Answers at the bottom of the page...

Puzzle 1: White to play and win in 4 moves.

Puzzle 2: White to play and win in 5 moves.

Puzzle 3: White to play and win in 3 moves.

Puzzle 4: White to play and win in 7 moves.

Puzzle 5: Black to play and win in 7 moves.

Puzzle 6: White to play and win in 4 moves.

ANSWERS

Puzzle 1

This is known as Smothered Mate.

1	Nf7+	Kg8       If ...Rxf7 then Qd8 forces mate in 2
2	Nh6+	Kh8
3	Qg8+	Rxg8
4	Nf7++ Mate

Puzzle 2

1	Nf4	Kh7
2	Bg5	Kh8
3	Ng6+	Kh7
4	Nf8+	Kh8
5	Bf6++ Mate

Puzzle 3

1	Qxf6+	exf6         If ...Kg8 then Nh6++ Mate
2	Bxf6+	Kg8
3	Nh6++ Mate

Puzzle 4

1	Rc7+	Kh8       1... Kf8 loses to 2. Rc8+ Rxc8; 3.bxc8/Q+ Kg7; 4.Qg8++ or 3...Ke7; 4. Bg5++
2	Bh6	a1/Q+
3	Kg2	Rg3+      ...Rg3+ is the only way to survive another move
4	hxg3	Qh1+      ...Qh1+ is the only way to survive another move
5	Kxh1	Rg8
6	b8/Q	fxg4         Black can't do anything about the attack
7	Bg7++ Mate

Puzzle 5

1		Ra3+
2	Kb2	Ra2+
3	Kb1	Raxc2       If Kc3 then Raxc2+, Kd3, Be4++
4	Bd2	Rexd2       White can only delay the attack by giving away pieces
5	Rb4	cxb4
6	g3	Bb3         White has no other possible moves
7	g4	Rf1++

Puzzle 6

1	Nf6+	Kg7/Kh8
2	Ng4+	Nd4/Ne5
3	Bxd4+/Bxe5+	Kg8
4	Nh6++ Mate