Puzzle 32 solution

Here's Black's first move, Bxg2+:

White has one legal move, Kg1. Black then mates with Gh3:

Puzzle 31 solution

Here's Black's helping move, Kf7:

Here's White's reply, Gh8 mate:

Puzzle 30 solution

Here's Black's first move, Gh2+:

White has one legal move, Kf2. Black then mates with Bg3:

Puzzle 29 solution

Here's White's first move, Ge8+.

Black has one legal move, Kh7. White then mates with Gxg7:

Puzzle 28 solution

Here's Black's first move, Nxf3+:

White has two legal moves, Kh1 and Kf1. In either case, Black mates with Gh2. Here's the final position when White plays Kf1:

Puzzle 27 solution

Here's White's first move, Rxh6+.

 Black has one legal move, gxh6. White then mates with Gxh6:

Puzzle 26 solution

Here's Black's first move, Ge3+:

White has two legal moves, Kh1 and Kh2. In either case, Black mates with  Gf1. Here's the final position when White plays Kh2: