Can you place 3 queens on a 6x6 chess board such that they can attack every square?
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Here's the solution:
It's interesting to note that the domination problem has very few solutions for 3 queens on a 6x6 chessboard as compared to other possibilities. (Neither of those links contains the answer! Just background info.)
Perhaps the key realisation is that
some squares which you'd intuitively expect to be attacked diagonally can be attacked orthogonally. With one queen at $a1$ covering the central white diagonal, it'd seem natural to use two more to cover the black diagonals to either side, including those difficult squares $b3/c2$ and $e6/f5$. But putting the other two queens on the next diagonals leaves not enough space to reach out to the edges ... and we realise there's a nice configuration to cover $b3/c2$ and $e6/f5$ orthogonally.
Before that, starting with
a queen at the corner is a counterintuitive move in which I was inspired by the 5 queens on an 8x8 chessboard problem.