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Can You Solve the Frog Riddle?

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In this riddle from TED-Ed, you're in a sticky situation. You're stranded in a rainforest and have accidentally eaten a poisonous mushroom. To survive the poison, you need to lick a very particular frog. But which frog is it?

You can watch the video below for more details, or read this description. The problem is simple: You are poisoned and you know that a particular species of frog produces the antidote, which will cure you if you lick it. But to make things more complex, you know that only female frogs of the species have the antidote—males do not. In this frog species, males and females look identical but males have a distinctive croak. (Males and females also occur in identical proportion in this species.) In one direction, you see a single frog. In another, a group of two frogs sitting together.

From the direction of the two frogs, you hear that distinctive "male frog" croak. Uh-oh! One of those two is definitely male.

As the poison sets in, you have to make a logical decision. You need to find a female frog with the antidote. Are your odds better going toward the group of two (one of which is definitely male), or toward the single unknown frog? And what are those odds, anyway?

Note that in this riddle you are not guaranteed to survive. You're just trying to take your best shot.

So which to choose, and why?

Watch the video below for a discussion of the problem and how the math stacks up behind one of the choices.

For more resources, consult this TED-Ed page. Once you've solved it (or if you've given up), you might also be interested in this related math problem.

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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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