` here are some possibilities (depending upon how black moves) 2-step solution: 1. white queen - d5 to e5 + check black queen captures white queen - e7 x e5 2. white rook captures black rook - f4 x f8 ++ check-mate 4-step: 1. white queen - d5 to e5 + check black queen - e7 to f6 (black rook f8 to f6) 2. white queen - e5 x f6 + check black rook - f8 x f6 (black queen e7xf6) 3. white rook - f4 x f6 black moves anything BUT king 4. white rook - f6 to f8 ++check-mate But, I cannot figure out a SOLID four move check mate because at step 3, the black king can move h8 to g8, so the above would not work.