For the N-queens problem, especially as N grows large, there is an interesting probabilistic solution that generally is (absurdly) fast. Put the N queens rando

For the N-queens problem, especially as N grows large, there is an interesting probabilistic solution that generally is (absurdly) fast. Put the N queens randomly on the board. Then repeatedly pick the queen that is attacked by the most other queens (if/when there are multiple, pick randomly), and place it in the spot where it is attacked by the least other queens (if/when there are multiple, pick randomly). Repeat until you have a solution.