Puzzle 1: Red to move and win
Solution

Red is only one pawn up and the pawn on Red’s 6th file is under attack. Red can protect this pawn by 1.R5.6, this is however a quite passive move and Black can probably defend the position. Instead, Red can abandon the pawn and attack immediately.
1. R5.2      
2 points
1. ... R2.4
  If Black does not capture the pawn, he is still without sufficient defence:
1. ... R2+2
2. R2+5 E5-7
3. R2.3 K6+1
4. P6+1 R2.6
    4. ... A5-4
5. R3-1 K6-1
6. P4+1 K6.5
7. P4+1 threatens 8. R3+1 checkmate
7. ... R2.7 can only delay the mate
8. R3-2 A4+5
9. R3+3 A5-6
10. R3.4 mate
1 point (answer 5)
  5. P6.5 A5+4
6. R3-1 mate
1 point (answer 4)

1. ... R2+3
Black wants to swing the rook to the other side and hopes for 2.R2+5 K6+1 3.P6+1? R2.7
2. R2+5 K6+1
    2. ... E5-7 doesn’t change the position.
  3. R2.3
1 point. The move order is essential in this position, after 3. P4.3? R2.7 4.R2.3 A5+4 5.P3+1 A6-5 Black’s rook is protected and Red can’t win with 6.P3.4 as in the line after 1. ... R2+6 (see below). If Black plays 1. ... R2+4 or 1. ... R2+5, Red can choose 3. P4.3 to achieve a faster win.
3. ... R2.8
4. P4.3 A5+4
    Otherwise Red wins easily with 5.R3+1 and 6.R3+1.
  5. P3+1 A6-5
    5. ... R8-3
6. P3+1 R8.7
7. R3-1
  6. R3-1 K6-1
7. P6.5 A4-5
    7. ... R8.6
8. P5.4 R6-3
      8. ... K6.5
9. R3+1 mate
    9. R3+1 mate
  8. R3.5
And Black has no defence against the combined attack of Rook and pawn, e.g. :
8. ... R8.6
9. P3+1 R6+5
10. K5+1 R6-3
11. R5.6 K6.5
    11. ... P1.2
12. R3.4 R6-5
13. R6+1 mate
  12. P3.4 P1.2
13. P4.5 K5.6
14. R6+1 mate
1 point (answer 6)

1. ... R2+6
2. R2+5 K6+1
Now Red can win as in the variation after 1. ... R2+3 but he has also a faster win:
3. P4.3 R2.5
4. A6+5 R5.7
5. R2.3 A5+4
6. P3+1 A6-5
7. P3.4 A5+6
8. R3-7
1 point (answer 7)
2. P4+1 E5-7
  2. ... A5+6
3. R2+5 K6+1
4. R2-1 K6-1
5. R2.6
1 point (answer 2)

2. ... K6.5
3. P4+1 A5-6
    3. ... K5.4
4. R2+5 A5-6
5. R2.4

3. ... R4+8
4. K5.6
  4. P4+1 K5.4
    4. ... K5.6
5. R2+5 K6+1
6. R2-1 K6-1
7. R2.6

4. ... K5+1
5. R2+4 mate
  5. P4.5 K4.5
6. R2+5 K5+1
7. R2-1 K5-1
8. R2.6
1 point (answer 3)
3. R2+5 K6.5
  3. ... A5+6
4. R2.3 K6+1
5. R3-1 K6-1
6. R3.6

3. ... R4+8 4.K5.6 is hopeless.
4. E5+7
Opening the central file and threatening 5.R2.3 mate
4. ... K5.4
  4. ... R4+8 5.K5.6 gives a hopeless endgame, all other moves will be refuted by 5.R2.3 checkmate.
5. R2.3 A5-6
6. R3.4 mate
1 point for the last moves of the main line (answer1)
Puzzle 2: Red to move and checkmate
Solution

Thanks to Udo Marks who composed this problem and allowed me to use it for this contest. Udo is a chess problem composer well known amongst friends of western chess problems. He has also created a lot of Shogi and Xiangqi problems. You can see examples of his work on his web page http://www.chess-problem.com/
The author originally asked for “Red to move and checkmate in 10”
It is interesting to watch how both red horses co-operate with the cannons to achieve a running mate:

1. H+-5 C+.5      
  1. ... P6.5
2. H5+6 K5.4
3. H6+8 mate
1 point (answer 6)

1. ... P4.5
2. H5+6 mate
2. H5+4 C5.6
3. H7+6 K5+1
  3. ... K5.4
4. H6+4 K4.5
5. H—-5 P6.5
    5. ... P4.5
6. H5+6 mate
  6. H5+6 mate
1 point (answer 5)
4. H6-5 P6.5
  4. ... P4.5 can be treated in the same way as 4. ... P6.5, Black has fewer alternatives.
5. H4-6 K5.4
  5 ... K5-1
6. H5+6 K5.4
7. H++4 K4+1
8. H6+4
1 point (answer 4)

5. ... K5+1
6. H5+3 K5.4
7. H6+8 P4+1
    7. ... P4.3
8. H3+4 mate
  8. H3+4 mate
1 point (answer 3)
6. H5+7 K4-1
  6. ... K4+1
7. H6+4 P4+1
    7. ... P4.3
8. H4-5 mate
  8. H4-5 mate
1 point (answer 2)
7. H7+8 C+.3
  7. ... K4+1
8. H6+8 mate
8. H6+7 P4+1
  8. ... P4.3
9. H7-5 K4+1
    9. ... K4.5
10.R5+3 mate
  10.H5+4 mate
9. H7-5 K4.5
  9. ... K4+1
10.H5+4 mate
10. H5+3 mate
1 point for the main line (answer1).
Puzzle 3: Red to move and checkmate
Solution

Blacks king lacks sufficient protection, the well co-ordinated red pieces don’t give Black’s king a break for rest and achieve a running mate:
1. P3.4      
1 point
1. ... K5-1
  1. ... K5.4
2. C3.6 A4-5
3. R3.6 A5+4
    3. ... C3.4
4. R6+1 K4+1
5. H7+6 mate
1 point
  4. R6+1 K4+1
5. H7+6 K4.5
6. H6+7 K5.4
7. P7.6 mate
2 points (answer 4)

1. ... K5+1
2. R3+1 mate
2. R3.5 K5.4
  2. ... A6+5
3. P4+1 K5.4
4. C3.6 mate
1 point (answer 3)

2. ... A4-5
3. C3+7 mate

2. ... E3+5
3. C3+7 A6+5
4. P4+1 mate
1 point
3. R5+3
1 point
3. ... K4+1
  3. ... K4.5
4. C3+7 A6+5
5. P4+1 mate
1 point (answer 2)
4. C3.6 A4-5
5. H7+6 C3.4
  5. ... A5+4
6. H4+5 mate
6. H6+5 C4.5
7. P7.6 A5+4
8. P4.5 A6+5
9. P6.5
1 point for the continuation of the main line (Answer1).