8 Mutually Non-Attacking Queens on Chessboard

Theorem

On a standard chessboard, it is possible to arrange a maximum of $8$ queens so that no queen is attacking any other queen.

There are $12$ such arrangements, up to rotation and reflection.

Solution $1$

Solution $2$

Solution $3$

Solution $4$

Solution $5$

Solution $6$

Solution $7$

Solution $8$

Solution $9$

Solution $10$

Solution $11$

Solution $12$

That there are only these $12$ can be proved by brute force.

$9$ queens cannot be so placed.

This is clear from the Pigeonhole Principle, which would have at least one row with $2$ queens on it, and so attacking each other.

$\blacksquare$