Solutions for 8/1p2k3/8/8/5Q2/8/ppp1p3/qrrbK3 w - - 0 1

[fkarger]

Hi,

I analysed
[d]8/1p2k3/8/8/5Q2/8/ppp1p3/qrrbK3 w - - 0 1
and according to ACT5.021 the solution is Qd2.

The main idea is: stalemate the black king several times in order to force Pawn b7 to b3.
Then force the Black king to a3 and set mate by Qa5.

My questions are:
1) Is Qd2 the only (unique) solution?
2) Do you know an engine which can solve this?
3) Which engines would you recommend for such long distance mates?

Many thanks in advance

[peter]

Chest has it in database:

Code: Select all

Engine: ChestUCI Ver.5.2 (0 MB)
von Franz Huber
FEN: 8/1p2k3/8/8/5Q2/8/ppp1p3/qrrbK3 w - -   (2+10)
Stellungs-Analyse:  C0/R0/K5/P2/X6   W:2/27
Parameter in Datenbank gefunden:  #50; 00:03+ @ C14/R0/K6/P2/X7;
Suche nach Spezial-Matt [C14/R0/K0/P2/X7] in 50 ...  (Hash=2044MB)
 50.16	 0:01 	 +M50 	1.Dd2 1423
Suche abgeschlossen ...  (Zeit=1.15s)
Berechnung abgebrochen !
Matt in 50 gefunden !  (1 Lösung in 00:01)
 50/50	 0:01 	 +M50 	1.Dd2 Kf6 2.Dc3+ Ke7 3.Dd3 Ke6 4.Dd4 Kf5 5.De3 Kg4 6.Df2 Kh3 7.Dg1 b6 8.Df2 Kg4 9.De3 Kh4 10.Df3 Kg5 11.De4 Kh5 12.Df4 Kg6 13.De5 Kh6 14.Df5 1422
Bester Zug: Df4-d2 Zeit: 0:16.282 min  K/s: 1.422.371  Knoten: 1.641.417

"All Solutions" was checked, so it should be the only one #50 (that Chest finds).

Here's Chest's full line to mate, pasted all new output at the end of the one but last:

[pgn]
[Event "?"]
[Site "?"]
[Date "2025.04.09"]
[Round "?"]
[White "?"]
[Black "?"]
[ECO "Ste"]
[Result "*"]
[SetUp "1"]
[FEN "8/1p2k3/8/8/5Q2/8/ppp1p3/qrrbK3 w - -"]

1. Qd2 Kf6 2. Qc3+ Ke7 3. Qd3 Ke6 4. Qd4 Kf5 5. Qe3 Kg4
6. Qf2 Kh3 7. Qg1 b6 8. Qf2 Kg4 9. Qe3 Kh4 10. Qf3 Kg5
11. Qe4 Kh5 12. Qf4 Kg6 13. Qe5 Kh6 14. Qf5 Kg7 15. Qe6 b5
16. Qd6 Kf7 17. Qh6 b4 18. Qd6 Kg7 19. Qe6 Kh7 20. Qf6 Kg8
21. Qg6+ Kh8 22. Qf7 b3 23. Qf8+ Kh7 24. Qf6 Kg8 25. Qh6
Kf7 26. Qg5 Kf8 27. Qg6 Ke7 28. Qf5 Ke8 29. Qf6 Kd7 30. Qe5
Kd8 31. Qe6 Kc7 32. Qd5 Kc8 33. Qd6 Kb7 34. Qc5 Ka8 35. Qb5
Ka7 36. Qd5 Kb8 37. Qc6 Ka7 38. Qc8 Kb6 39. Qd7 Ka6 40. Qc7
Kb5 41. Qd6 Kc4 42. Qe5 Kb4 43. Qe7+ Kc3 44. Qd7 Kc4
45. Qd6 Kc3 46. Qd5 Kb4 47. Qc6 Ka3 48. Qd6+ Ka4 49. Qb6
Ka3 50. Qa5# *
[/pgn]

[fkarger]

Thank you peter!

I would also like to know if other moves are winning too (so mate > 50 would be acceptable too).

[peter]

I would also like to know if other moves are winning too (so mate > 50 would be acceptable too).

