On one level, chess seems like a simple game: 64 individual black or white squares, 16 pieces per side, and two competitors striving for conquest.
Dig a little deeper though, and the game offers incredibly complex possibilities, posing challenges to chess theorists and mathematicians that can go unsolved for decades or even centuries.In July 2021, one such challenge was finally solved – at least, up to a point. Mathematician Michael Simkin, from Harvard University in Massachusetts, put his mind toIf you know your chess, you know that the queen is the most powerful piece on the board, able to move any number of squares in any direction.
For eight queens on a standard 8 x 8 board, the answer is 92, although most of these are rotated or reflected variants of just 12 fundamental solutions. But what about 1,000 queens on a board that's 1,000 x 1,000 squares? What about a million queens? Simkin's approximate solution to the problem is What you're left with is not the precise answer, but it's as close as it's possible to get right now. With a million queens, the figure comes out as a number with five million digits after it – so we won't reproduce it for you here.
"If you were to tell me I want you to put your queens in such-and-such way on the board, then I would be able to analyze the algorithm and tell you how many solutions there are that match this constraint,"