2. Qd7 For some reason, it took a long time to spot this move.
(2. Rxh8 wins eventually. This is the best I could find for a long time. Qxc7 (2. .. Qxh8 3. e8=N+ (3. Qd8 Kf7 4. Qd7 Kf6 5. e8=Q Qxe8 6. Qxe8) 3. .. Kg6 4. Qxg7+ Qxg7 5. Nxg7 Kxg7 6. f4 Kf6 (6. .. gxf3+ 7. Kxf3 Kf6 8. Kf4 a6) 7. Kf2 Ke7 8. Ke3 Kd6 9. Kd4 a6 (9. .. a5 10. Kc4) 10. Kc4 a5 11. b3) 3. e8=Q Bxh8 4. Qxh8+ Kg6 5. Qg8+ Kf6 6. Qe6+ and White should win, but it will take a long time to prove it.)
2. .. Rxh5 3. Qd8 Qxd8 4. exd8=Q+ White is winning.
Other first move alternatives for black were worse:
C. 1. … Qa8 2. Rxh8 Qxh8/Bxh8 3. Qd8 Qxd8 4. exd8=Q Q vs. B endgame.
D. 1. … Qg8 2. Qd6+ (Rxh8 same as A) Kf7 3. Rxf5+ Bf6 (Ke8 Qd8#) 4. Rxf6+ Kg7 5. Rg6+ Kf7 6. Rxg8 Rxg8 7. Qd8 Either R takes Q or Q takes R, this should be blank Q up.
I don’t have a lot of time for this problem this morning, but I would definitely think to look at e7 here since Qxe7 will lose to Rxf5 check. so black will have to find a square for his queen:
1. e7 Qb8
I don’t see any other valid defense since white is threatening Qd6+ and Qe6 mate. The other square from which to guard this threat, g8, is still bad: [1. …Qg8 2.Qd6 Kf7 3.Rf5 Bf6 4.Qf6 Ke8 5.Qd6+- surely]. Continuing:
2. Qd7! Qe5 (Rh5 3.Qe6 Kg5 4.e8Q) 3. Rh8 Qe4 (Bh8 4.e8Q) 4. Kh2! Qe7 (what else?) 5. Qe7 Ke7 6. Rh7 Kf8 7. b3 and this is an easily won ending for white.
After 1. e7 Qb8 is the toughest defense. White wins fairly easily against all the other defenses.
(1. .. Qxe7 2. Rxf5+ Kxf5 3. Qxe7 Bxb2 4. Qxb4 Be5 5. Qe7 Bd4 6. Qe6+ Kg5 7. Qe4 Bg7 8. Qf4+ Kh5 9. Qf5+ Kh6 10. Qxg4)
(1. .. Qe8 2. Qd6+ Kf7 3. Qe6#)
(1. .. Qg8 2. Qd6+ Kf7 3. Rxf5+ Ke8 (3. .. Bf6 4. Rxf6+ Kg7 (4. .. Ke8 5. Qd8#) 5. Rg6+ Kf7 (5. .. Kh7 6. Rh6+ Kg7 7. Qg6# or Qf6#) 6. Qe6+ Ke8 7. Rxg8+ Rxg8 8. d6 followed by d7#) 4. Qd8#)
(1. .. Qc8 2. Qd6+ Kf7 3. Rxh8 Bxh8 (3. .. Qxh8 4. Qe6+ Ke8 5. d6 with d7# to come.) 4. Qd8)
(1. .. Qa8 2. Qd6+ Kf7 3. Qe6+ Ke8 4. Rxh8+ Bxh8 5. Qg8+ Kxe7 6. Qxa8)
2. Qd7 For some reason, it took a long time to spot this move.
(2. Rxh8 wins eventually. This is the best I could find for a long time. Qxc7 (2. .. Qxh8 3. e8=N+ (3. Qd8 Kf7 4. Qd7 Kf6 5. e8=Q Qxe8 6. Qxe8) 3. .. Kg6 4. Qxg7+ Qxg7 5. Nxg7 Kxg7 6. f4 Kf6 (6. .. gxf3+ 7. Kxf3 Kf6 8. Kf4 a6) 7. Kf2 Ke7 8. Ke3 Kd6 9. Kd4 a6 (9. .. a5 10. Kc4) 10. Kc4 a5 11. b3) 3. e8=Q Bxh8 4. Qxh8+ Kg6 5. Qg8+ Kf6 6. Qe6+ and White should win, but it will take a long time to prove it.)
