Huge work... But it will be done certainly!

[Hobacle]

And, here's my main line of the 13...Kf3 variation:
[pgn][Event "?"]
[Site "?"]
[Date "2022.10.02"]
[Round "?"]
[White ""]
[Black ""]
[Result "*"]
[FEN "8/p2N3n/p3Q1n1/p1p2rpb/p5kr/2P4p/1KPP3B/8 b - - 25 13"]
[SetUp "1"]

13... Kf3 14. Qe3+ Kg2 15. Qg1+ Kf3 16. Qf1+ Kg4 17. Qe2+ Rf3 18. Qe6+ Rf5 19.
c4 a3+ 20. Ka2 Kf3 21. Qe3+ Kg2 22. Qg1+ Kf3 23. Qf1+ Kg4 24. Qe2+ Rf3 25. Qe6+
Rf5 26. c3 Kf3 27. Qe3+ Kg2 28. Qg1+ Kf3 29. Qf1+ Kg4 30. Qe2+ Rf3 31. Qe6+ Rf5
32. Kxa3 Kf3 33. Qe3+ Kg2 34. Qg1+ Kf3 35. Qf1+ Kg4 36. Qe2+ Rf3 37. Qe6+ Rf5
38. Ka4 Kf3 39. Qe3+ Kg2 40. Qg1+ Kf3 41. Qf1+ Kg4 42. Qe2+ Rf3 43. Qe6+ Rf5
44. Kxa5 Kf3 45. Qe3+ Kg2 46. Qg1+ Kf3 47. Qf1+ Kg4 48. Qe2+ Rf3 49. Qe6+ Rf5
50. Kxa6 Kf3 51. Qe3+ Kg2 52. Qg1+ Kf3 53. Qf1+ Kg4 54. Qe2+ Rf3 55. Qe6+ Rf5
56. Kxa7 Kf3 57. Qe3+ Kg2 58. Qg1+ Kf3 59. Qf1+ Kg4 60. Qe2+ Rf3 61. Qe6+ Rf5
62. Ka6 Kf3 63. Qe3+ Kg2 64. Qg1+ Kf3 65. Qf1+ Kg4 66. Qe2+ Rf3 67. Qe6+ Rf5
68. Ka5 Kf3 69. Qe3+ Kg2 70. Qg1+ Kf3 71. Qf1+ Kg4 72. Qe2+ Rf3 73. Qe6+ Rf5
74. Ka4 Kf3 75. Qe3+ Kg2 76. Qg1+ Kf3 77. Qf1+ Kg4 78. Qe2+ Rf3 79. Qe6+ Rf5
80. Kb3 Kf3 81. Qe3+ Kg2 82. Qg1+ Kf3 83. Qf1+ *
[/pgn]

Before I beliefe in this one line, that takes > 100 moves to mate, I'd like to see this one denied, we had already way back then:

forum3/viewtopic.php?p=920375#p920375

As Ajedrecista showed, it was too long for one move even, yet DTM could be kept in hash backward to about move nr.40 with DTM 73 all in all. >100 now after a White deviation at 32nd move. Old line transposes to the new one at 32., why should Kxa3 be better there than d4 in old line was, sparing about 40,50 moves to mate?

Because I thought d4 was much harder to calculate, so I change to another easier line.
If someone finds direct DTMs of the 17 or 19 positions, then the cook can be claimed.

[Hobacle]

Well, to claim the cook doesn't mean to find the shortest solution, but a solution shorter than the author's solution. Now the author's solution has 226 moves, so if we find a solution shorter than 200 moves, it will be ok.

[peter]

Well, to claim the cook doesn't mean to find the shortest solution, but a solution shorter than the author's solution. Now the author's solution has 226 moves, so if we find a solution shorter than 200 moves, it will be ok.

Than even your( probably too long) line, leading to a mate in 116 maybe, was "ok" already.
Problem is "prove" or not.
If your line is too long = no prove as for shortest DTM, and of course, if it can be proved being too long, it's somewhat doubtable at all.
Just take mine and let's see, if somebody proves it being too short

[Hobacle]

Problem is "prove" or not.
If your line is too long = no prove as for shortest DTM, and of course, if it can be proved being too long, it's somewhat doubtable at all.
Just take mine and let's see, if somebody proves it being too short

That's true but I still need to calculate all possible defenses by Black in my line, such as 29...Ke4 and 35...Ke4, to claim the cook. This is the reason why I need to find direct DTMs of those 19 positions.

