airport mentioned in point #5 happens to be on the equator.

Here's the video:

For a bit more from TED-Ed on this riddle, check out this lesson page. If you want to read a solution to a very similar puzzle without watching the video above, try this Math is Fun puzzle page.

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February 4, 2017 - 8:00pm
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