Mathematician Answers Chess Problem About Attacking Queens
upstart writes:
Mathematician Answers Chess Problem About Attacking Queens:
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.
"It is very easy to explain to anyone," said Erika Roldan, a Marie Skodowska-Curie fellow at the Technical University of Munich and the Swiss Federal Institute of Technology Lausanne.
Simkin proved that for huge chessboards with a large number of queens, there are approximately (0.143n)n configurations. So, on a million-by-million board, the number of ways to arrange 1 million non-threatening queens is around 1 followed by about 5 million zeros.
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