I still owe you the solution to my chess problem:
I've used long notation in my solution, which will make it easier to follow I hope.
This is how the notation works: a move immediately following a move number is a move from White. The first capital indicates the piece that moves (K=king, R=rook, N=knight). For a pawn move this capital is absent. Next to follow is the square of origin. Then comes a cross or a dash, indicating whether something is taken or not. After that comes the destination square. Optional extra's are a plus, indicating check, and '=Q', which means a pawn promoting to queen. Finally, an exclamation mark indicates a good move and a question mark a bad move.
1.Rh7-c7The most natural move and also the best; 1.Rh7xa7 gets White nowhere after 1...Rc8xc5+ 2.Kc1-d2 Rc5-b5, e.g. 3.b6-b7 Rb5-b6 4.Ra7-a8 Nd8xb7 5.Ra8-b8 Rb6xa6
1.b6-b7 Rc8xc5+ (check!) 2.Kc1-d2 Rb7-b5 is also a draw.
1...Rc8-b81...Rc8xc7 2.b6xc7 is followed by 3.c7-c8=Q with an easy win.
After 1...Rc8-a8, White can pick up the pawn: 2.Rc7xa7 and now:
a) 2...Ra8xa7 3.b6xa7 and the pawn promotes.
b) 2...Ra8-b8 3.b6-b7 followed by 4.Ra7-a8 with an easy win, e.g. 3...Kb3-c4 4.Ra7-a8 Nd8-c6 5.Ra8xb8 Nc6xb8 6.a6-a7
c) 2...Ra8-c8 3.Ra7-c7 (back again!) and the pawns become unstoppable: 3...Rc8-b8 4.b6-b7 followed by 5.a6-a7 etcetera.
2.Rc7-b7!The greedy 2.Rc7xa7 is insufficient. This is shown in the following dull line:
2.Rc7xa7 Kb3-c4 3.Ra7-c7 (otherwise Kc4xc5 on the next move) 3...Kc4-b5 4.a6-a7 (otherwise Kb5xa6) 4...Rb8-a8 5.Kc1-d2 (the king must try and help; 5.b6-b7 Nd8xb7 6.Rc7xb7+ Kb5xc5 does not work) 5...Nd8-c6 and White cannot make progress, for instance 6.b6-b7 Ra8xa7 7.b7-b8=Q Nc6xb8 8.Rc7xa7 Kb5xc5 leaves an unwinnable K+R vs K+N endgame.
The idea 2.b6-b7 and 3.Rc7-c8 also does not work: 2.b6-b7 Kb3-a4 3.Rc7-c8 Nd8xb7! 4.Rc8xb8 Nb7xc5 and the a-pawn will fall as well, again leaving K+R vs K+N.
2...Nd8xb7The most challenging try. Other options leave White an easy win:
a) 2...Rb8xb7 3.a6xb7 Nd8xb7 4.b6xa7 or 3...Nd8-c6 4.b6xa7
b) 2...Rb8-a8 3.Rb7xa7 tranposes to the line 1...Rc8-a8 2.Rc7xa7 above.
c) 2...Rb8-c8 3.b6xa7+ (check!) 3...Kb3-a4 4.Rb7-b8 and a7-a8=Q is unstoppable.
3.b6xa7The point is that the rook must move and then 4.a6xb7 gives White two unstoppable pawns. But Black has a little trick...
3...Rb8-h8!Now 4.a6xb7 is met by 4...Kb3-c3! threatening 5...Rh8-h1 mate. Neither pawn promotion prevents this and the king cannot escape:
a) 5.Kc1-d1 Kc3-d3 6.Kd1-e1 Kd3-e3 (it's not a perpetual check, but a perpetual mate threat!) 7.Ke1-f1 Ke3-f3 8.Kf1-g1; now 8...Kf3-g3 does not work, but Black has 8...Rh8-g8+! 9.Kg1-h2 Rg8-h8+ 10.Kh2-g1 Rh8-g8+ 11.Kg1-f1 Rg8-h8! with repetition.
b) 5.Kc1-b1 Rh8-h1+! (not 5...Kc3-b3? 6.b7-b8=Q+!) 6.Kb1-a2 Rh1-h2+ 7.Ka2-a3 Rh2-h1 (this is similar to what we saw in variation a) 8.Ka3-a4 Kc3-c4 9.Ka4-a5 Kc4xc5 (end of the line; 10.Ka5-a6?? would run into 10...Rh1-a1 mate) 10.Ka5-a4 Kc5-c4 with repetition.
I should note that I did not come up with this defensive trick. I saw it in a book on endgames and it formed the inspiration for my study. I came up with the following idea to combat it:
4.a7-a8=Q!!Rather amazingly, White must give up this strong pawn in order to lure the Black rook back.
As a sidenote: promotion to rook is not sufficient: 4.a7-a8=R Nb7xc5! 5.Ra8xh8 Nc5xa6 is a draw again.
4...Rh8xa8 5.a6xb7 Ra8-h8Black tries to set up the same trick again. He has no time to lose, otherwise for instance: 5...Ra8-b8 6.c5-c6 Kb3-c3 7.c6-c7 Rb8-h8 and now 8.c7-c8=Q+ with check!
6.Kc1-d2!The final finesse. 6.c5-c6? Kb3-c3 would be a draw again. 6.Kc1-d1 is not good enough because of 6...Kb3-c4 7.c5-c6 Kc4-d3!
White's pawns cannot be stopped:
6...Kb3-c4?! 7.c5-c6 Kc4-d5 8.c6-c7From a practical point of view, Black had better get rid of one of the pawns, e.g. with 6...Rh8-b8 7.c5-c6 Kb3-b4 8.c6-c7 Rb8xb7 9.c7-c8=Q, forcing White to win K+Q vs K+R, but this is theoretically speaking easy.
The main line can be seen in
this animated gifFeel free to ask any questions.
Pages: 
