[HoustonHokie]

How many rooks could you place on a chess board so that none of them are able to attack the others?

Make the following assumptions:

1. They have to move according to the normal rules

2. Any rook can attack any other rook - i.e., color is not important

3. The rooks can be placed anywhere on the board

4. There are only rooks on the board

5. The board is a normal 8x8 chess board

How about bishops? Or knights? Or queens?

Finally, suppose you placed a single queen on the board in a location of your choosing. Now you try to place as many rooks, bishops, or knights as possible so that they can neither attack nor be attacked by the queen or each other. What are your new answers, and how do they vary with the location chosen for the queen?

[Prime]

I refrained from answering the all queens puzzle, because I already knew the answer. It's actually a well-known math / computer science problem. I won't spoil the solution though. You can read about it on Wikipedia, though, if you'd like (I'd provide a link, but the title would give away the answer).

Upon further reflection, it is possible to put 8 queens on the board.

Queens in red:

Cannot do more than 8 (same proof as for rooks post #13). As for the proof that we can place 8 queens, we now have an example, which is a proof.