2024/05/13 DPA: "Beware Of 'Free' Stuff"
White to move.
White is down a Queen for a Bishop. Therefore, the tempting 1. Nf5+ Ke6 2. Nxe3 Bxe3 3. Bxe3 Rxe3 only gets equality. So this is probably not the solution.
Currently the Black King has only one escape square: e7. What move can control this square? 1. Ba3#.
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When I try to visualize which squares are covered and which are not, I typically start with looking at all 8 squares surrounding the King, starting in the upper left. ie "The upper left is blocked by a Black pawn. The upper middle is controlled by the light-squared Bishop. The upper right is X-rayed by the dark-squared Bishop." etc.
Another way is to break it down to dark and light squares. ie "The light squares are controlled by the Bishop and Knight and pawn. 2 of the 4 dark squares are blocked by Black's own pieces and the other two are controlled by the other Bishop."