[peter]

Problem is "prove" or not.
If your line is too long = no prove as for shortest DTM, and of course, if it can be proved being too long, it's somewhat doubtable at all.
Just take mine and let's see, if somebody proves it being too short

That's true but I still need to calculate all possible defenses by Black in my line, such as 29...Ke4 and 35...Ke4, to claim the cook. This is the reason why I need to find direct DTMs of those 19 positions.

Ok, the easiest one (nr.1)


[fen]8/3N3n/6n1/2p2Qpb/2P4r/1KPPk2p/7B/8 b - - 0 1[/fen]


after these first moves

1... Nf4 2. Qxc5+ Kd2 3. Qf2+ Ne2 4. Bg3 h2 5. Qe1+ Kxd3 6. Ne5+ Ke3 7. Bxh4 Ke4 8. Qh1+ Kxe5 9. Qxh2+ Kf5 10. Bf2 Nf6 11. c5 Ng4 12. Qh3 Bf7+ 13. Kb2 Kg6

and some Forward- Backward, this one output:

8/5b2/6k1/2P3p1/6n1/2P4Q/1K2nB2/8 w - - 0 1

Analysis by HekaStockfishNNUE 280920F:

14.Dxg4 Sf4 15.Lh4 Se6 16.c6 Lg8 17.c7 Sxc7 18.Dxg5+ Kh7 19.De7+ Kg6 20.Dxc7 Kf5 21.Lg3 Kg6 22.De5 Lf7 23.Lh4 Kh7 24.Df6 Kg8 25.Lg5 Kf8 26.Ka3 Kg8 27.Lh6 La2 28.Dg7#
+- (#15) Tiefe: 109/30 00:02:13 10923MN
Weiß setzt Matt

From there keeping DTM in hash gets stuck again at further Backward.

Hope it helps, won't start that all over 19 times (meaning deleting hash each time with starting new position loaded) just to get 19 moves nearer (King's walk taking the pawns along the a-line one by one) to the still by displacing Queen, Knight and the whole King- pawn- group rather differing postion nr.19 compared to the one of the original puzzle.
How to "prove" connection then by lines, even with having DTM of nr. 19?
Guess it would be about 19 moves longer DTM but the one of nr.1, so let's say about 45, 47, 50,
regards

[Hobacle]

Ok, the easiest one (nr.1)


[fen]8/3N3n/6n1/2p2Qpb/2P4r/1KPPk2p/7B/8 b - - 0 1[/fen]


after these first moves

1... Nf4 2. Qxc5+ Kd2 3. Qf2+ Ne2 4. Bg3 h2 5. Qe1+ Kxd3 6. Ne5+ Ke3 7. Bxh4 Ke4 8. Qh1+ Kxe5 9. Qxh2+ Kf5 10. Bf2 Nf6 11. c5 Ng4 12. Qh3 Bf7+ 13. Kb2 Kg6

and some Forward- Backward, this one output:

8/5b2/6k1/2P3p1/6n1/2P4Q/1K2nB2/8 w - - 0 1

Analysis by HekaStockfishNNUE 280920F:

14.Dxg4 Sf4 15.Lh4 Se6 16.c6 Lg8 17.c7 Sxc7 18.Dxg5+ Kh7 19.De7+ Kg6 20.Dxc7 Kf5 21.Lg3 Kg6 22.De5 Lf7 23.Lh4 Kh7 24.Df6 Kg8 25.Lg5 Kf8 26.Ka3 Kg8 27.Lh6 La2 28.Dg7#
+- (#15) Tiefe: 109/30 00:02:13 10923MN
Weiß setzt Matt

From there keeping DTM in hash gets stuck again at further Backward.

