Atlas Obscura explains why this seemingly simple question is so difficult to solve.
The riddle is based on what is known as the Queens Puzzle, first devised in 1850. Eight queens must be placed on a standard chessboard so that no two pieces can take one another. According to a release from the university, “This means putting one queen each row, so that no two queens are in the same column, and no two queens in the same diagonal.” Solutions are not hard to imagine, but the problem becomes more complex when the chessboard grows—say 100 queens on a 100-by-100 chessboard.
New research from computer science professors Ian P. Gent, Christopher Jefferson, and Peter Nightingale refers to a still more challenging variant in which the board is even larger, but some queens have already been placed. In an interview with the Clay Mathematics Institute, Gent said this problem, technically known as the “n-Queens Completion Problem,” falls into a class of high-level math puzzles known as “NP-Complete.” Any algorithm that could solve it, Gent said, could therefore be used indirectly to solve others in the class—and be a contender for the Millennium Prize.
Check out the official release from St. Andrew’s here.