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Can You Solve the Counterfeit Coin Puzzle?

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Mathematicians have long plagued humankind with a style of puzzle in which you must weigh a series of items on a balance scale to find one oddball item that weighs more or less than the others. They're known collectively as balance puzzles, and they can be maddening...until someone comes along and trots out the answer.

Within the world of balance puzzles, the 12-coin problem is well-known (there's also a nine-coin variant, and a horrendous 39-coin variant). There is in fact a generalized solution for such puzzles [PDF], though it involves serious math knowledge.

In the video below, we are presented with a version of the 12-coin problem in which we must determine a single counterfeit coin in a dozen candidates. The problem is, we're only allowed the use of a marker (to make notes on the coins) and three uses of a balance scale. Here are the detailed conditions:

1) All 12 coins look identical.

2) Eleven of the coins weigh exactly the same. The twelfth is very slightly heavier or lighter.

3) The only available weighing method is the balance scale. It can only tell you if both sides are equal, or if one side is heavier than the other.

4) You may use the scale no more than three times.

5) You may write things on the coins with your marker, and this will not change their weight.

6) There's no bribing the guards or any other trick.

So how do we solve this specific case? Watch the video to find out.

For a bit more on this puzzle, check out this TED-Ed 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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