Harvard Mathematician Has Solved 150-Year-Old Chess Conundrum
Update: 2022-01-27 16:19 IST
Harvard Mathematician Has Solved 150-Year-Old Chess Conundrum
Two competitors compete for control of 64 individual black or white squares, each with 16 pieces. But go a little deeper, and the game opens up a world of extraordinarily complicated possibilities, giving difficulties to chess theorists and mathematicians that can take decades, if not centuries, to solve.
One such challenge was finally solved in July 2021 at least to a point. Michael Simkin of Harvard University in Massachusetts applied his intellect to the n-queens problem, which has perplexed academics since its inception in the 1840s.
People e familiar with chess, people are aware that the queen is the most powerful piece on the board, capable of moving any number of squares in any direction. The n-queens problem poses the following question with a specific number of queens (n), how many different arrangements are conceivable where none of the queens can take any of the others? The answer that will be followed up is 92 for eight queens on a typical 8 by 8 board, albeit most of these are rotated.
Regarding 1,000 queens on a 1,000 × 1,000-square-foot board? What if there were a million queens? Simkin's solution is (0.143n)n, which is the number of queens multiplied by 0.143 and raised to the power of n. What you have now isn't the exact answer, but it's as close as you can get for the time being. They won't duplicate the statistic here because it comes out as a number with five million digits after it when there are a million queens.
Simkin worked on the equation for about five years, using a range of tactics and methodologies and encountering a few roadblocks along the way. Finally, the mathematician was able to compute the bottom and upper boundaries of feasible answers using several methods and discovered that they were nearly identical.
Simkin explained that he wanted you to arrange your queens on the board in a certain way, that be able to examine the algorithm and tell you how many alternatives satisfy this requirement. It helps in the reduction to an optimization problem in formal terms.
Simkin and a colleague at the Swiss Federal Institute of Technology Zurich, Zur Luria, worked on a torodial or modular variant of the n-queens issue early on. Because the diagonals wrap across the boards in particular one, a queen could, for instance, move diagonally off the right edge of the board and return on the left. This gives each queen symmetry of attack, but it's not how a traditional chessboard performs: a queen in the corner of the board does n't possess as numerous attack angles as one in the middle.
Although the pair's research on the toroidal problem eventually came to a halt despite publishing some results, he was able to incorporate some of the outcomes into his ultimate solution. The study demonstrates that as the boards get wider and the number of queens grows, the queens tend to gather along the sides of the board, having fewer queens in the middle, where they are vulnerable to attack. This information allows for a more balanced approach.