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Ok, this is four moves, but it assumes that the black queen falls for the white queen sacrifice:

R-e7, Qxd3,
Knight xf4 check, Rxe7
Kxg6 check, k-e4
Pawn-f3 checkmate

Need to look at what else black can do to defend

If the black queen instead takes the bishop on a2 that doesn't help:

Rxe7, Qxa2
Kxg5, Rxc7
Q-e4 checkmate

But if the black rook simply takes mine on e7, then I am back to square one, but down a rook

Right:

  1. Re7 Rxe7
    and black - again - wins. :)

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