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YouTube // TED-Ed

Can You Solve the Prisoner Hat Riddle?

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YouTube // TED-Ed

If you like brain teasers, we've got a doozy for you. In this TED-Ed lesson, Alex Gendler walks us through the "prisoner hat riddle," a classic puzzle. In this version, you and nine other humans have been abducted by aliens. The aliens would like to eat you all, but not if you can prove your intelligence. So they propose a test.

The aliens line you up, placing you in order of height (tallest in the back, shortest in front), and place black or white hats on each of you. You must face forward, and you mustn't look at your own hat. Starting with the person in the back, each person must say a single word: "black" or "white" to guess the color of the hat on his or her own head, despite not being able to see it. If nine of you get it right, you live. If you don't, you're lunch. The good news? You get to talk it through as a group first.

This is a classic puzzler because it requires the group to devise a way to signal hat-color information without directly saying it. I'll admit, I watched the setup, paused the video, and thought about it a bit. I did not solve this riddle. Can you? (The answer is explained after about 90 seconds of setup.)

You can read more about this lesson from TED-Ed. If you like this kind of puzzle, you need to check out their Math in Real Life video series.

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History
When Math Discoveries Led to Banned Numbers
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iStock

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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