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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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Health
The Math Behind the Classic Eye Chart Is Surprisingly Complex
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Next time you're forced to take a vision exam at the DMV, take a moment to appreciate the complex math that went into the eye chart. What seems like a fairly straightforward way to assess eyesight is actually the result of specific calculations that can tell you a lot about how the human eye works.

As The Verge explains in the video below, eye charts measure one aspect of healthy vision: visual acuity. This is our ability to make out fine details in our surroundings—kind of like the resolution of a computer screen, but instead of pixels, it's measured in degrees. It's easy for our eyes to tell the difference between two points of light coming from different directions, but if those points start to move closer together they will eventually blur into one. The angle created just as two lines of light become too close for our eyes to distinguish them is called the resolution limit. In healthy adults, it measures one-sixtieth of a degree, or one arcminute wide.

When a doctor asks you to read an eye chart, the resolution limit is what they're looking for. The letters in the middle of an eye chart are all designed to be exactly one arcminute thick. If your vision is sharp, you should be able tell the difference between the white spaces and the black lines of the text from 20 feet away. 

A perfect 20/20 score on an eye chart test doesn't mean you have perfect vision: Visual acuity, along with color, contrast, and depth perception, are all important parts of healthy eyesight. And a higher resolution limit isn't always a sign of a permanent problem: For people who spend their days staring at a screen, it may be caused by the eye fatigue brought on by Computer Vision Syndrome. If this is a problem for you, here are some ways to tweak your behavior.

[h/t The Verge]

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Could You Pass the Mensa Intelligence Test?
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The biggest perk of being in Mensa just might be the bragging rights. Membership is reserved for society’s most elite intellectuals, and the only path to induction is to score in the 98th percentile or higher on their notorious IQ test. Think you have the smarts to join the top .0001 percent of thinkers? Before you apply for the real thing, flex your brain by answering a few sample questions from the test.

The practice questions shared on Popular Science cover the skills Mensa looks for in its members: verbal, spatial, and mathematical reasoning. To ace the test, you’ll need to be just as capable of recognizing obscure vocabulary as you are of doing complex math in your head.

The real Mensa IQ test is really two tests: a timed test with 50 questions and one with seven sections. (Scoring in the 98th percentile on either test qualifies you to join.) Answering all four of the questions posted to PopSci correctly doesn’t necessarily mean you’re intelligent enough for Mensa, but it should give you a confidence boost if you’re thinking about applying. If you do miss a question or two, maybe hold off on taking the official test until you’ve had more time to prepare: Scoring below the 98th percentile bars you from joining the exclusive club for life. You can take the practice test now by heading over to PopSci.

[h/t Popular Science]

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