October Puzzle
Puzzle 1
Puzzle 1 from a game Lu Kham - Ho Vinh Hoa

The correct move is 1.H7+5

1.H7-8? was a serious mistake. Black won by 1. ... P4+1
2.H8+6 (or 2.A5-6 H7+8 3.K4+1 P6+1 checkmate, Answer 2) 
H7+8 3.K4+1 P4.5 (Answer 1) and Red has no defence against 
4. ... H8-7 checkmate.

After 1.H7+5 Black can not win, see e.g.:
1.H7+5 P6.5 2.H5-3 P5+1 (or 3. ... P5.6 4.H3+4 K5+1 5.H4-3)
3.H3-5 P4.5 (Black has no better plan, since Red's pawn
can idle with P1.2 ... P2.1 ... P1.2 ...) 4.A6-5 P5+1
5.H5-3 (Answer 3) and Black can't win.
Puzzle 2
Puzzle 2 

The better move is 1.C9+4

After 1.R7.5 R9.5 Black has the threat 2. ... C++3
3.E7+5 R5-3. If Red tries 2.R5.1 or 2.R5.9 he has
to fight to get a draw after 2. ... R5+1 3.R1.5
(but not 3.E7+5 C-+5 checkmate or 3.R1.9 R5+1 checkmate)
R5.1 4.R5-1 R1-1 (Answer 1). Likewise, Red can't expect
more than a draw after 1.R7.5 R9.5 2.A5+6 R5+1 3.A-+5 R5-1 4.C9+4 R5.1
5.R5-1 (or 5.E7+5 R1-3 6.R5-1 [6.R5.9?? C-+5 7.K5.6 C-.4 checkmate])
5. ... R1-3 (Answer 2)

1.C9+4 offers Red much better chances. Now, Black is on the
receiving end. See e.g.:
1.C9+4 R9.1 2.C9.5 A6+5 3.R7-1 C++1 4.R7.3 E7+9
5.R3.2 R1.7 6.R2-1 C++1 7.R2+2 (Answer 3) 
Puzzle 3
Puzzle 3 

The better move is 1. H3+4. Actually, it's very difficult
to profoundly analyse this complicated position. I'll give
only a few lines and hope that there won't be too many
protests. Of cause, we could try to go more into detail
with a discussion in the forum section.

1. C5+3? as seen in the actual game is premature and allows
Black to activate his pieces and launch a promising counter attack.
1.C5+3? H7+8! 2.R1.4 R9.7 3.C5+1 (3.H3-1 C2+6 4.A6+5 H+-6 or
3.H3-2? H-+6 are worse) 3. ... R7+6 4.R6.2 R7-1 5.H8+7 R1.4
6.C6+3 R4+3 7.C5-1 R4+1 (Answer 1) and Black has
a lot of active plans like C2+2 or C8.7 or H8+7. In the actual
game Red played 8.E7+5 R7+2 9.R4+4? (9.K5+1 is necessary but
Red has many problems after 9.K5+1 R7.6 10.K5.4 H8-6) 9. ... R4.5.
Black's pieces are much more active.

Red could have avoided that by playing 1.H3+4, he can take Black's
central pawn later. Again, the game is far from being over but
now Red has better chances to develop an initiative. See some 
exemplary lines:

A) 1.H3+4 H7+8 2.H4-2 C8+4 3.C5+3 C8.1 4.C6.9 R1.4
5.R6+4 K5.4 6.R1.6 C2.4 7.R6+5 (Answer 2) threatening 8.C9.6
B) 1.H3+4 H8+7 2.C5+3 C8.7 3.C6+2 R9.6 4.C6.3 R6+4 5.C3+4 C2.7 
6.E7+5 R1.2 7.H8+7 (Answer 3)