Hope it helps, won't start that all over 19 times (meaning deleting hash each time with starting new position loaded) just to get 19 moves nearer (King's walk taking the pawns along the a-line one by one) to the still by displacing Queen, Knigth and the whole King- pawn- group rather differing postion nr.19 compared to the one of the original puzzle.
How to "prove" connection" then, even with having DTM of nr. 19?
Guess it would be about 19 moves longer DTM but the one of nr.1, so let's say about 47, 50,
regards

I used SF11 to get a #33 after 1...Nf4 in this position yesterday. But my hash was not big enough to keep it to beginning.
Maybe Jörg Oster's Matefish 2.0 (based on SF11) can help us?
And about the connection, these 19 positions are after Ke4, d3+, Ke3, Qxf5 instead of Kg4 in 19 different variations in my line.

[peter]

And about the connection, these 19 positions are after Ke4, d3+, Ke3, Qxf5 instead of Kg4 in 19 different variations in my line.

But the pawns of White's are displaced all a whole row forward too, aren't they?
DTM as for pos. nr. 1 yet seems to be some shorter, 13...Nf4 was a shortcut but 12.Qh3 a detour:

8/8/8/2P2kpb/6n1/1KP5/4nB1Q/8 w - - 0 1

Analysis by HekaStockfishNNUE 280920F:

12.Dxh5 Sf4 13.Dh7+ Ke6 14.De4+ Se5 15.Ld4 Sfd3 16.c6 Kd6 17.Lxe5+ Sxe5 18.Dd4+ Kc7 19.Dxe5+ Kxc6 20.Kc4 Kb6 21.Dd6+ Kb7 22.Kc5 g4 23.Db6+ Kc8 24.Kc6 g3 25.Dc7#
+- (#14) Tiefe: 100/28 00:00:52 4386MN
Weiß setzt Matt

[Hobacle]

And about the connection, these 19 positions are after Ke4, d3+, Ke3, Qxf5 instead of Kg4 in 19 different variations in my line.

But the pawns of White's are displaced all a whole row forward too, aren't they?

[pgn][Event "?"]
[Site "?"]
[Date "2022.10.02"]
[Round "?"]
[White ""]
[Black ""]
[Result "*"]
[FEN "8/p2N3n/p3Q1n1/p1p2rpb/p5kr/2P4p/1KPP3B/8 b - - 25 13"]
[SetUp "1"]

13... Kf3 14. Qe3+ Kg2 15. Qg1+ Kf3 16. Qf1+ Kg4 17. Qe2+ Rf3 18. Qe6+ Rf5 19.
c4 a3+ 20. Ka2 Kf3 21. Qe3+ Kg2 22. Qg1+ Kf3 23. Qf1+ Kg4 24. Qe2+ Rf3 25. Qe6+
Rf5 26. c3 Kf3 27. Qe3+ Kg2 28. Qg1+ Kf3 29. Qf1+ Kg4 30. Qe2+ Rf3 31. Qe6+ Rf5
32. Kxa3 Kf3 33. Qe3+ Kg2 34. Qg1+ Kf3 35. Qf1+ Kg4 36. Qe2+ Rf3 37. Qe6+ Rf5
38. Ka4 Kf3 39. Qe3+ Kg2 40. Qg1+ Kf3 41. Qf1+ Kg4 42. Qe2+ Rf3 43. Qe6+ Rf5
44. Kxa5 Kf3 45. Qe3+ Kg2 46. Qg1+ Kf3 47. Qf1+ Kg4 48. Qe2+ Rf3 49. Qe6+ Rf5
50. Kxa6 Kf3 51. Qe3+ Kg2 52. Qg1+ Kf3 53. Qf1+ Kg4 54. Qe2+ Rf3 55. Qe6+ Rf5
56. Kxa7 Kf3 57. Qe3+ Kg2 58. Qg1+ Kf3 59. Qf1+ Kg4 60. Qe2+ Rf3 61. Qe6+ Rf5
62. Ka6 Kf3 63. Qe3+ Kg2 64. Qg1+ Kf3 65. Qf1+ Kg4 66. Qe2+ Rf3 67. Qe6+ Rf5
68. Ka5 Kf3 69. Qe3+ Kg2 70. Qg1+ Kf3 71. Qf1+ Kg4 72. Qe2+ Rf3 73. Qe6+ Rf5
74. Ka4 Kf3 75. Qe3+ Kg2 76. Qg1+ Kf3 77. Qf1+ Kg4 78. Qe2+ Rf3 79. Qe6+ Rf5
80. Kb3 Kf3 81. Qe3+ Kg2 82. Qg1+ Kf3 83. Qf1+ Ke4 84. d3+ Ke3 85. Qxf5 *

[/pgn]

[peter]

And about the connection, these 19 positions are after Ke4, d3+, Ke3, Qxf5 instead of Kg4 in 19 different variations in my line.

