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Looks like Kf5 opens the door.
Kf5 Kh8 and then what?
It “feels” as though the solution would start
1. Kf5 Kh8 (if … e6+ 2. Qxe6 soon transposes)
2. Qc8+ Qg8
3. Qc3+ Qg7
4. Qh3+ Kg8
5. Qb3+ Kh8 (if the e pawn were missing, Black still can’t play … Kf8 because of 6. Qb8+ Ke7 7. Qc7+ Kf8 8. Qd7 mate)
6. Qb8+ Qg8
7. Qb2+ Qg7
8. Qh2+ Kg8
9. Qa2+ Kh8
10. Qa8+ Qg8
and now since the long diagonal is not blocked (the c8-h3 diagonal is blocked by the White king and the b8-h2 diagonal is blocked by the Black pawn) White can force the Black king to move to a more precarious position by
11.Qh1+ Kg7
12. Qa1+
but now I bog down. 🙁
12. … Kf8
13. Qa5 suggests itself, e.g.,
13. … Qh8
14. Qd8+ Kg7
15. Qxe7+ Kh6
16. Qh4+ Kg7
17. Qf6+ Kg8
18. Qf7 mate
or
13. … e6+
14. Kg5 Qh8
15. Qd8+ Kg7
16. Qf6+ Kg8
17. Qf7 mate
or
13. … Qc4
14. Qd8+ Kg7
15. Qxe7+ Kg8 (… Kh6 or … Kh8 16. Qh7 mate)
16. Qh7+ Kf8
17. g7+ followed by
18. g8=Q
But what about 12. … Kh6?
I don’t see anything conclusive against that, which suggests I’m missing something obvious or one of my earlier moves was wrong. 🙁
Boy, that was stupid. Let’s try
1. Kf5 Kh8
2. Qc8+ Qg8
3. Qc3+ Qg7
4. Qh3+ Kg8
5. Qb3+ Kh8
6. Qb8+ Qg8
7. Qb2+ Qg7
8. Qh2+ Kg8
9. Qa2+ Kh8
10. Qa8+ Qg8
11.Qh1+ Kg7
12. Kg5!!
Now a pawn move allows 13. Qh6 mate and 12. … Qe6 allows 13. Qh7+ Kf8 14. g7+ and 15. g8=Q.
So let’s try
12. … Qh8
13. Qa1+ Kg8
14. Qa2+ Kg7 (14. … Kf8?? 15. Qf7 mate)
15. Qb2+ Kg8
16. Qb3+ Kg7
17. Qc3+ Kg8
18. Qc4+ Kg7
19. Qd4+ Kg8
20. Qd5+ Kg7
21. Qe5+ Kg8
22. Qe6+ Kg7
23. Qf7 mate
So that leaves us with
12. … Kf8
13. Qa8+ Kg7
14. Qa1+ Kf8
15. Qe5
Maybe. I need to look at this some more.
Aha! There it is! In that last line, instead of 15. Qe5, let’s try
1. Kf5 Kh8
2. Qc8+ Qg8
3. Qc3+ Qg7
4. Qh3+ Kg8
5. Qb3+ Kh8
6. Qb8+ Qg8
7. Qb2+ Qg7
8. Qh2+ Kg8
9. Qa2+ Kh8
10. Qa8+ Qg8
11.Qh1+ Kg7
12. Kg5!! Kf8
13. Qa8+ Kg7
14. Qa1+ Kf8
15. Kh6!!! Qd5
to guard the a8 square, and now
16. Qh8+ Qg8
17. Qd4 Ke8
is there anything else that doesn’t also lose immediately?
18. Qa4+ followed by 19. Qa8+ mating or winning the queen.
Does that do it?
Well, I’m doing this without a chessboard, so I’m probably making a mistake somewhere.
i think bob has it…seeing as how this motif is similar to a previous puzzle i managed to calculate up to 16.Qh8 Qg8 but then went down the wrong path with 17. g7+ Kf7 18. Qh7 etc..completely missed the Qd4 Qa4 idea.