A million dollar chess game

One of the most ancient chess table games allows not only to develop tactical thinking, but also to improve other useful skills. For example, there are a lot of logical tasks for arranging figures on a chessboard in a certain sequence. And for the decision of one of them, researchers from St. Andrews University (Great Britain) offer a million dollars.
Get rich will help a variation of the riddle called "the task of eight queens." In the original, the statement reads as follows: place 8 queens on a standard chessboard measuring 64 by 64 squares so that neither of them is under the impact of the other. That is, based on the fact that the queen beats all the cells located vertically, horizontally and diagonally, there should not be other figures on the "path" of each of them. With due diligence, almost any person can find a solution and it would be strange if scientists would give a million for solving this problem (especially since the problem has been known since the middle of the 19th century). Difficulties begin when we decide to increase the number of cells and figures on the field.
It is logical to assume that the larger the field, the more difficult it is to find a solution. And then the scientists decided to connect the computer to the search for a solution. But faced with another problem: when the size of the board exceeds 1000 per 1000 cells, the computer freezes. Therefore, the experts suggested that all interested persons develop an algorithm for solving the problem, or prove that it does not exist at all. According to the researchers, anyone who is able to write a similar program will be able to modify it for other more important tasks.