Take out your chessboard, prepare to watch it for a long time, and let us present you with a 150-year challenge: Could you arrange eight ladies on a chessboard in such a way that none of them attack each other? Let’s say it’s possible, how many ways to do it?
This is the first form of mathematical problem known as the n-queen problem. In 1848 a German chess the magazine published the first 8-on-8 chessboard problem, and by 1869 the n-queens dilemma arose. Since then, mathematicians have given many results for n-queens, and now Michael Simkin, a doctoral student at Harvard University’s Center for Mathematical Sciences and Applications, has almost solved this problem, proving for the first time a result that was previously only supposed to be use computer simulations, According to Quanta Magazine.
Instead of asking how many ways there are to position eight ladies on a conventional 8-by-8 chessboard (where there are 92 potential work configurations), the problem asks how many ways to put n queens on an n-by-n board. This could be 50 ladies on board 50 to 50 for example.
Simkin proved that there is approximately (0.143n)n configurations for large chessboards with a large number of ladies. This means that on board a million to a million there are approximately 1 million ways to line up 1 million non-threatening ladies, followed by about 5 million zeros!
But how did he find that? By tracking the number of spaces that were not attacked after revealing the position of each additional position of a new queen, Simkin was able to calculate the maximum number of configurations. He therefore concludes that he has almost found the exact number of n-queens configurations, as this maximum figure coincides with its minimum almost completely, and his proof provides the 150-year-old challenge with long-awaited clarity.
Although that doesn’t mean that mathematicians will stop playing with this problem in an attempt to learn more about it, Simkin’s conclusion has definitely removed most of the dust and mystery that has clouded the minds of many people.