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The Three Utilities Problem | Graph Theory Breakthrough


Getty/Photo Illustration by PM
Jacob Holm was flipping through proofs from an October 2019 research paper he and colleague Eva Rotenberg an associate professor in the department of applied mathematics and computer science at the Technical University of Denmark had published online, when he discovered their findings had unwittingly given away a solution to a centuries-old graph problem.
Holm, an assistant professor of computer science at the University of Copenhagen, was relieved no one had caught the solution first. “It was a real ‘Eureka!’ moment,” he says. “It suddenly seemed obvious.”
Holm and Rotenberg were trying to find a shortcut for determining whether a graph is “planar” that is, if it could be drawn flat on a surface without any of its lines crossing each other (flat drawings of a graph are also called “embeddings”). ....

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Viral TikTok Math Problem Is Making People Cry: 87 Divided by 29

Viral TikTok Math Problem Is Making People Cry: 87 Divided by 29
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Viral Math Puzzle for MIT Applicants: Can You Solve This Problem?


The algebra problem is just one simple prompt and it s still hard.
The solution has to do with distribution.
On his popular YouTube channel, MindYourDecisions, mathematician Presh Talwalkar frequently digs up samples of classic college entrance exams.
You love challenging math problems. So do we. Let s solve them together.
Talwalkar challenges his followers to see how they’d fare in the days before standardized testing.
In one of his most recent videos, Talwalkar unearthed a question from an 1876 algebra exam given to applicants at the Massachusetts Institute of Technology.
It’s a simple prompt:
A father said to his son, “Two years ago I was three times as old as you; but in fourteen years I shall be only twice as old as you. What were the ages of each?” ....

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