But the pawns of White's are displaced all a whole row forward too, aren't they?

[pgn][Event "?"]
[Site "?"]
[Date "2022.10.02"]
[Round "?"]
[White ""]
[Black ""]
[Result "*"]
[FEN "8/p2N3n/p3Q1n1/p1p2rpb/p5kr/2P4p/1KPP3B/8 b - - 25 13"]
[SetUp "1"]

13... Kf3 14. Qe3+ Kg2 15. Qg1+ Kf3 16. Qf1+ Kg4 17. Qe2+ Rf3 18. Qe6+ Rf5 19.
c4 a3+ 20. Ka2 Kf3 21. Qe3+ Kg2 22. Qg1+ Kf3 23. Qf1+ Kg4 24. Qe2+ Rf3 25. Qe6+
Rf5 26. c3 Kf3 27. Qe3+ Kg2 28. Qg1+ Kf3 29. Qf1+ Kg4 30. Qe2+ Rf3 31. Qe6+ Rf5
32. Kxa3 Kf3 33. Qe3+ Kg2 34. Qg1+ Kf3 35. Qf1+ Kg4 36. Qe2+ Rf3 37. Qe6+ Rf5
38. Ka4 Kf3 39. Qe3+ Kg2 40. Qg1+ Kf3 41. Qf1+ Kg4 42. Qe2+ Rf3 43. Qe6+ Rf5
44. Kxa5 Kf3 45. Qe3+ Kg2 46. Qg1+ Kf3 47. Qf1+ Kg4 48. Qe2+ Rf3 49. Qe6+ Rf5
50. Kxa6 Kf3 51. Qe3+ Kg2 52. Qg1+ Kf3 53. Qf1+ Kg4 54. Qe2+ Rf3 55. Qe6+ Rf5
56. Kxa7 Kf3 57. Qe3+ Kg2 58. Qg1+ Kf3 59. Qf1+ Kg4 60. Qe2+ Rf3 61. Qe6+ Rf5
62. Ka6 Kf3 63. Qe3+ Kg2 64. Qg1+ Kf3 65. Qf1+ Kg4 66. Qe2+ Rf3 67. Qe6+ Rf5
68. Ka5 Kf3 69. Qe3+ Kg2 70. Qg1+ Kf3 71. Qf1+ Kg4 72. Qe2+ Rf3 73. Qe6+ Rf5
74. Ka4 Kf3 75. Qe3+ Kg2 76. Qg1+ Kf3 77. Qf1+ Kg4 78. Qe2+ Rf3 79. Qe6+ Rf5
80. Kb3 Kf3 81. Qe3+ Kg2 82. Qg1+ Kf3 83. Qf1+ Ke4 84. d3+ Ke3 85. Qxf5 *

[/pgn]

At the 19 positions, white pawns all have walked one step, d2 to d3 already too, a move that comes in given line not until 84th, at position 19, there are black a-pawns still on board, at nr.1 only the black a-pawns have been taken.
No direct line as far as I can see to the line after original starting position as above to one of the 19 postions.
You can of course construct one intentionally, but who says (proves), it's then best DTM then still after connecting nr.19 to original starting pos.?
BTW I edited the last one posting you answered to after your answer once again.

