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YouTube // TED-Ed
YouTube // TED-Ed

Can You Solve the Prisoner Boxes Riddle?

YouTube // TED-Ed
YouTube // TED-Ed

Here's a riddle. Ten band members have had their musical instruments placed randomly in boxes. Each band member gets five shots at opening boxes, trying to find their own instrument. (Thus, a 50% chance of each individual finding the desired instrument.) They're not allowed to communicate about what they find. If the entire band fails to find their instruments, they're all fired...and the odds of them all finding their instruments via random guessing is 1 in 1,024. But the drummer has an idea that will radically increase their odds of success. What's the big idea?

This puzzle is based on the 100 Prisoners Problem, though it has been simplified just a bit, and lightened up to be about a band (in the original 100 Prisoners Problem scenario, the punishment is death rather than loss of a job). Here's what the TED-Ed video gives us as the rules:

1. Instruments have been randomly placed in 10 boxes.

2. The pictures on the boxes don't necessarily correspond to the instruments inside.

3. Each musician can open up to 5 boxes. They have to close all of the boxes they open.

4. All 10 musicians must find their own instruments.

5. The musicians can't in any way communicate to each other what they find.

Given all this, it seems rather hopeless. But think on it. What could you do if you talked it through beforehand, as this puzzle allows? Watch this video for the setup, and then pause it when it tells you to, in order to have a good long think. I'd like to think I could come up with a solution like this, were my band (or band of prisoners) in a similar situation. Enjoy:

For more on the original 100 Prisoners Problem, check out this nice writeup. There's also more info from TED-Ed (check the "Dig Deeper" bit for useful links).

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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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fun
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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