Well, I guess there will be ways to mate with other one first moves too, especially if you don't mind 50 moves- rule, shortest way besides 1.Qd2 won't be to be found as easily because Chest seems not to work with best parameters given in database for the very starting position. E.g. after 1.Qc7+?! I tried up to search depth 75, here after 1.Qc7 Ke6:

Code: Select all

FEN: 8/1pQ5/4k3/8/8/8/ppp1p3/qrrbK3 w - -   (2+10)
Stellungs-Analyse:  C0/R0/K4/P2/X5   W:2/23
Suche nach Spezial-Matt [C14/R0/K6/P2/X7] in 75 ...  (Hash=2044MB)
Suche abgeschlossen ...  (Zeit=1.77s)
Kein Matt in 75 gefunden !  (00:01)
Bester Zug:---- Zeit: 0:01.875 min  K/s: 848.217  Knoten: 1.502.193 

Yet Sting gives #58 at original position, even with a rather short output- line:

8/1p2k3/8/8/5Q2/8/ppp1p3/qrrbK3 w - -

Engine: Sting10x (8192 MB)
von Marek Kwiatkowski
...
39.27 0:15 +M58 1.Dd2 (233.780.898) 15419

After some Forward- Backward of Chest's line:

8/1p2k3/8/8/5Q2/8/ppp1p3/qrrbK3 w - -

Engine: Sting10x (8192 MB)
von Marek Kwiatkowski
...
50.27 0:06 +M50 1.Dd2 Kf6 2.Dc3+ Ke7 3.Dd3 Ke6 4.Dd4 Kf5
5.De3 Kg4 6.Df2 Kh3 7.Dg1 b6 8.Df2 Kg4
9.De3 Kf5 10.Dd4 Kg5 11.De4 Kf6
12.Dd5 Kg6 13.De5 Kf7 14.Df5+ (90.590.376) 14284

And a little longer DTM after 1.Qc7 Ke6:

[d]8/1pQ5/4k3/8/8/8/ppp1p3/qrrbK3 w - -

Engine: Sting10x (8192 MB)
von Marek Kwiatkowski
...
29.00 0:00 +M203++ 2.Dd8 Ke5 3.Dd7 Ke4 4.Dd6 Kf5 5.Dc5+ Ke6
6.Dd4 Kf5 7.De3 Kg4 8.Df2 b6 9.Dg2+ Kf4
10.Dg1 Ke5 11.De3+ Kd5 12.Df4 (3.299.150) 15785

Then I tried to let Sting play out on its own after 1.Qc7+ Ke6, but that failed, because with 10'+2" Sting comes to 0.00- eval soon, obviously seeing 50 moves- rule getting into horizon, not knowing, it doesn't count here, because we judge with "puzzle- rules", regards

[peter]

Here's how an older CorChess (HCE to be chosen still then and less nullmove- pruning compared to SF) did play out on its own with 15'+5" and 30 threads:

[pgn][[Event "Stellung ausspielen (CorChess3 03522, Schnellschach 15min+5sek) "]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "Cyclic, Zugzwang"]
[Black "Author, ?.."]
[Result "1-0"]
[SetUp "1"]
[FEN "8/1p2k3/8/8/5Q2/8/ppp1p3/qrrbK3 w - - 0 1"]
[PlyCount "1"]
[GameId "443644790180"]
[SourceTitle " www.glarean-magazin.ch "]
[Source "W. Eigenmann"]
[SourceDate "2022.09.29"]
[SourceVersion "1"]
[SourceVersionDate "2022.09.29"]
[SourceQuality "1"]

