Puzzle 1: Red to move and win
Solution

Red is still in possession of an advisor and in contrary to his opponent he has a pawn which is not a veteran. Still, Black would have good drawing chances if his pieces could occupy the central file, e.g. by 1. ... C6.5 and 2. ... H4+5. On top of that, Red's pawn is under attack. Nevertheless, Red can achieve a winning position with some tactical tricks.

1. C-.4      
1 point for this surprising sacrifice. Red sets a trap for the black cannon.
1. . . . C6+6
  1. . . . H4+5
2. C4+6 K6.5
    2. . . . H5-6
3. C3.4
 

1. . . . H4+5
2. C4+6 K6.5
3. C4.2 K5-1
4. C2-6 K5.4
5. E1-3 H5+6
6. C2.6
The pair of cannons will win against the lonely horse.
1 point (Answer5)

1. . . . H4-5
2. C4+6 K6-1
   

After 2. . . . H5+6 3.C3.4
Black will lose the horse.
  3. C4.2 K6-1
4. C2-6 K6.5
5. E1-3 K5.4
6. C2.6
And again the horse is without chances against two cannons.
1 point (Answer6)
2. C3.4 H4+6
Black's horse is pinned and the cannon will be imprisoned by Red's next move. Furthermore Red's king controls the central file, Black has almost no room for action.
3. E1-3
1 point
3. . . . C6.5
  3. . . . C6-2
Now neither of Black's pieces can leave the 6th file!
4. E3+1 C6-1
5. C4+1 C6-1
6. C4+1 P4.3
7. E9-7 stalemate
1 point (Answer4)
4. P5.4
1 point, Red must not play 4.C4+4 C5-8!
4. . . . C5.6
  4. . . . K6-1
5. C4+4 K6-1
    5. . . . C5.6
6. C4-5 mate
  6. C4.2 C5.6
7. C2-4
Threatening C2.4 checkmate
7. . . . C6-1
8. K5.4
With easy win, 1 point (Answer3)
5. P4.3 P4.3
  5. . . . C6.5
6. C4+4 followed by C4.2 and C2-4
6. K5-1 C6-2
  6. . . . P3.4
7. K5.4 K6.5
8. C4+4
1 point, (Answer2) Red can easily win this endgame, e.g. by capturing Black's last.

6. . . . P3.2 7.K5.4 is as well hopeless for Black
7. E9-7 C6-1
8. C4+1 C6-1
9. C4+1 stalemate
1 point for the last moves of the main line (Answer1)
Puzzle 2: Red to move and win
Solution

Red's mating attack is straight forward, both horses and the rook show perfect team-work.
R7+3      
1 point
1. . . . A5-4
  1. . . . E1-3
2. H8+7 mate
2. H8+6 K5+1
3. H6-4 K5.6
  3. . . . K5+1
4. R7-2 mate

3. . . . K5-1
4. R7.6 mate
4. H4+2
1 point
4. . . . K6.5
  4. . . . K6+1
5. R7-2 mate
5. H9+7 K5+1
  5. . . . K5-1
6. R7.6 mate
6. H7+6
1 point
6. . . . K5-1
  6. . . . K5.6
7. R7-2 mate
7. H6-7 K5+1
8. R7.5
1 point
8. . . . K5.6
  8. . . . A6+5
9. R5-1 K5.6
10.R5.4 K6.5
11.H7+6
1 point (Answer2)
9. R5.4 K6.5
10.H7+6 K5-1
11.H2-4 mate
1 point for end of the main line (answer1)
Puzzle 3: Red to move and checkmate
Solution

Both parties have a strong attack, but both have as well weakened their defence. Black's main threat is 1. ... R9.6 followed by 2. ... C9+2 checkmate. Red has no running mate at hand, but his surprising first move sets up fatal threats.

1. H2+4      
2 points for this key move. At first sight this move looks paradox. The following lines will reveal why it is important that this horse can potentially control the field d8. In contrary to the solutions I gave in the past (and I will probably give in the future), I want to treat the different answer moves of Black separetely. These answers are: A) 1. ... R9.6, B)1. ... H3-1, C) 1. ... C9-6 D) 1. ... A5-6

A) 1. ... R9.6
2. R4.5 C5-5
  2. ... A4+5
3. C9+6 A5-4
    3. ... E3+1
4. C8+3 mate
 

4. R6+3 K5+1
5. R6-1 mate
Answer2

2. ... K5+1
3. R6+2 K5-1
4. R6+1 K5.4
    4. ... K5+1
5. R6-1 K5-1
6. C9+6 E3+1
7. C8+3 mate
Answer4
  5. C9+6 E3+1
6. C8+3 mate
1 point (Answer3)

2. ... K5.6
3. R6+3 mate
3. R6+3 K5.4
4. C9+6 E3+1
5. C8+3 checkmate
1 point (Answer1)
 
B) 1. ... H3-1
2. C8+3 R9.6
  2. ... C9-6
Now 3.R4.5 K5+1 4.R6+2 doesn't work because of 4. ... C9.4
3. R6+2 R9.6
    3. ... C9-1
This defence turns out to be quite tough and wasn't treated correctly in the book I took this problem from. Unfortunately the beauty of the problem is significantly reduced by this line. I hope that you still like it and I pray that this line is correct.
4. R4.5 K5.6
      4. ... C5-5
5. R6+1 mate
    5. R5.3
Threatening 6.R6.4 and 7.R3+1 mate
5. ... H7-8
      5. ... R9.6
6. R6.4 R6-7
7. R3+1 mate
Answer8
    6. R6.4 K6.5
7. R3-1
Threatening R3.5 mate
7. ... E5+7
8. R3.2
Threatening R2+2 mate
8. ... C9.7
      8. ... R9.8 9.R2-6 C9+9 10.R2-1 doesn't help.
    9. R2.3 R9-8
      9. ... C5.7
10.R3-2 C++3
11.E5-3 C7+9
Or 11. ... R9-8 12.R3.5 mate
12.R3-5 R9-8
13.R3+7 P++1
14.R3.5 mate
Answer9

9. ... C7.6 is hopeless, but it can delay the checkmate, e.g. 10.R3+2 C5.6 11.R4+1 K5+1 12.R3-1 K5+1 13.R3-3 R9-7 14.R3.5 K5.4 15.R4.6 R9.4 16.R5.6 K4.5 17.R+-1 C6-4 18.R-.5 mate
    10.R3-2
Threatening R3.5 mate
10. ... C5-4
11.R3+3 C5.8
      11. ... C5+6
12.A4+5 R9+9
13.A5-4 ...
    12.R4.5 K5.6
13.R3.4 mate
Answer7
2 points, if lines after 3. ... C9-1 are mostly correct
  4. R4.5 K5.6
5. R6+1 mate
1 point (Answer6)
3. R4.5 K5+1
  3. ... K5.6
4. R6+3 mate
4. R6+2 K5-1
5. R6+1 K5+1
6. R6-1 checkmate
1 point (Answer5)
 
C) 1. ... C9-6
2. C9+5 H7+8
Or other moves
3. R4.5 A4+5
  3. ... K5+1
4. R6+2 K5-1
5. R6+1 K5+1
    5. ... K5.4
6. C8+3 E3+1
7. C9+1
  6. C8+2 mate
1 point
4. C8+3 A5-4
  4. ... E3+1
5. C9+1 mate
5. R6+3 K5+1
6. R6-1
1 point (answer10)
 
D) 1. ... A5-6
2. R6+3 K5.4
3. C9+6 E3+1
4. C8+3 mate