Puzzle 1 from a free game seen in Toronto Chinatown
The correct move is 1. R7.6
It seems that Red can win after
1.R2+5? A5-6 2.P3.4 A4+5? 3.P4.5 K5+1 4.R2-1 K5-1 5.R2.6 R4-2
6.R7.6 yielding a textbook endgame which is easily won for Red.
However, Black has a surprising defense:
1.R2+5? A5-6 2.P3.4 C4.5!
Red has to capture this cannon, because of 3.K5.4?? R4.6 checkmate
After 3.P4.5 A4+5 (Answer1) we see an endgame 2 rooks vs. rook and complete
defense (i.e. rook, 2 elephants and 2 advisors) This is a theoretical
draw if Black manages to achieve the correct setup for his pieces,
that is, rook on the open file and defensive pieces in the center and
on the baseline. At the moment Black has not reached this ideal
defensive setup and Red can try to hinder Black from reaching the
best position for his pieces. There are a couple of lines where
Black has to be very careful but I don't see a forced win for Red.
With 1.R7.6! Red can secure the win:
1. ... R4-2 (other moves can't help because two rooks and one pawn
always win against one rook and complete defense)
2.P3.4 A5-6 (only defense against the threat 3.R2+5 A5-6 4.R2.4 checkmate)
3.P4+1 K5.6 (or 3. ... K5+1 R2+4 checkmate)
4.R2+5 K6+1 5.R2-1 K6-1 6.R2.6 (Answer2) with a simple technical win