1. Qd2 $1 {#50} (1. Qc7+ $6 Ke6 {book} 2. Qd8 {1.46/55 53} Ke5 {1.42/66 51} 3. Qd3 {4.75/37 21} Kf4 {2.73/52 60} 4. Qd4+ {2.73/62 50 (Dd5)} Kg3 {2.46/56 70 (Kf3)} 5. Qf2+ {2.30/45 49} Kg4 {2.33/36 76} 6. Qf7 {2.73/37 102 (Df6)} b6 {2.56/50 118 (Kg3)} 7. Qf6 {2.73/35 31} Kg3 {2.43/55 114 (b5)} 8. Qf2+ {2.43/50 23 (Dg5+)} Kg4 {2.43/57 48 (Kh3)} 9. Qf6 {2.43/52 18 (Df7)} b5 {2.43/48 107 (Kg3)} 10. Qd4+ {2.37/54 19} Kf3 {2.33/54 61} 11. Qe5 {2.52/108 141 (Dd3+)} Kg2 {2.35/42 92 (Kg4)} 12. Qg5+ {2.35/47 33 (Dd5+)} Kf3 {2.30/47 31 (Kh2)} 13. Qf5+ {2.30/52 38 (Dg1)} Kg3 {2.26/43 46} 14. Qe4 {2.26/42 137 (Df2+)} b4 {2.16/43 24} 15. Qh1 {1.60/53 114 (De3+)} b3 {1.53/39 28} 16. Qg1+ {#38/33 21} Kh3 {9.83/40 42} 17. Qf2 {152.65/28 95} Kg4 {97.01/28 1} 18. Qh2 {152.65/26 30 (De3)} Kg5 {27.62/36 16} 19. Qh7 {152.65/26 18} Kg4 {33.19/32 3} 20. Qd3 {152.65/26 7 (Dg8+)} Kh5 {24.87/37 4 (Kg5)} 21. Qe4 {152.65/27 6 (Dd4)} Kh6 {49.76/37 9} 22. Qe6+ {152.65/21 5 (Dd3)} Kg5 {48.20/28 3 (Kg7)} 23. Qe3+ {152.65/22 6 (Dd6)} Kg6 {71.94/32 4} 24. Qf4 {152.65/23 5 (Dd3+)} Kh5 {48.03/35 9 (Kg7)} 25. Qe3 {152.65/20 5 (Df2)} Kg4 {14.33/34 3 (Kg6)} 26. Qd3 {152.65/24 5 (Df2)} Kh5 {36.76/46 7} 27. Qf5+ {152.65/27 6 (Dd4)} Kh6 {37.64/30 3} 28. Qf6+ {152.65/26 5 (Dd5)} Kh5 {47.33/40 7 (Kh7)} 29. Qf4 {152.65/21 5} Kg6 {48.38/27 1} 30. Qf8 {152.65/18 5 (Dg4+)} Kh7 {47.33/30 5} 31. Qf7+ {152.65/26 6 (Dc5)} Kh6 {44.14/33 6} 32. Qf5 {152.65/22 5} Kg7 {88.10/29 1} 33. Qc5 {152.65/21 5 (De6)} Kf6 {44.06/37 7 (Kf7)} 34. Qc6+ {152.65/23 5 (Dd4+)} Kg5 {72.89/43 11 (Kf7)} 35. Qe4 {152.65/25 4 (Dc4)} Kh6 {74.78/28 5 (Kf6)} 36. Qg4 {152.65/23 6 (De3+)} Kh7 {112.92/24 1} 37. Qf5+ {152.65/22 6 (Dh5+)} Kh8 {76.35/34 4 (Kg7)} 38. Qf6+ {152.65/26 5 (De4)} Kg8 {111.67/35 10} 39. Qe5 {152.65/24 5} Kf7 {112.92/33 3 (Kf8)} 40. Qg5 {152.65/26 6} Ke6 {93.76/31 7} 41. Qf4 {152.65/24 4} Kd5 {111.67/29 2 (Ke7)} 42. Qf5+ {152.65/27 5} Kd6 {#23/51 4} 43. Qe4 {#22/36 6 (Df6+)} Kd7 {#21/54 5} 44. Qe5 {#21/27 2} Kc6 {#21/53 6} 45. Qd4 {#20/43 3} Kc7 {#19/55 8} 46. Qd5 {#19/54 9} Kc8 {#18/56 6} 47. Qd6 {#18/52 6} Kb7 {#17/54 5} 48. Qc5 {#17/67 1} Ka8 {152.65/57 3} 49. Qb5 {#16/58 4} Ka7 {#15/59 1} 50. Qd5 {#15/57 9} Kb8 {#14/53 10} 51. Qc6 {#14/56 6} Ka7 {#13/50 6} 52. Qc8 {#13/50 5} Kb6 {#12/51 1} 53. Qd7 {#12/50 5} Ka6 {#11/48 5 (Kc5)} 54. Qc7 {#11/47 2} Kb5 {#10/41 1} 55. Qd6 {#10/43 1} Kc4 {#9/65 7} 56. Qe5 {#9/61 2} Kb4 {#8/70 10} 57. Qd5 {#8/67 3} Kc3 {#7/73 4} 58. Qd2+ {#7/58 3} Kc4 {#6/53 1} 59. Qd6 {#6/76 3} Kc3 {#5/79 10} 60. Qd5 {#5/73 18} Kb4 {#4/61 1} 61. Qc6 {#4/83 3} Ka3 {#3/245 0 (Ka5)} 62. Qc5+ {#3/245 0} Ka4 {#2/245 0} 63. Qb6 {#2/245 0} Ka3 {#1/245 0} 64. Qa5# {#1/245 0}) 1-0
[/pgn]
Mate arises one move before 50 after 15...b3, transposition to #50 from 20th here once and at some positions later on again. If this really is best DTM after 1.Qc7+?! is questionable, and as well if 1.Qc7+?! really is second best, regards

[fkarger]

That is a fascinating analysis that gave me some ideas!

