Puzzle 1: Red to move and win
Solution

Red wants to utilise mate threats to transform the position into a won technical endgame. An exchange of the cannon against the black rook would lead to the easily won endgame rook vs. 2 advisers. Red will also be happy if he achieves the endgame rook and cannon vs. rook as long as he controls the central file. Thus, the main goal for Red is to capture both of Black’s advisers while retaining the control over the central file.

1. R5-4
     
,With this key move (2 points) Red decisively restricts the mobility of the black rook. The black rook can’t idle behind the red cannon because this would result in a forbidden perpetual check. Solitary checks would not change the nature of the position and are therefore not mentioned later on.
1. . . . R9.8
  1. . . . K5.4
2. R5.6 K4.5
    2. . . . A5+4 yields similar positions as in the main line, since it is insignifi­cant whether black rook and red cannon are on the first, second or third file.
 

3. K4.5 R9.8
4. C1.2 R8.7
5. C2.3
Black is in Zugzwang. If the black rook moves sidewards, Red will play C3+7 mate. The only alternative 5.R7-1 results in the hopeless endgame 2 advisers vs. rook. 2 points for this side line (Answer 4).

2. C1.2 R8.7
  2. . . . K5.4 yields positions similar to the main line or the side line after 1. ... K5.4
3. C2.3 K5.4
4. R5.6 A5+4
  4. ... K4.5 5. K4.5 yields the final position of Answer4.

5. R6+5 K4.5
6. R6.5 K5.4

  6. . . . A6+5
7. C1.5
    7. ... R9-7
8. R5.3 K5.4
9. R7+1
  7. ... R7.5
8. R5-1 K5.4
    8. . . . R5.1
9. C5+6 R1-7
10.K4.5
  9.R5+2 R5.1
10.K4.5
Red controls the central file in the endgame rook and cannon vs. rook and has achieved a book win. 2 points for this line (Answer3).
7. K4.5 K4+1
 
  7. . . . A6+5
8. C3.5 A5-6
    8. . . . A5+4 9. R5.6 K4.5 10. R6.5 or
8. ... A5+6 R5.4 along with R4.5 likewise yield the desired endgame for Red.
  9. C5.6 A6+5
10.R5+1
2 points for this line (Answer2)

8. R5-1 R7.4
9. C3+7 R4-2
10.R5+3
With the threat R5.6 checkmate.
11. ... A6+5
11.R5-1 Red has gained control over the central file, therefore the endgame rook and cannon vs. rook is a book win. 2 points for the correct continuation of the main line (Answer 1).

Puzzle 2: Red to move and checkmate
Solution

Red does not have enough time to strengthen his attack with quiet moves like 1.H4+6, since Black threatens 1. ... H6+7 along with 2. ... C9+4 checkmate. Red can parry the mate threat with 1.R8+3 A5-4 2.R8-8. This position would be better for Red but he does not have an immediate kill, since Black can temporarily lock out the red rook from the attack with 2.... A4+5 3.H4+6 S3.2 (3.... S3.2 4.R8.7 S2.3 5.R7.8 S3.2 is a legal repetition of moves because the attacking piece is a soldier).
However, Red can avoid these positions and achieve a running mate:

1. H9+8      
Red can as well start with 1.R8+3 A5-4 2.R8-1 A4+5 3.H9+8. In most variations positions of the main line will follow (just one move later), only after Black’s defence 3. ... A5-4 4.H8-6 K5+1 Red needs a different plan, he can win with 5.H6-8 C4-1 6.R8.6 K5+1 7.H4+3 K5.6 8.R6.4 checkmate.
1. ... A5-4
  1. . . . C4-2
2. H8-6 C4+9
3. H6+8 A5-4
    3. . . . C4-9
4. H8-6 matt
Amusing swing of the red horse

  4. H8-7 A4+5
5. R8+3 A5-4
6. R8.6 mate
1 point for this side line (Answer3)
2. H8-6 K5+1  
  2. . . . A4+5
3. R8+3 A5-4
4. R8.6 K5+1
    4. ... K5.4
5. H6+8 mate
  5. C9-1 K5+1
6. H4+3 mate
1 point for this side line (Answer2)
3. C9-1
2 points for the key move of the main line
3. ... K5-1
  3. . . . K5.4
4. R8+2 mate

3. . . . K5+1
4. R8.5 mate
4. H6-4 K5+1
5. R8+2 C4-1
  5. ... K5+1
6. H-+3 K5.6
7. R8.4 mate
6. R8.6 K5+1
7. H-+3 K5.6
8. R6.4 mate
1 point for the correct continuation of the main line (Answer1)
Puzzle 3: Red to move and checkmate)
Solution

Since the various mate threats of the black soldiers cannot be parried there is no defensive hope for Red. He has to find a running mate.

1. R2+9 E5-7      

1. . . . A5-6
2. H3+4 K5+1
3. R2-1 mate or R1+3 mate, 1 point
   
2. C7+2
This key move (3 points) is difficult to find. The idea behind it will become obvious after move 8 of the main line. Red removes the cannon to avoid that it would stand in the way of the red horse later on.
2. . . . E1-3
3. R2.3 A5-6
4. H3+4 K5+1
5. H4-6 K5.4
  5. . . . K5+1 6. R3-2 mate
5. . . . K5.6 6. R3-1 mate
5. . . . K5-1 6. H6+7 K5+1 7.R3-1 mate
6. R3-1 A4+5
 
  6. . . . K4+1
7. R1+2 E3+5
8. R1.5 K4.5
9. R3-1 mate (1 point, Answer3)

6. ... A6+5 will likewise be answered by 7. R3.5.
7. R3.5 A6+5
 
  7. . . . K4-1
8. R5+1 K4.5
    8. . . . K4+1
9. H6+4 K4+1
10.R1.6 mate
  9. H6+7 K5+1
    9. K5.4 R1.6 mate
  10.R1+3 mate (2 points, Answer 4)
8. H6+8
Without move 2 this horse would not give a check!
8. ... K4+1
 

8. . . . K4-1
9. R1+4 A5-6
10.R1.4 mate

9. R1.6 K4.5
10.R6.5 K5.6
 
 

10. . .. K5.4
11.H8+7 K4-1
12.R5.6 A5+4
13.R6+2 mate (1 point, Answer2)

11.H8-6 K6-1
12.R5.4 A5+6
13.R4+2 mate
2 points for the correct continuation of the main line (Answer1)