Math problems are more interesting when they are posed as horror stories.
The Josephus Problem gets its name from Titus Flavius Josephus, a first-century Jewish scholar.
The story goes that he was with 40 other soldiers when they were surrounded by conquering Romans - imagine that scene in Games of Thrones, where Ramsay Bolton's men trap Jon Snow's army in a tight circle and start moving in.
Rather than give themselves up, the soldiers decided to commit suicide en mass, but by killing each other rather than themselves, to avoid any last-minute changes of heart. Sitting in a circle, the first soldier would kill the man to the left of him, the next living soldier would kill the man to his left, and so on around the circle.
When the circle of slaughter got back to the start, the process would repeat with the smaller group of people. Finally, the last man alive would fall on his sword.
Josephus' problem was that he was much keener on living than dying - but he didn't want to let his fellow soldiers in on that secret. So, where should he position himself in the circle to be the last man standing?
In a delightful short video, Klara Sjöberg demonstrates the extreme and alarming freakout that you can trigger in a mechanical calculator by trying to divide a number by zero; in a followup, Lynn Grant tweets "That is why the old Friden calculators had a 'Divide Stop' key."
Clever and wonderfully-presented: The Incredible Palindromic Hat-Trick. You may be unimpressed if you feed it small numbers. Feed it big ones!
Rather than attempt to describe this, I’ll just quote the artist verbatim: This is the first million integers, represented as binary vectors indicating their prime factors, and laid out using the UMAP dimensionality reduction algorithm by Leland Mcinnes. Each integer is represented in a high-dimensional space, and gets squished down to 2D so that numbers […]
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