Puzzle 21 solution

Here's White's first move, Rxb8+.

Black has one legal move, Kxb8. White then mates with Ga7:

Puzzle 20 solution

Here's Black's first move, Ge1+:

White has one legal move, Kh2. Black then mates with Gf1:

Puzzle 19 solution

Here's White's first move, Gc8+.

Black has one legal move, Kf6. White then mates with Gf5:

Puzzle 18 solution

Here's Black's first move, Gxf3+:

 

White has one legal move, Gg2. Black then mates with Rxh2:

 

Puzzle 17 solution

Here's White's first move, Gd5+.

 

Black has two legal moves, Kc8 and Kb8. If White plays Kc8, Black mates with Gxa8. If White plays Kb8, Black mates with Gc6. Here's the final position in the latter case:

 

Puzzle 16 soluton

Here's Black's first move, Gf3+:

 

White has one legal move, Kf1. Black then mates with either Gh1 or Gh2. Here's the final position in the latter case:

Puzzle 15 solution

Here's White's first move, Gh5+.

Black has three legal moves: g6, Ng6, and Gf7. If Black plays g6, White mates with Gg7. If Black plays Ng6, White mates with Gxg7. If Black plays Gf7, White mates with Gxf7. Since checkmates with more of the checkmated player's pieces left on the board are more impressive, here's the first checkmate mentioned above: