There appears to be a flaw in the solution given (on page 79) to problem IV on page 13 of Chess Life July 2011. After the solution key move 1. … Nd4!, only two White replies are considered: 2. Qa4 (leading to black mating in two), and 2. Rxd5 (leading to Black having an overwhelming material advantage).
The natural 2. Qxd5+ is not considered, but this move appears to lead to a complicated but drawish endgame, although perhaps Black has winning chances. This outcome fails to meet the challenge presented with the group of problems: “Your task is to find the fastest winning line of play, usually the forced win of a decisive amount of material.”
After 2. Qxd5+ Rxd5 3. Rxd5, 3. … Rxd1+ seems forced. After 4. Kf2, Black has a slight (not decisive) material advantage: rook, knight, and three pawns vs. rook and five pawns. All White’s pawns have structural weaknesses of isolation and doubling, and White’s king can’t move without loss of material. One Black’s pawn is isolated , and the Black knight is pinned, limited mobility of Black’s knight and rook.
Black can force/invite a simplification to a roughly even king and pawn ending, but White seems to have some winning chances. For example: 4. … Kf7 (to gain a tempo), 5. Rd6 Rd2+ 7. Ke3 Nxf3 8. Rxd2 Nxd2 9. Kxd2 Ke6 10. Kd3 Kd5 11. h4 h5 12. b3 g6, 13. b4 and White wins.
Therefore Black must avoid this simplification, and it is likely that Black must therefore give up the knight to try to win a rook and pawns vs. rook and pawns endgame. Here is an example of the difficulty of Black achieving this: 7. … Rxh2 8. Rxd4 (8. Kxd4 Rd2+ 9. Ke5 Rxd5 10. Kxe5 h5 wins) 8. … Rxb2, 9.Rd5 g6 (9. … Ke3 10. Re4+ Kd6 (10. … Kf6 Rd5 repeats) 11. Ke4 g6 12. Rd5+ Ke6 13. Re6+ , then 13. … Kd6 or Kf6 14. Rd5 Ke6 repeats) 10. f5 g5 (10. … gxf 11. Kxf draws) 11. f6 Kxf6 12. Rd6+ Kf5 13. Rxb6 h4 14. Rb8 h5 15. b6 h6 16. b7 h7 17. Rh8 draws.
After several days of analysis, I am unable to find any forced Black win. My 1941 edition of Basic Chess Endings by Reuben Fine includes no discussion of rook, knight, and pawns vs. rook and pawns. I would be very interested to see how Black can force a win in this variation. Perhaps a reader can find one, possibly with computer assistance.
I would also very much like to see the complete score of the game from which the problem is based: Samuel Reshevsky vs. Sidney Bernstein, U.S. Championship 1936. If a reader has access to a copy of New York 1936: The first modern United States chess championship by John Samuel Hilbert, and Peter P Lahde, I would much appreciate their posting this game score.