King and a Lot of Rooks

Relevant wiki: Chess Puzzles

Note that wherever the King is placed, no Rook can be placed in its same row or column, but a Rook can be placed on any of the other empty squares. For a $m\times n$ , there are $mn-(m+n)+1=mn-m-n+1$ squares where a Rook can be placed, as each row consists of $m$ squares and each column consists of $n$ squares, and we're counting the King square twice.

When $m=8$ and $n=8$ , $64-8-8+1=49$ Rooks can be placed on the board. This is biggest number because if we place one more Rook, it will be placed on the King row or column, thus, will be attacking the King.

It really doesn't matter where you keep the king.A rook cannot be placed in the same column or row that all.So just count the remaining squares and that's your answer 49

Easy. WhAt Is 7x7? tHe answer of 7x7 is the answer of the question😂

You can see that you should not put a rook on the letter coordinate the king is on, neither should you for the number coordinate it is on. Hence, since a side is 8 units, the number of rooks you can place is 8-1 (excluding the letter coordinate) times 8-1(excluding the number coordinate. Therefore the answer is 49. Generalising it for an $m^2$ sided chessboard, the maximum number of rooks you can place such that it is not threatening the king is $(m-1)^2$

the king will take out a row and a column from the board so that he won't be under attack so generally on an m n board you can place (m-1) (n-1) so the answer is 49

To generalize for a chessboard of dimensions $m \times n$ , we need to put the king in the corner. We then have to take a column and a row off. This will reduce the height and width by 1, maxing our "block" of rooks a size of $(m-1) \times (n-1)$ . Then, we set m and n equal to 8, making our "block" of rooks a whopping size of 49.

Wherever the king is, just keep all rooks where they're not in same row or column. If you keep it in the top right corner, you see a 7 by 7 square of rooks. Bonus question: whats the answer if it's not stalemated?

$\boxed{49}$ is maximum.

Assume the king is placed at the corner of chess board, now we ignore that particular row and column. This leaves 7x7=49 possible squares where the rook can be placed.

Another answer would be placing the king and counting the squares after placing rooks.