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Why Jigsaw Puzzles Almost Never Have the Number of Pieces it Says on the Box

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This piece was originally published on God Plays Dice.

Patrick Honner tweeted a few days ago:

So let’s say that a number is a “puzzle number” if it’s of the form m x n with m ≤ n ≤ 2m — that is, a puzzle has to have an aspect ratio between 1 (square) and 2. (The choice of 2 is arbitrary here, but any other constant would be more arbitrary.) We can easily work out the first few puzzle numbers:

2 = 1×2, 4 = 2×2, 6 = 2×3, 8 = 2×4, 9 = 3×3

which is enough to find them in the OEIS: that’s A071562, defined as “Numbers n such that the sum of the middle divisors of n (A071090) is not zero.” (What’s a “middle divisor”, you ask? It’s a divisor of n that’s between (square root n/2) and (square root 2n.)) Titling it…



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Clever virus, stupid Premier | The Spectator Australia

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For something made in China, Coronavirus is surprisingly good.

How else to make sense of the latest non-sensical restrictions aimed at stopping the spread of the disease in Victoria except that Covid-19 is the world’s first smart virus?

Premier Daniel Andrews and his quarantine of experts yesterday announced that it was safe for Victorians to get their gardens landscaped but not safe for them to worship at church. 

Communist China has managed to produce a disease that has it in for Christians but allows you to work on backyard feng shui. Figures.

The virus is amazingly specific in its prejudices.

It has no interest in swimmers doing laps at an outdoor public pool. But it apparently lurks on fairways, lying in wait for…



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South Korea Has COVID Under Control. Here’s What Daily Life Looks Like Now

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Seoul South Korea nightlife

Photo by Chinh Le Duc via Unsplash

Though a COVID-19 vaccine remains elusive, the view of the global pandemic is pretty different depending on where you’re standing. Lives and norms in the United States have shifted dramatically in many areas since the first Americans tested positive for COVID-19 back in February, giving rise to Zoom hangouts, the etiquette of socially distanced dating, the grim ups and downs of testing availability, and the disastrous attempts to return prematurely to work, school, and so-called “normal” life.

But the rest of the world isn’t struggling with COVID-19 in quite the same ways we are—for instance, under South Korea’s governmental guidance and safety measures, only 393 people have died from COVID-19.

We…



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Scientists Discovered an ‘Improbable’ World That Shouldn’t Exist

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​Artist concept of LTT 9779 system. Image: Ricardo Ramirez

Artist concept of LTT 9779 system. Image: Ricardo Ramirez

Imagine a world where a year passes more quickly than a single Earth day. That’s what’s shaking at LTT 9779b, a giant exoplanet whose existence and properties are currently inexplicable given its extreme proximity to its Sun-like star, which it orbits every 19 hours.

Located about 260 light years from Earth, LTT 9779b is the first known example of an Neptune-sized world with this type of “ultrashort” orbital period of less than a day, according to a study published on Monday in Nature Astronomy.

The strange world is also the sole member of an entirely new class of exoplanet called the “ultrahot Neptune.”

“LTT 9779b promises to shed light on the nature of Neptune-type…



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