A Cubed Number Puzzle Is Solved. Only One Is Left

UK's Andrew Booker figures out which three cubed numbers add up to 33
By John Johnson,  Newser Staff
Posted Apr 4, 2019 9:55 AM CDT
Updated Apr 4, 2019 10:00 AM CDT
Mathematician Conquers Vexing Numbers Problem
Stock photo.   (Getty/LagartoFilm)

For more than half a century, modern mathematicians have been trying to crack two stubborn numbers problems—and a UK professor just solved one of them. As Live Science explains, the problem itself seems fairly straight-forward: Which three cubed numbers add up to 33? The University of Bristol's Andrew Booker devised a new algorithm to hunt for an answer to the puzzle—a Diophantine equation in math-speak—and "did a jump for joy" when a university supercomputer spit out the answer after three weeks, he says in this Numberphile video. The three numbers: 8,866,128,975,287,528; -8,778,405,442,862,239; and -2,736,111,468,807,040. Cube them, add them up, and you get 33.

Not all such equations are anywhere near as tough. As Quanta points out, you can get to 29 by cubing 3, 1, and 1, and adding them. And for some numbers, it's mathematically impossible to get a Diophantine solution. But for all numbers under 100 that should have solutions, mathematicians had found them, except for 33 and 42. Booker's solution—he's getting credit for a clever algorithm, not just the brute force of computing—leaves only 42 as the holdout. If that number rings a bell, a post from the University of Bristol might explain why: As fans of the Hitchhiker's Guide to the Galaxy know, 42 just happens to be the answer to the meaning of life. (More mathematics stories.)

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