9 queens sudoku
There is a famous chess puzzle that calls for placing 8 queens on a chessboard such that no two queens can attack each other. In other words, no two queens can be on the same row, column or diagonal. This puzzle is of some historical interest in that it caught the attention of mathematicians like Gauss and Cantor, but nowadays it is easy enough to solve by computer that it is given as a homework problem in programming courses.
A sudoku is 9-by-9 instead of 8-by-8 like a chessboard, but the restriction on rows and columns is similar. A sudoku doesn’t have any restrictions on diagonals, but it does have the restriction on 3-by-3 blocks. What happens if we add the sudoku block restriction to the 9 queens problem? The 9 queens problem is known to have 352 solutions, and it turns out that 144 of them satisfy the sudoku restriction.
The next question is whether 9 of these 9-queens patterns can be combined into a sudoku. The answer is no. There is just no way to do it without the patterns interfering with each other.