2. .. Rxh5 3. Qd8 Qxd8 4. exd8=Q+ White is winning.
1.e7 Qb8
(1…Qxe7 2.Rxf5+ Kxf5 3.Qxe7)
(1…Rxh5 2.exf8=Q+ Bxf8)
(1…Qe8 2.Qd6+ Kf7 3.Qe6#)
(1…Qf7 2.Qd6+ Qe6 3.Qxe6#)
(1…Qg8 2.Qd6+ Kf7 3.Rxf5+ Ke8 4.Qd8#)
2.Qd7 Qe5 3.Rxh8 Qe4+ 4.Kh2 Qxe7 5.Qxe7+ Kxe7 6.Rh7 Kf8 7.b3
1.e7 Qb8
(1…Qxe7 2.Rxf5+ Kxf5 3.Qxe7)
(1…Rxh5 2.exf8=Q+ Bxf8)
(1…Qe8 2.Qd6+ Kf7 3.Qe6#)
(1…Qf7 2.Qd6+ Qe6 3.Qxe6#)
(1…Qg8 2.Qd6+ Kf7 3.Rxf5+ Ke8 4.Qd8#)
2.Qd7 Qe5 3.Rxh8 Qe4+ 4.Kh2 Qxe7 5.Qxe7+ Kxe7 6.Rh7 Kf8 7.b3
1. e7!
A.
1. … Qxe7
2. Rxf5+! Kxf5
3. Qxe7 Bf8
4. Qxa7
B.
1. … Rxh5
2. exf8=Q Bxf8
3. Qxa7
Both are winning endgames, Q+5p vs. R+B+3p.
Other first move alternatives for black were worse:
C.
1. … Qa8
2. Rxh8 Qxh8/Bxh8
3. Qd8 Qxd8
4. exd8=Q
Q vs. B endgame.
D.
1. … Qg8
2. Qd6+ (Rxh8 same as A) Kf7
3. Rxf5+ Bf6 (Ke8 Qd8#)
4. Rxf6+ Kg7
5. Rg6+ Kf7
6. Rxg8 Rxg8
7. Qd8
Either R takes Q or Q takes R, this should be blank Q up.
E.
1. … Qe8??
2. Qd6+ Kf7
3. Qe6#
F.
1. … Qf7??
2. Qd6+ Qe6
3. Qxe6#
1.e7 – Dxe7
2. Txf5+ – Kxf5
3. Dxe7
1. e7 – De8
2. Dd6+ – Kf7
3. De6#
I don’t have a lot of time for this problem this morning, but I would definitely think to look at e7 here since Qxe7 will lose to Rxf5 check. so black will have to find a square for his queen:
1. e7 Qb8
I don’t see any other valid defense since white is threatening Qd6+ and Qe6 mate. The other square from which to guard this threat, g8, is still bad: [1. …Qg8 2.Qd6 Kf7 3.Rf5 Bf6 4.Qf6 Ke8 5.Qd6+- surely]. Continuing:
2. Qd7! Qe5 (Rh5 3.Qe6 Kg5 4.e8Q)
3. Rh8 Qe4 (Bh8 4.e8Q)
4. Kh2! Qe7 (what else?)
5. Qe7 Ke7
6. Rh7 Kf8
7. b3 and this is an easily won ending for white.
I had alternatives ABCDEF, but irritatingly enough this was one too little:-)