If you have a few chess sets at home, try the following exercise: Arrange eight queens on a board so that none of them are attacking each other. If you succeed once, can you find a second arrangement? A third? How many are there?
This challenge is over 150 years old. It is the earliest version of a mathematical question called the n-queens problem whose solution Michael Simkin, a postdoctoral fellow at Harvard University’s Center of Mathematical Sciences and Applications, zeroed in on in a paper posted in July. Instead of placing eight queens on a standard 8-by-8 chessboard (where there are 92 different configurations that work), the problem asks how many ways there are to place n queens on an n-by-n board. This could be 23 queens on a 23-by-23 board — or 1,000 on a 1,000-by-1,000 board, or any number of queens on a board of the corresponding size.
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