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Using the two high-quality genomes that exist for Neandertals and Denisovans, researchers find clues to gene activity...
A new report from the Intergovernmental Panel on Climate Change (IPCC) concludes that humanity has done little to slow...
Astronomers have discovered an Earth-sized planet in the habitable zone of a red dwarf—a star cooler than the sun—500...
Three years ago, Jennifer Francis of Rutgers University proposed that a warming Arctic was altering the behavior of the...
Officials last week revealed that the U.S. contribution to ITER could cost $3.9 billion by 2034—roughly four times the...
An experimental hepatitis B drug that looked safe in animal trials tragically killed five of 15 patients in 1993. Now,...
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Stay in the Tub, Archimedes
21 November 2003 (All day)
Perhaps it wouldn't make him run naked through the streets shouting "eureka," but Archimedes would no doubt be pleased that one of his puzzles has been completely solved more than 2000 years later.
In the third century B.C.E., Archimedes posed a geometric mindbender: How can one get a particular set of 14 irregular triangles and quadrilaterals to fit together into one big square? Finding one solution isn't that hard, but nobody knew how many solutions there are. "When you first start looking at it, it seems like it might have thousands and thousands of solutions," says mathematician Ed Pegg, who works at Wolfram Research, a mathematics software company in Champaign, Illinois.
But just this month, puzzlemaker Bill Cutler of Palatine, Illinois, put the 2-millennium-old poser to rest. Using a computer's brute force, Cutler figured out by trial and error that there were only 536 solutions to the puzzle, excluding rotating and reflecting the final assembled square. One element that made the problem tractable was that there are three pairs of pieces that need always be together--one side of each of those pieces is a length that only fits together with its partner.
That constraint as well as the fact that there were obviously lots of solutions limited Archimedes' puzzle's appeal, says Pegg. "It really wasn't all that good of a puzzle," he says. "So it went by the wayside." Nevertheless, he thinks that the solution to the ancient problem is a victory.