The key move is Rh1. This is difficult to find because it makes no threat -- instead, it puts black in zugzwang, a situation in which every move leads to a disadvantage, yet the player must move. Each of black's nineteen legal replies allows an immediate mate. For example, if black defends with 1...Bxh7, the d5 square is no longer guarded, and white mates with 2.Nd5#. Or if black plays 1...Re5, black blocks that escape square for its king allowing 2.Qg4#. Yet if black could only pass (i.e., make no move at all), white would have no way to mate on its second move.
White Mates in 2
Problems with answers
White Mates in 2
Image:chess_zhor_26.png
Image:chess_zver_26.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Image:chess_zver_26.png
Image:chess_zhor_26.png
White to move and mate in two.
Image:chess_zhor_26.png
Image:chess_zver_26.png
a8 b8 c8 d8 e8 f8 g8 h8
a7 b7 c7 d7 e7 f7 g7 h7
a6 b6 c6 d6 e6 f6 g6 h6
a5 b5 c5 d5 e5 f5 g5 h5
a4 b4 c4 d4 e4 f4 g4 h4
a3 b3 c3 d3 e3 f3 g3 h3
a2 b2 c2 d2 e2 f2 g2 h2
a1 b1 c1 d1 e1 f1 g1 h1
Image:chess_zver_26.png
Image:chess_zhor_26.png
White to play and mate in two.
Rcc7! with the threat 2.Nc3. There are eight defences by the black knight on d4, each met by a different white mate: 1...Nxb3 2.Qd3#; 1...Nb5 2.Rc5#; 1...Nc6 2.Rcd7#; 1...Ne6 2.Red7#; 1...Nf5 2.Re5#; 1...Nf3 2.Qe4#; 1...Ne2 2.Qxh5#; and 1...Nc2 2.b4#. When a black knight moves to the maximum number of eight squaures like this,it is known as a knightwheel.

1.

2 .

1.Qc3+ followed by 2.Qe1 forks the Black Rook and Bishop.

 1.Qd4 attacks the Black Knight and threatens mate. 

3.
4.