Three Elegant Problems

White to move and win

Black to move and win

Black to move and win

Answers after the jump…

(1) 1.Qh4+ Rh5 2.Nf5 gxf5 3.Re6+ Bf6 4.Qxf6#

(2) 1…Qe8! 2.Bxe8 Rxe8 3.Kd1 Be2+ 4.Ke1 Bg4+ 5.Kf1 Bh3+ 6.Kg1 Re1#

(3)1…g5! (and mate follows, if hxg5, then Bc7#, and if 2.Ke5 Rf3 netting the king.