Harvard University scholars have decided the 150-year-old mathematical task associated with the location of the queens on chess boards of various sizes. Formally, a chess problem is the task of optimization, so mathematics were able to develop an algorithm for obtaining only an approximate response. This is reported in the preprint of articles published on the ARXIV website.
It is known that there are 92 ways to arrange eight queens on a standard chessboard so that none of them can attack the other. Initially, this task was proposed in the German chess journal in 1848, and the answer was received two years later. In 1869, a larger version of the task was proposed, on which mathematics found the answer only last year. It consists in finding the number of combinations of the location of n queen on the size of N on n cells.
mathematics were calculated that there are about 0.143n in N-th degrees of methods to place the query so that none of them was under the attack of another. At the same time, scientists could not get an accurate answer, and the number 0.143 indicates the average level of uncertainty of a possible result. First, the researchers identified the lower limit of the number of possible configurations, and then applied the maximum entropy method to find the top border.
accurate answer is somewhere in the middle between two borders in a relatively small mathematical space. According to mathematicians, theoretically, you can get closer to this value even more.