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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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History
When Math Discoveries Led to Banned Numbers
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The literature world has seen more than its share of controversy. The best stories tend to provoke the strongest reactions—both positive and negative—in readers, which is why so many classic books have been banned at one point or another. But even a more objective field like math isn’t immune to conflict. In its new video, TED-Ed rounds up the numbers that caused such a stir when they were introduced that they were banned in math circles.

One of the earliest examples comes from ancient Greece. A mathematician named Hippasus was having trouble solving certain equations with fractions and whole numbers alone, so he came up with irrational numbers to make these values easier to express. The ruling school of thought at the time dictated that everything in nature could be explained elegantly with the numbers that already existed. Threatened by Hippasus’s new notion, his fellow mathematicians rejected the irrational numbers and had him exiled.

Other numbers have been banned for legal reasons. When Arab traders brought their positional number system, which included zero, to Italy in the Middle Ages, Florence banned it from record-keeping fearing that they would be easier to forge than Roman numerals. The Arabic way of counting also led to the rise of negative numbers, which were regarded with disdain by many experts into the 19th century. For more banned numbers, including some that are prohibited today, check out the full story below.

[h/t TED-Ed]

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Euclid
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Live Smarter
An Ex-Google Engineer Just Reinvented the Measuring Cup
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Euclid

Recognizing a problem most people didn’t even know they had, former Google and Facebook software engineer Joshua Redstone has made a bold claim for his recent Kickstarter venture: He’s developed a better measuring cup.

According to the Boston Business Journal, Redstone spent four years tinkering with a solution to something that had long annoyed him as an amateur chef: Traditional measuring cups, which are stocky and not very well tapered, don’t do a great job of accurately measuring their own contents. Redstone believes the shape of a cup determines its success, particularly when a cook overfills a liquid or solid by a tiny amount. The smaller the volume, the more the problem is magnified.

Euclid

Redstone’s cup, Euclid, resolves the issue. According to the Kickstarter page: “With traditional measuring cups, the smaller the amount, the harder it is to measure accurately. The culprit? The shape. Straight sides magnify errors when measuring lower down in the cup. Some have tried to solve this problem with conical measuring cups, but their results fall short of Euclid’s by up to 60 percent. Euclid is the only measuring cup with a mathematically optimal, tapered design for consistent accuracy across amounts.”

Euclid is just about ready to overshoot its $30,000 Kickstarter goal. Backers can pay $24 for the cup now, or wait until it’s available at retail for a slightly higher price to be determined. The cup is scheduled for release in May 2018.

[h/t Boston Business Journal]

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