Place five queens on a chess board so that every square on the board is attacked. It’s an old and famous problem; there are lots of solutions and it’s pretty easy to find one. Try it for yourself and see!

Now try using just three queens and two rooks. Not so easy this time; the solution is unique if you ignore trivial rotations and reflections of the whole board. What about other attacking forces? Four queens and two pawns maybe?

The image above is a snapshot of my solver. Click here to go to the solver itself. I wrote it over ten years ago when Java applets were flavor of the month. Most modern computers and tablets don’t have Java available by default and most tablets won’t let you install Java at all; you can still install Java as a free plug-in in most PC browsers though.