I have white rooks on c7 and c5, white bishop on b6, white knight on d4, white king on b3, black king on d6 and black pawn on d2. white moves first. How can I get checkmate in three moves?
[FEN "8/2R5/1B1k4/2R5/3N4/1K6/3p4/8 w - - 0 1"]
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[FEN "8/2R5/1B1k4/2R5/3N4/1K6/3p4/8 w - - 0 1"] 1.Kc4 d1=Q 2.Rd5#
So two moves, not three.
The first thing to note is that the Black King cannot move. The second thing to note is that (most) non-forcing moves by White will allow Black to Queen the pawn - with check. This fails the challenge.
Experimentation will show that moving the Rook on c7 (for example R7c6+) allows the King to escape to d7 or e7. The other frcing move is Rd7+ but of course that isn't helpful. Since the c7 Rook is protected by the Bishop, we can try moving the other Rook. We have to find forcing moves, so the first one I see is R5c6+. But this lets the King escape to d5 or e5. Another forcing move is Rd5+ but the Black King would eat it. But it's so close to checkmate. There's no forcing move with the Bishop. The Knight has 2 forcing moves, but neither seems to help.
So we move the White King to c4 to support the Rook we intend to put on d5. This has the additional benefit of not costing us a tempo if Black queens the pawn. That realization is fundamental here. The White Knight blocks the Queen from capturing the Rook on d5.