N queens are to be placed on an N by N chessboard so that no two attack each other. A queen can move (or attack) vertically, horizontally, or diagonally.

This problem is difficult because of the many constraints between the queens. Each queen that is placed on the board prevents any other queen from being placed on the same row, column, or diagonals. Thus, a queen can constrain the placement of queens all the way on the other side of the board. This means that every queen potentially affects every other queen. As the size of the board increases, this means that the number of constraints increases exponentially.

Finding just one solution is relatively easy. Finding all solutions using standard search techniques requires exponential time.