Puzzle 1 from an endgame textbook

The correct move is 1.R8-1 followed by 2.R8.4

An immediate 1.R8.4 is insufficient, Black can hold in
this line:
1.R8.4? R5-2 2.R4-1 (or 2.P7+1 K4.5 3.R4.6 R5+4 4.P7.6 K5.6
5.R6.2 R5-1 draw, Answer 1) A6-5 3.P7+1 (or Black can capture 
the pawn) 3. ... K4+1! (Now Black is threatening to exchange 
the rooks with 4. ... R5.6) 4.R4.2 R5+4 5.R2-1 R5-4 6.R2-3 R5+4 
7.R2.6 K4.5 8.R6.4 R5-2 (Answer 2) draw. Red can't make 
any progress because of Black's threat R5.6.

After 1.R8-1! K4-1 2.R8.4 Black has no sufficient defense:

a) 2. ... R5-2 3.P7+1 A6-5 (or 3. ... K4.5 4.P7.6 R5+6
5.K4-1 R5-6 6.R4.2 K5.6 7.P6.5) 4.R4.3 A5-6 5.P7.6 K4.5 
6.R3.4 A6+5 7.P6.5 R5-1 8.R4+1 checkmate, Answer 3

b) 2. ...  R5.6 3.K4.5 R6+1 4.R4+1 K4+1 5.P7+1 K4+1
6.R4.6 checkmate, Answer 4

c) 2. ... A6-5 3.P7+1 R5+1 4.R4.3 as in a)
     

Puzzle 2

The better move is 1.R5+3. I found this position in the journal
Xiangqi Tiandi, Nr.5 from year 2000, on page 109. An old game
from 1957 is discussed and in a variation not played in the
actual game the authors give 1.R5+3 with two question marks.
However, I don't agree with this assessment.

1.R5+3 is threatening a discovered check, but Red has to
choose the right continuation after 1.R5+3 H4+3.

a) 2.R5.7? does not work. Black will win after
2. ... C7.5! 3.R2.3 (3.R7-2 H3+4 checkmate) R6-6 4.R3.4 K5.6
and Black has still no good defence against H3+4 (Answer 1)
b) 2.R2.3 is not as bad, but still problematic for Red:
2. ... R6-6 3.R5+1 K5+1 4.R3.4 H3+1 (Answer 2) and Black's 
chances are better although the king is lacking a safe position.
c) 2.R5.3! is the winning move:
2. ... A5-6 (the alternatives loose even faster) 3.R2-1! 
(Red is planning 4.R3+1 and 5.R3.5 checkmate) 3. ... R3.6
4.R3.5 (but not 4.R3+1 H3+4!) A6+5 5.R5+1 K5.6 6.R5.6
(with threats 7.R6+1 or 7.C5.4) 6. ... R++3 7.A5-4 R6+5
8.K5+1 R6-1 9.K5-1 C7.5 10.C5.4 (Answer 3) and Black's 
compensation is insufficient.
If Black does not play 1. ... H4+3 Red's advantage is obvious, e.g.:
A) 1.R5+3 R3+1 2.R5.3 A5-6 3.R3-2 (Answer 4) and Red has material 
advantage and a strong attack.
B) 1.R5+3 R6-6 2.R5.7
C) 1.R5+3 H4-6 2.R5.4 (R5.7 also wins) A5+6 3.H7+5

Red's alternative for the first move, 1.R5+1, is playable, Red will
also preserve some advantage after e.g. 1.R5+1 R3.5 2.H7+5 R6.5
3.H5+3 A5-6 4.H3+4 A4+5 5.R2.3 C7.5 6.C5+3 H4+3 (Answer 5) but Black's
drawing chances are much better than in the line after 1.R5+3
     

Puzzle 3 from a game played in 1982

I'm afraid, there is no good move for Black in this position.
When I chose it for the contest I thought that 1. ... E5-7
is clearly superior because 1. ... K6+1, as played in the
actual game, yields a clear win for Red:

1. ... K6+1 2.A4+5 R1.2 3.C5.2 R2+6 4.C3+1 K6+1 5.R2-1 R2.6
(threatening checkmate) 6.E7+5
and Red has to exchange a rook for a cannon to avoid
a fast checkmate:
6. ... R5+1 7.C2+5 R6.8 8.C3-1 R8-4 9.R2-1 (Answer 1) and
Red will win, although there may be some technical
problems.

Thus, the idea of 1. ... E5-7 could be to lure Red's rook
from the important second file. Indeed, after 1. ... E5-7
2.R2.3 K4+1 the original plan 3.A4+5 followed by C5.2 is
not so promising, as Red can play R5.8 in many lines.

Nevertheless, Black seems to be lost after 1. ... E5-7
as well. Red can change the plan and exploit the weakness
of Black's defence (an elephant is missing!) by 2.R2.3
K6+1 3.C3.7. I still believe that this position is a bit
more complicated than the position in Answer 1. But
Red's advantage is overwhelming, see some lines as examples:
a) 3.C3.7 R5-2 4.A4+5 R1.2 5.C7+1 A5+6 6.C5.4 K6.5 7.R3.6 R2+7
8.E7+5 R2-1 9.R6.7 R2.9 10.C7.9 R9+3 11.C4-2 R9-1 12.R7-2 (Answer 2)
b) 3.C3.7 R1+2 4.C7+1 A5-6 5.R3-1 K6+1 6.R3-2 K6-1 (6. ... R5.6
7.R3+1 K6-1 8.C5+6 checkmate) 7.R3.1 (Answer 3)
c) 3.C3.7 R1+1 4.R3-3 R1.3 5.C7.4 R5.6 6.C4-1 (Answer 4)
I'm very sorry for having chosen such an unsuitable position,
each participant will get a point for this position regardless
of his answer.