The n-queens or eight queens challenge was first posed in 1848 by the German chess player Max Bezzel.
Since then, this problem had remained unsolved, until now.
The challenge is to place eight queens on the chess board without threatening each other. It should be remembered that the queens are the most powerful pieces in this game and can move in any direction in an unlimited way.
Bezzel’s problem asks how many arrangements are possible for the queens to be far enough apart that they don’t attack each other.
Although the challenge could be solved in 1869, later a more extended version of the problem was born that remained without being deciphered until August of last year.
At the time, Michael Simkin of the Harvard Center for Mathematical Sciences and Applications offered an answer that can be considered almost definitive.
According to Simkin, there are some (0.143n)n ways to position queens so that none attack each other on giant n-by-n chessboards.
Your equation doesn’t provide the exact answer, but merely points out that this figure is as close as you can get to the real number at this point.
According to Simkin, on a giant board with a million queens, 0.143 would be multiplied by a million, resulting in 143,000.
This figure must be raised to the power of a million, which is the same as multiplying itself a million times. The final figure obtained is a number with five million digits.
“If you told me that I want you to place your queens in such and such a way on the board, then I could parse the algorithm and tell you how many solutions there are that meet this constraint,” Simkin explained.
“In formal terms, it reduces the problem to one of optimization.”
The article where the chess player exposes his solution to this problem can be consulted at this link.