Puzzle 1 from an endgame textbook

The correct move is 1.C4-2

Red is in posession of the central file. If he can win
Black's pawn without losing control of the central file
he has a technically won endgame. In some positions he
might also try the typical method in this endgame 
(see line B after 1.K5+1?) and try to win without capturing 
the pawn. However, the pawn is already close to Red's palace 
and Red has to be precise to achieve the win.

1.K5+1? allows 1. ... R8.4 Now Red cant try two plans,
but Black can defend the position successfully in both cases:
A) Red tries to capture Black's pawn
1.K5+1 R8.4 2.R5-1 R4-1 3.K5-1 P2+1 4.C4-1 (threatening C4.8)
4. ... R4-3 5.K5+1 P2+1 6.R5+3 (6.C4+7 R4+3 7.K5-1 P2.3 will
also yield a draw) 6. ... P2.3 7.C4+4 (planning 8.R5+4 9.C4.9
10.C9+4 11.C9.6 but Black won't allow that) 7. ... R4+3
8.K5+1 (8.K5-1 P3.4 9.K5.4 R4.8 and Red has lost the central
file) 8. ... R4+1 9.C4-4 (9.K5-1 R4-1 10.K5+1 is a legal
repetition of moves under Asian rules) 9.R4.5 C4.5 10.R5.4
and Red can't make any progress, Answer 1.
B) Red tries to adopt the typical plan in the endgame rook
ans cannon vs. rook without attacking Black's pawn
1.K5+1 R8.4 2.C4+1 (If Black idles in this position Red will
win, see e.g. 2. ... R4-4 3.R5+6 K4+1 4.C4.9 R4.1
5.R5-4 R1.4 6.C9+6 P2.3 7.R5+3 K4+1/K4-1 8.R5+1 K4-1/K4+1 
9.C9.6 R4.7 10.R5-4 Answer 2) 2. ... P2.3 3.R5+6 K4+1
4.C4.9 P3+1 5.C9+6 P3.4 6.K5.4 (Red has lost control of the central
file and won't be able to regain it) 6. ... R4.1 7.C9.8 (7.K4+1 R1-2
.K4-1 R1+1) 7. ... R1-1 8.R5-3 P4.5 9.R5-5 R1.5 10.K4.5 draw, Answer 3 

After 1.C4-2 Black has to play 1. ... R8-8 to avoid the immediate 
checkmate 2.R5.6. In this line Red can win with exact play:

1.C4-2 R8-8 2.R5+6 K4+1 3.R5-7 R8+1 (3. ... P2.3 4.C4+2 and
Red can capture Black's pawn without losing control of the
central file) 4.C4+1! with these lines:
a) 4. ... R8.4 5.R5.8 R4.5 (or Red will play R8.5) 6.C4.5 R5.8
(6. ... R5.4 7.C5+1 is similiar) 7.C5+1 R8+6 8.R8+6 K4-1 9.R8.5
and Red wins, Answer 4
b) 4. ... R8+7 5.K5+1 R8-7 (5. ... R8.4 6.R5.8) 6.C4+1 P2+1
7.C4-1 P2+1 8.K5-1 R8.4 9.C4-1 R4.2 10.R5+1 P2.1 11.C4.9 R2+7
12.K5+1 and Red wins, Answer 5

Puzzle 2 from a Chinese text book

1. C-+1 is the correct move.
The difference between C-+1 and C-+2 becomes obvious in the lines
after 1. ... R9+1. Red has a clear win after
1.C-+1 R9+1 2.C+.8 C4.2 3.H3-5 E5+3 4.C8-1! because of the threat
5.C8.5 (see e.g. 4. ... H7+5 5.C5+3 A5+6 6.C8.5 Answer 1), in the 
identical line after 1.C-+2 it is not possible for Red to play 5.C8.5, 
therefore Black's chances to organize a successful defence are much better.
1. C-+2 R9+1 2.C+.8 C4.2 3.H3-5 E5+3 4.H5+6 A5+4 5.C8+1 is too slow because
of 5. ... H7+6 and Black's king can escape (Answer 2)

Black has no better defence than 1. ... R9+1 as Red's threats 2.R4+6 
or 2.R4+5 are very dangerous:
1. C-+1 P9+1 2.R4+6 H7-6 3.H3+4 P3.4 4.C-+4 checkmate, Answer 3
1. C-+1 R9+2 2.R4+5 C4-1 (2. ... H7+5 3.C+-3 C8-2 4.H3+1) 3.H3+5 C4.6 
4.C+.7 H7+6 5.K4.5 H6+5 6.C7+4 checkmate, Answer 4 
     

Puzzle 3 from the game LIU Xing - LIN HongMin played in the
WangWei Tournament 1994. This game was covered in the XiangQi
Review Volume V, Number 2.

1. ... E7+5 is the better move

Red has sacrificed a piece and has a dangerous attack. An important
plan for Red is a double cannon check on his 6th file (e.g. C5.6
followed by C6+1 and C3.6) For this reason, Black may have planned
to evacuate his king by 2. ... A5-4 followed by 3. ... K4.5 and
4. ... K5-1. Therefore, he has chosen 1. ... H6-5 to prevent
2. C5.6 A5-4 3.R7-1. However, this plan didn't work in the
game and Black's horses were very passive:

1. ... H6-5? 2.C5.8! (Now Black can not follow his original
plan, since 2. ... A5-4 3.C8+6 is attacking Black's rook and
threatening 4.R7-1 K4+1 5.C8-1 checkmate. Thus, Black has no
good defence against Red's plan to transfer the cannons to
the 6th file) 2. ... R8-1 (other moves are not better)
3.C8-1 (this cannon has still the option of C8+7 but it's
also preparing for C8.6) P5+1 (3. ... A5-4 4.C8+7 yields
positions similiar to the actual game, 3. ... H3-4 4.C3.6 A5+6
5.C8+7 is also good for Red) 4.C3.6 A5-4 5.C8+7 K4.5 6.R7-1 K5-1
7.C8+1 A4+5 8.R7+1 H3-4 (After 8. ... A5-4 9.R7-2 Red has his piece
back and a much better position) 9.C8.9 C8.7 10.E7+5 H5+6 11.C6+6
and Black resigned (Answer 1).

After 1. ... E7+5 Black's chances are much better. The active horse
makes it much more difficult for Red to pursue his plans. See e.g.:

1. ... E7+5 2.C5.8? H6+5 3.C3.5 H5-3 4.C8-1 C8.7 Answer 2
1. ... E7+5 2.C5.6 H6+5 3.C3.5 H5-3 4.C6-1 H++2 5.C5.7 R8.7 Answer 3