Revenge of the Chess pieces
What is the minimum number of chess pieces that we need to place on a chessboard such that every square either contains a chess piece, or can directly be attacked by a chess piece?
The chess pieces are the pawn, rook, knight, bishop, queen and king.
Image credit: Wikipedia Alan Light
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1 solution
[This is not a proper solution]
This image from Wikipedia shows that 5 works.
To show that 3 queens cannot dominate the board, note that the queen on a particular color dominates 15 squares of that color and 7 squares of the other color. Now, in which ever way you pose the pieces, the best you can get is that you'll be dominating 15+7+7 of one color and 7+15+15 of the other. However, since you have 32 squares of both colors, covering just 15 + 7 + 7 won't suffice.
I'm not sure why 4 does not work but in the worst case it can be proven with an exhaustive search