[Hobacle]

Sadly I found several mistakes in my version 2. Sorry for that. Anyhow here's my version 2.1, with 20 similar positions and all the variations lead to them:

Code: Select all

1. 8/3N3n/6n1/2p2Qpb/2P4r/1KPPk2p/7B/8 b - - 0 1
2. 8/3N3n/6n1/2p2Qpb/K1P4r/2PPk2p/7B/8 b - - 0 1
3. 8/3N3n/6n1/K1p2Qpb/2P4r/2PPk2p/7B/8 b - - 0 1
4. 8/3N3n/K5n1/2p2Qpb/2P4r/2PPk2p/7B/8 b - - 0 1
5. 8/K2N3n/6n1/2p2Qpb/2P4r/2PPk2p/7B/8 b - - 0 1
6. 8/p2N3n/K5n1/2p2Qpb/2P4r/2PPk2p/7B/8 b - - 0 1
7. 8/3N3n/p5n1/K1p2Qpb/2P4r/2PPk2p/7B/8 b - - 0 1
8. 8/p2N3n/6n1/K1p2Qpb/2P4r/2PPk2p/7B/8 b - - 0 1
9. 8/p2N3n/p5n1/K1p2Qpb/2P4r/2PPk2p/7B/8 b - - 0 1
10. 8/3N3n/p5n1/p1p2Qpb/K1P4r/2PPk2p/7B/8 b - - 0 1
11. 8/p2N3n/6n1/p1p2Qpb/K1P4r/2PPk2p/7B/8 b - - 0 1
12. 8/p2N3n/p5n1/2p2Qpb/K1P4r/2PPk2p/7B/8 b - - 0 1
13. 8/p2N3n/p5n1/p1p2Qpb/K1P4r/2PPk2p/7B/8 b - - 0 1
14. 8/p2N3n/6n1/p1p2Qpb/p1P4r/K1PPk2p/7B/8 b - - 0 1
15. 8/p2N3n/p5n1/2p2Qpb/p1P4r/K1PPk2p/7B/8 b - - 0 1
16. 8/p2N3n/p5n1/p1p2Qpb/2P4r/K1PPk2p/7B/8 b - - 0 1
17. 8/p2N3n/p5n1/p1p2Qpb/p1P4r/K1PPk2p/7B/8 b - - 0 1
18. 8/p2N3n/p5n1/2p2Qpb/p1P4r/p1PPk2p/K6B/8 b - - 0 1
19. 8/p2N3n/p5n1/p1p2Qpb/2P4r/p1PPk2p/K6B/8 b - - 0 1
20. 8/p2N3n/p5n1/p1p2Qpb/p1P4r/2PPk2p/1K5B/8 b - - 0 1

[pgn][Event "?"]
[Site "?"]
[Date "2022.10.02"]
[Round "?"]
[White ""]
[Black ""]
[Result "*"]
[FEN "8/p2N3n/p3Q1n1/p1p2rpb/p5kr/2P4p/1KPP3B/8 b - - 25 13"]
[SetUp "1"]

