2 queen, $5\times 5$ chess board problem Prove the following:
In $5\times 5$ chess board the least amount of queens you need in order to threaten on each square is 3.
(Square threat: the queens threatens on each square in the diagonals,row and column from the queens position).  
I just need to show that you can't threaten the whole $5\times 5$ board with 2 queens.

You can place at most 1 queen in the center, and then for symmetry of rotating and mirroring, you should have at least 1 queen on A1, A2, or B2.
Now allow that the other one can also be placed outside of the center.
Then a simple case analysis.. (Finding e.g. triplets that can't be covered)