Though I thought that the 50 move rule shouldnt be a big problem here, because you can force black to move the b pawn.

I will investigate deeper and report.

[peter]

Though I thought that the 50 move rule shouldnt be a big problem here, because you can force black to move the b pawn.

50 moves are a big problem here for sure, if you mind them at all. If engine on its own played all best moves for Black here as well as for White is rather doubtable with such STC. Will be difficult to prove, if it's really forced won within 50 moves

[fkarger]

Here's how an older CorChess (HCE to be chosen still then and less nullmove- pruning compared to SF) did play out on its own with 15'+5" and 30 threads:

[pgn][[Event "Stellung ausspielen (CorChess3 03522, Schnellschach 15min+5sek) "]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "Cyclic, Zugzwang"]
[Black "Author, ?.."]
[Result "1-0"]
[SetUp "1"]
[FEN "8/1p2k3/8/8/5Q2/8/ppp1p3/qrrbK3 w - - 0 1"]
[PlyCount "1"]
[GameId "443644790180"]
[SourceTitle " www.glarean-magazin.ch "]
[Source "W. Eigenmann"]
[SourceDate "2022.09.29"]
[SourceVersion "1"]
[SourceVersionDate "2022.09.29"]
[SourceQuality "1"]

1. Qd2 $1 {#50} (1. Qc7+ $6 Ke6 {book} 2. Qd8 {1.46/55 53} Ke5 {1.42/66 51} 3. Qd3 {4.75/37 21} Kf4 {2.73/52 60} 4. Qd4+ {2.73/62 50 (Dd5)} Kg3 {2.46/56 70 (Kf3)} 5. Qf2+ {2.30/45 49} Kg4 {2.33/36 76} 6. Qf7 {2.73/37 102 (Df6)} b6 {2.56/50 118 (Kg3)} 7. Qf6 {2.73/35 31} Kg3 {2.43/55 114 (b5)} 8. Qf2+ {2.43/50 23 (Dg5+)} Kg4 {2.43/57 48 (Kh3)} 9. Qf6 {2.43/52 18 (Df7)} b5 {2.43/48 107 (Kg3)} 10. Qd4+ {2.37/54 19} Kf3 {2.33/54 61} 11. Qe5 {2.52/108 141 (Dd3+)} Kg2 {2.35/42 92 (Kg4)} 12. Qg5+ {2.35/47 33 (Dd5+)} Kf3 {2.30/47 31 (Kh2)} 13. Qf5+ {2.30/52 38 (Dg1)} Kg3 {2.26/43 46} 14. Qe4 {2.26/42 137 (Df2+)} b4 {2.16/43 24} 15. Qh1 {1.60/53 114 (De3+)} b3 {1.53/39 28} 16. Qg1+ {#38/33 21} Kh3 {9.83/40 42} 17. Qf2 {152.65/28 95} Kg4 {97.01/28 1} 18. Qh2 {152.65/26 30 (De3)} Kg5 {27.62/36 16} 19. Qh7 {152.65/26 18} Kg4 {33.19/32 3} 20. Qd3 {152.65/26 7 (Dg8+)} Kh5 {24.87/37 4 (Kg5)} 21. Qe4 {152.65/27 6 (Dd4)} Kh6 {49.76/37 9} 22. Qe6+ {152.65/21 5 (Dd3)} Kg5 {48.20/28 3 (Kg7)} 23. Qe3+ {152.65/22 6 (Dd6)} Kg6 {71.94/32 4} 24. Qf4 {152.65/23 5 (Dd3+)} Kh5 {48.03/35 9 (Kg7)} 25. Qe3 {152.65/20 5 (Df2)} Kg4 {14.33/34 3 (Kg6)} 26. Qd3 {152.65/24 5 (Df2)} Kh5 {36.76/46 7} 27. Qf5+ {152.65/27 6 (Dd4)} Kh6 {37.64/30 3} 28. Qf6+ {152.65/26 5 (Dd5)} Kh5 {47.33/40 7 (Kh7)} 29. Qf4 {152.65/21 5} Kg6 {48.38/27 1} 30. Qf8 {152.65/18 5 (Dg4+)} Kh7 {47.33/30 5} 31. Qf7+ {152.65/26 6 (Dc5)} Kh6 {44.14/33 6} 32. Qf5 {152.65/22 5} Kg7 {88.10/29 1} 33. Qc5 {152.65/21 5 (De6)} Kf6 {44.06/37 7 (Kf7)} 34. Qc6+ {152.65/23 5 (Dd4+)} Kg5 {72.89/43 11 (Kf7)} 35. Qe4 {152.65/25 4 (Dc4)} Kh6 {74.78/28 5 (Kf6)} 36. Qg4 {152.65/23 6 (De3+)} Kh7 {112.92/24 1} 37. Qf5+ {152.65/22 6 (Dh5+)} Kh8 {76.35/34 4 (Kg7)} 38. Qf6+ {152.65/26 5 (De4)} Kg8 {111.67/35 10} 39. Qe5 {152.65/24 5} Kf7 {112.92/33 3 (Kf8)} 40. Qg5 {152.65/26 6} Ke6 {93.76/31 7} 41. Qf4 {152.65/24 4} Kd5 {111.67/29 2 (Ke7)} 42. Qf5+ {152.65/27 5} Kd6 {#23/51 4} 43. Qe4 {#22/36 6 (Df6+)} Kd7 {#21/54 5} 44. Qe5 {#21/27 2} Kc6 {#21/53 6} 45. Qd4 {#20/43 3} Kc7 {#19/55 8} 46. Qd5 {#19/54 9} Kc8 {#18/56 6} 47. Qd6 {#18/52 6} Kb7 {#17/54 5} 48. Qc5 {#17/67 1} Ka8 {152.65/57 3} 49. Qb5 {#16/58 4} Ka7 {#15/59 1} 50. Qd5 {#15/57 9} Kb8 {#14/53 10} 51. Qc6 {#14/56 6} Ka7 {#13/50 6} 52. Qc8 {#13/50 5} Kb6 {#12/51 1} 53. Qd7 {#12/50 5} Ka6 {#11/48 5 (Kc5)} 54. Qc7 {#11/47 2} Kb5 {#10/41 1} 55. Qd6 {#10/43 1} Kc4 {#9/65 7} 56. Qe5 {#9/61 2} Kb4 {#8/70 10} 57. Qd5 {#8/67 3} Kc3 {#7/73 4} 58. Qd2+ {#7/58 3} Kc4 {#6/53 1} 59. Qd6 {#6/76 3} Kc3 {#5/79 10} 60. Qd5 {#5/73 18} Kb4 {#4/61 1} 61. Qc6 {#4/83 3} Ka3 {#3/245 0 (Ka5)} 62. Qc5+ {#3/245 0} Ka4 {#2/245 0} 63. Qb6 {#2/245 0} Ka3 {#1/245 0} 64. Qa5# {#1/245 0}) 1-0
[/pgn]
Mate arises one move before 50 after 15...b3, transposition to #50 from 20th here once and at some positions later on again. If this really is best DTM after 1.Qc7+?! is questionable, and as well if 1.Qc7+?! really is second best, regards

