Puzzle 1 from an endgame textbook

The correct move is 1. ... C8-4

After 1. ... C8+5?? Red can force the win:
1. ... C8+5 2. K6.5 C8.6 (2. ... C8-9 comes too late:
3.C+.4 C8.6 4.C5.4 checkmate; 2. ... C8-7 can only
delay the checkmate: 3.C+.4 C8.5 4.C5+7 K6.5 5.C4+3 K5-1
6.C5+1 K5.4 7.C5.7 K4+1 8.C7-3 K4-1 9.C7.6 K4+1 10.C4.6)
3.C+.4 K6-1 4.C5.6 C6.5 5.C6+3 C5.6 6.C6.4 checkmate, Answer 1

With 1. ... C8-4 Black can hold the position:
1. ... C8-4 2.K6.5 (or 2.C+.4 K6.5) C8.6 and Black can idle
with the king (K6+1 K6-1 K6+1 ...) The only way to prevent
Black from idling with the king is 3.C+.1 K6+1 4.C1+7 K6-1
5.C5.2 K6+1 6.C2+8 but now Black can idle with the cannon:
6. ... C6.5 7.C2-3 C5.6 draw, Answer 2

Puzzle 2 from a Chinese master game played in 1990

The better move is 1. ... H4+5

After 1. ... C5+4? 2. P7+1 Black will lose a piece because of
the threats 3. P7.6 and 3.H8+7, see e.g.:
A) 1. ... C5+4 2.P7+1 K5.6 3.P7.6 (better than 3.P7+1 H4+3 exchanging
a piece) H4+2 4.P6.7 and Black's horse is lost, Answer 1
B) 1. ... C5+4 2.P7+1 P5+1 3.H8+7 K5.6 4.H7-6 E1+3 5.H6+4, Answer 2

1. ... H4+5 is much better, after 1. ... H4+5 2.H8+6 K5.6 Red has still
a slight advantage but a draw is the most likely outcome.

Puzzle 3 from a Chinese master game played in 1993.

1.C2+6 is the better move.

1. R6+5 is not as good because it allows the defence 1. ... R6-1
yielding an unclear position:
A) 1.R6+5 R6-1 2.P3+1 P5+1 3.R5.3 (3.R5+1 R2.7 4.C2+6 R6.7 5.C2.5 H7+5
6.R5+2 R-.5 7.R6.5 yields a drawish position, Answer 2) R6+5 4.H3+5 E7+5
5.P3+1 R2.8 6.C2.3 H5+6 7.P3+1 H6+8, Answer 1, Black has lost an
elephant but the active horse offers some compensation.
B) 1. R6+5 R6-1 2.C2.3 P5+1 3.R5+1 R2+2, Answer 3

After 1.C2+6 the position isn't totally clear either but Red's chances are
clearly better:
a) 1.C2+6 R6.8 2.C2.5 H7+5 3.R5.4 (My source suggests 3.H3+4 which is also
interesting, but I think 3.R5.4 is even stronger) 3. ... H5-7 (3. ... P5+1??
4.R4+6! K5+1 5.R6+8, Answer 4) 4.R4+5 E5-3 5.R6+5 and
Red's pieces are very active, Answer 5
b) 1.C2+6 A6+5 2.R6+5 K5.6 3.A6+5 P1+1 4.R5.6 P5+1 5.C2.5 R6-1 6.C5.7 Answer 6
c) 1.C2+6 A6+5 2.R6+5 K5.6 3.A6+5 E5-3 4.C2.5 R6-1 5.R5.6 R6.5 6.R+.5 H7+5
7.R6+3 H5-7 8.R6.7 E3+5 9.R7.9 Answer 7
d) 1.C2+6 H5-3 2.R6+6 R2-2 3.H3-5 (3.H3+5 R6-2 is quite complicated) A6+5
4.R6-1 Answer 8, Red has a pawn plus and very active pieces
e) 1.C2+6 H5-3 2.R6+6 H3-1 3.H3+5 E7+5 (3. ... A4+5 4.H5-4; 3. ... R6-2 4.R6+2)
4.R6.5 A6+5 5.R+.3 Answer 9