13... Kf3 14. Qe3+ Kg2 15. Qg1+ Kf3 16. Qf1+ Kg4 17. Qe2+ Rf3 18. Qe6+ Rf5 19.
c4 a3+ (19... Kf3 20. Qe3+ Kg2 21. Qg1+ Kf3 22. Qf1+ Kg4 23. Qe2+ Rf3 24. Qe6+
Rf5 25. c3 Kf3 26. Qe3+ Kg2 27. Qg1+ Kf3 28. Qf1+ Kg4 (28... Ke4 29. d3+ Ke3
30. Qxf5 {Pos.20}) 29. Qe2+ Rf3 30. Qe6+ Rf5 31. Ka3 Kf3 32. Qe3+ Kg2 33. Qg1+
Kf3 34. Qf1+ Ke4 35. d3+ Ke3 36. Qxf5 {Pos.17}) 20. Ka2 Kf3 (20... a4 21. c3
Kf3 (21... a5 22. Kxa3 Kf3 (22... a6 23. Kxa4 Kf3 24. Qe3+ Kg2 25. Qg1+ Kf3 26.
Qf1+ Kg4 (26... Ke4 27. d3+ Ke3 28. Qxf5 {Pos.10}) 27. Qe2+ Rf3 28. Qe6+ Rf5
29. Kxa5 Kf3 30. Qe3+ Kg2 31. Qg1+ Kf3 32. Qf1+ Ke4 33. d3+ Ke3 34. Qxf5
{Pos.7}) 23. Qe3+ Kg2 24. Qg1+ Kf3 25. Qf1+ Kg4 (25... Ke4 26. d3+ Ke3 27. Qxf5
{Pos.14}) 26. Qe2+ Rf3 27. Qe6+ Rf5 28. Kxa4 Kf3 29. Qe3+ Kg2 30. Qg1+ Kf3 31.
Qf1+ Kg4 (31... Ke4 32. d3+ Ke3 33. Qxf5 {Pos.11}) 32. Qe2+ Rf3 33. Qe6+ Rf5
34. Kxa5 Kf3 35. Qe3+ Kg2 36. Qg1+ Kf3 37. Qf1+ Ke4 38. d3+ Ke3 39. Qxf5
{Pos.8}) 22. Qe3+ Kg2 23. Qg1+ Kf3 24. Qf1+ Kg4 (24... Ke4 25. d3+ Ke3 26. Qxf5
{Pos.18}) 25. Qe2+ Rf3 26. Qe6+ Rf5 27. Kxa3 Kf3 28. Qe3+ Kg2 29. Qg1+ Kf3 30.
Qf1+ Kg4 (30... Ke4 31. d3+ Ke3 32. Qxf5 {Pos.15}) 31. Qe2+ Rf3 32. Qe6+ Rf5
33. Kxa4 Kf3 34. Qe3+ Kg2 35. Qg1+ Kf3 36. Qf1+ Ke4 37. d3+ Ke3 38. Qxf5
{Pos.12}) 21. Qe3+ Kg2 22. Qg1+ Kf3 23. Qf1+ Kg4 24. Qe2+ Rf3 25. Qe6+ Rf5 26.
c3 Kf3 27. Qe3+ Kg2 28. Qg1+ Kf3 29. Qf1+ Kg4 (29... Ke4 30. d3+ Ke3 31. Qxf5
{Pos.19}) 30. Qe2+ Rf3 31. Qe6+ Rf5 32. Kxa3 Kf3 33. Qe3+ Kg2 34. Qg1+ Kf3 35.
Qf1+ Kg4 (35... Ke4 36. d3+ Ke3 37. Qxf5 {Pos.16}) 36. Qe2+ Rf3 37. Qe6+ Rf5
38. Ka4 Kf3 39. Qe3+ Kg2 40. Qg1+ Kf3 41. Qf1+ Kg4 (41... Ke4 42. d3+ Ke3 43.
Qxf5 {Pos.13}) 42. Qe2+ Rf3 43. Qe6+ Rf5 44. Kxa5 Kf3 45. Qe3+ Kg2 46. Qg1+ Kf3
47. Qf1+ Kg4 (47... Ke4 48. d3+ Ke3 49. Qxf5 {Pos.9}) 48. Qe2+ Rf3 49. Qe6+ Rf5
50. Kxa6 Kf3 51. Qe3+ Kg2 52. Qg1+ Kf3 53. Qf1+ Kg4 (53... Ke4 54. d3+ Ke3 55.
Qxf5 {Pos.6}) 54. Qe2+ Rf3 55. Qe6+ Rf5 56. Kxa7 Kf3 57. Qe3+ Kg2 58. Qg1+ Kf3
59. Qf1+ Kg4 (59... Ke4 60. d3+ Ke3 61. Qxf5 {Pos.5}) 60. Qe2+ Rf3 61. Qe6+ Rf5
62. Ka6 Kf3 63. Qe3+ Kg2 64. Qg1+ Kf3 65. Qf1+ Kg4 (65... Ke4 66. d3+ Ke3 67.
Qxf5 {Pos.4}) 66. Qe2+ Rf3 67. Qe6+ Rf5 68. Ka5 Kf3 69. Qe3+ Kg2 70. Qg1+ Kf3
71. Qf1+ Kg4 (71... Ke4 72. d3+ Ke3 73. Qxf5 {Pos.3}) 72. Qe2+ Rf3 73. Qe6+ Rf5
74. Ka4 Kf3 75. Qe3+ Kg2 76. Qg1+ Kf3 77. Qf1+ Kg4 (77... Ke4 78. d3+ Ke3 79.
Qxf5 {Pos.2}) 78. Qe2+ Rf3 79. Qe6+ Rf5 80. Kb3 Kf3 81. Qe3+ Kg2 82. Qg1+ Kf3
83. Qf1+ Ke4 84. d3+ Ke3 85. Qxf5 {Pos.1} *

[/pgn]