Maybe there is an error in that game.
Because black was able to play Kg2.
If I understand the position you cant force the black King to leave that corner
once it stands near to or on h1.

[Ajedrecista]

Hello Frank:

Maybe there is an error in that game.
Because black was able to play Kg2.
If I understand the position you cant force the black King to leave that corner
once it stands near to or on h1.

We discussed a problem called 'The Untouchable King' a month ago, that dealed with the mating king side not allowed to move (like here) and the queen doing all the work, mostly staying at knight jumps (like here again):

Re: Minichess puzzle.

There were ways to force the mated king side to leave corners and drove it anywhere. I do not know if that can be applied here since the chessboard is more populated than in that problem.

Regards from Spain.

Ajedrecista.

[lech]

---
And a little longer DTM after 1.Qc7 Ke6:

[d]8/1pQ5/4k3/8/8/8/ppp1p3/qrrbK3 w - -

Engine: Sting10x (8192 MB)
von Marek Kwiatkowski
...
29.00 0:00 +M203++ 2.Dd8 Ke5 3.Dd7 Ke4 4.Dd6 Kf5 5.Dc5+ Ke6
6.Dd4 Kf5 7.De3 Kg4 8.Df2 b6 9.Dg2+ Kf4
10.Dg1 Ke5 11.De3+ Kd5 12.Df4 (3.299.150) 15785

Then I tried to let Sting play out on its own after 1.Qc7+ Ke6, but that failed, because with 10'+2" Sting comes to 0.00- eval soon, obviously seeing 50 moves- rule getting into horizon, not knowing, it doesn't count here, because we judge with "puzzle- rules", regards

Peter, I recommend (how_to_use.txt file) to use exactly 1024M HASH. I don't know how Sting works when you use more.
Auto-play can be (?) a good method e.g. for cyclic mechanisms (long solution), rather.
When you see a checkmate in the output, it is better to stop the search and restart without clearing the hash.
I tried it (1024MB, 1 thread) and I can't see a mate. Please, check it with more threads (1024 MB) again.