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Can You Solve the Control Room Riddle?

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In this riddle from TED-Ed, you've got a tricky math problem to solve.

In the riddle, you're trying to infiltrate the headquarters of an enemy organization, locate a secret control panel, and shut down their death ray. There are various reasons why this isn't easy.

First off, the enemy headquarters is a ten-story pyramid. It has a regular structure, where the top level contains one room, the floor below that has two rooms, and so on—the ground floor has 10 rooms. The control panel is hidden behind a painting, on the highest floor that satisfies the conditions listed below.

Each room has exactly three doors to three other rooms on that floor...except the control panel room, which only connects to one room. (Thus, the control panel room only has one door in it.)

There are no hallways, and you can ignore stairs while figuring the layout of the building.

You have no floor plan.

You only have enough time to search a single floor before the alarm system goes off.

Given the rules above, can you figure out which floor the control room (with its associated control panel) is on? Watch this video, and pause at the one-minute mark (when instructed), for a video view of the same problem. The solution is then presented, with a step-by-step breakdown of how to get there.

To figure out the solution, it may help to start drawing room maps, starting at the highest floor. If you're interested in this kind of puzzle, read up on graph theory.

For more on this puzzle, check out this TED-Ed page, and be sure to visit the "Dig Deeper" section, which includes links to the puzzle author's website, Doctor Ecco.

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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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