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Puzzle 6:White to play and win in 2 moves.
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Puzzle 7:Black to play and win in 3 moves.
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Puzzle 8:White to play and win in 3 moves.
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Solution:
Puzzle 1:
1 Nf7+_ Kg8 If ...Rxf7 then Qd8 forces mate in 2
2 Nh6+_ Kh8
3 Qg8+_ Rxg8
4 Nf7++ Mate
Puzzle 2:
1 Qxf6+_ exf6 If ...Kg8 then Nh6++ Mate
2 Bxf6+_ Kg8
3 Nh6++ Mate
Puzzle 3:
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 4:
1 Rh8+_ Kxh8
2 Rh1+_ Kg8
3 Rh8+_ Kxh8
4 Qh1+_ Kg8
5 Qh7++ Mate
Puzzle 5:
1 Qxh7+_ Kxh7
2 Rh3++ Mate
Puzzle 6:
1 Nf6+_ Kh6
2 Bf8++ Mate
Puzzle 7:
1 _ Bh3+
2 Kg1_ Qf3
3 Qe2/Any other move_ Qg2++ Mate
Puzzle 8:
1 Qf8+_ Bxf8
2 Nf6+_ Kh8
3 Rxh7++ Mate
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<PGeon> Very nice puzzles - thanks for posting them. 
The pattern in #8 with the Rook & Knight mating in the corner is called an Arabian Mate.
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