Nonattacking queens on 3x3 board, why is there no solution?

Question

I have drawn a 3x3 board, I can place a queen in the bottom left corner and one in the middle of right column. To me, this seems like they are nonattacking, but the Internet brings up no solution for a 3x3 board. Why So?

Answer 1

Without a link to the specific webpage, it’s hard to know what’s going on. However, the non-attacking queens problem is usually defined as being about placing $N$ queens on an $N\times N$ board. That problem has no solution for $N=3$. Your proposal isn’t a solution to it because you only have two queens.

Answer 2

I think you are right and the internet is wrong.

Answer 3

It is worth noting that we can prove that it is impossible to place $3$ queens on a $3 \times 3$ board such that no queen attacks another. Clearly, the center square cannot be occupied, since it attacks every other square.

If a corner square is occupied, this leaves exactly two squares that are not attacked; specifically, those that are one knight's move away from the occupied corner. But these two squares mutually attack each other, so it is impossible to place two more queens. Hence no queen can occupy a corner.

Having eliminated the center and the corners, we conclude that three queens must be placed among the four edge squares, but again this is trivially impossible since any occupied edge attacks the other three edge squares.