Mate in 13

[acase]

Here's a mate in 13 that seems to give engines trouble, however I haven't tried every engine, just the usual suspects (Huntsman1, several crystal versions, several versions of Stockfish, a few versions of Shashchess, Plenty Chess, Obsidian and a few others)

[d]8/5R2/2p3K1/8/2P1P1PP/1p1BBPP1/prp1p3/bk1bR3 w - - 0 1

I'll post a PGN later.

[towforce]

Chess.com's analysis mode is struggling, and I cannot solve it visually: moves that put white pieces into checkmating positions seem to let trapped black pieces escape.

[peter]

Here's a mate in 13 that seems to give engines trouble, however I haven't tried every engine, just the usual suspects (Huntsman1, several crystal versions, several versions of Stockfish, a few versions of Shashchess, Plenty Chess, Obsidian and a few others)

[d]8/5R2/2p3K1/8/2P1P1PP/1p1BBPP1/prp1p3/bk1bR3 w - - 0 1

Indeed even Huntsman is stuck a while with 1.e5?, after some Forward- Backward then:

8/5R2/2p3K1/8/2P1P1PP/1p1BBPP1/prp1p3/bk1bR3 w - - 0 1

Analysis by The Huntsman 1:

1.Td7 c5 2.Lxe2 c1D 3.Tdxd1 Tc2 4.Lxc1 Txc1 5.Txc1+ Kb2 6.Txa1 Ka3 7.h5 b2 8.h6 Kb3 9.h7 b1D 10.h8D Kc2 11.Dd8 Db3 12.Ld1+ Kc3 13.Te3+ Kxc4 14.Dd5+ Kb5 15.Txb3+ Ka5 16.Txa2#
Tiefe: 81/32 00:00:19 1403MN
+- (#16)

Yet in meantime, I tried the light version of the Chesss MoreMover

viewtopic.php?p=978905#p978905

This one with 25 threads finds it almost at once:

J.G.Island Chess Moremovers 9.0.0
#13 8/5R2/2p3K1/8/2P1P1PP/1p1BBPP1/prp1p3/bk1bR3

1. Be3-h6 c6-c5 2. Kg6-g5 Kb1-c1 3. Kg5-h5 Kc1-b1 4. g4-g5 Kb1-c1 5. g5-g6 Kc1-b1 6. Rf7-f4 Kb1-c1 7. Rf4-g4 Kc1-b1 8. f3-f4 Kb1-c1 9. f4-f5 Kc1-b1 10. Rg4-f4

These 10 moves given to Huntsman then are confirmed by this one output at starting position again after backwarding them:

8/5R2/2p3K1/8/2P1P1PP/1p1BBPP1/prp1p3/bk1bR3 w - - 0 1

Analysis by The Huntsman 1:

1.Lh6 c5 2.Kg5 Kc1 3.Kh5+ Kb1 4.g5 Kc1 5.g6+ Kb1 6.Tf4 Kc1 7.Tg4+ Kb1 8.f4 Kc1 9.f5+ Kb1 10.Tf4 Kc1 11.Tff1+ Kb1 12.Txd1+ exd1D+ 13.Txd1#
Tiefe: 76/26 00:00:04 185MN
+- (#13)

Do you have a source of the position?

[acase]

Here's a mate in 13 that seems to give engines trouble, however I haven't tried every engine, just the usual suspects (Huntsman1, several crystal versions, several versions of Stockfish, a few versions of Shashchess, Plenty Chess, Obsidian and a few others)

[d]8/5R2/2p3K1/8/2P1P1PP/1p1BBPP1/prp1p3/bk1bR3 w - - 0 1

Indeed even Huntsman is stuck a while with 1.e5?, after some Forward- Backward then:

8/5R2/2p3K1/8/2P1P1PP/1p1BBPP1/prp1p3/bk1bR3 w - - 0 1

Analysis by The Huntsman 1:

1.Td7 c5 2.Lxe2 c1D 3.Tdxd1 Tc2 4.Lxc1 Txc1 5.Txc1+ Kb2 6.Txa1 Ka3 7.h5 b2 8.h6 Kb3 9.h7 b1D 10.h8D Kc2 11.Dd8 Db3 12.Ld1+ Kc3 13.Te3+ Kxc4 14.Dd5+ Kb5 15.Txb3+ Ka5 16.Txa2#
Tiefe: 81/32 00:00:19 1403MN
+- (#16)

Yet in meantime, I tried the light version of the Chesss MoreMover

viewtopic.php?p=978905#p978905

This one with 25 threads finds it almost at once:

J.G.Island Chess Moremovers 9.0.0
#13 8/5R2/2p3K1/8/2P1P1PP/1p1BBPP1/prp1p3/bk1bR3

1. Be3-h6 c6-c5 2. Kg6-g5 Kb1-c1 3. Kg5-h5 Kc1-b1 4. g4-g5 Kb1-c1 5. g5-g6 Kc1-b1 6. Rf7-f4 Kb1-c1 7. Rf4-g4 Kc1-b1 8. f3-f4 Kb1-c1 9. f4-f5 Kc1-b1 10. Rg4-f4

These 10 moves given to Huntsman then are confirmed by this one output at starting position again after backwarding them:

8/5R2/2p3K1/8/2P1P1PP/1p1BBPP1/prp1p3/bk1bR3 w - - 0 1

Analysis by The Huntsman 1:

1.Lh6 c5 2.Kg5 Kc1 3.Kh5+ Kb1 4.g5 Kc1 5.g6+ Kb1 6.Tf4 Kc1 7.Tg4+ Kb1 8.f4 Kc1 9.f5+ Kb1 10.Tf4 Kc1 11.Tff1+ Kb1 12.Txd1+ exd1D+ 13.Txd1#
Tiefe: 76/26 00:00:04 185MN
+- (#13)

Do you have a source of the position?

Hello Peter,
Indeed I do have a source for it, it's actually a mate in 15, but I started it on the 3rd move because that was where the engines were having problems with it, here is the PGN of the original:

[pgn][Event "Mate in 15"]
[Site "Columbus, Ohio"]
[Date "2021"]
[Round "?"]
[White "Bernard Courthiau"]
[Black "?"]
[Result "1-0"]
[Time "07:17:53"]
[TimeControl "0"]
[SetUp "1"]
[FEN "5B2/5R2/2p3K1/8/2P1P1PP/1p1BpPP1/prp1p3/bk1bR3 w - - 0 1"]
[Termination "normal"]
[PlyCount "29"]
[WhiteType "Human"]
[BlackType "Human"]

1. Bc5 Kc1 2. Bxe3+ Kb1 3. Bh6 c5 4. Kg5 Kc1 5. Kh5+ Kb1 6. g5 Kc1 7. g6+ Kb1 8. Rf4 Kc1 9. Rg4+ Kb1 10. f4 Kc1 11. f5+ Kb1 12. Rf4 Kc1 13.
Rff1+ Kb1 14. Rxd1+ exd1=Q+ 15. Rxd1# 1-0
[/pgn]

And here is a link to the problem:
https://pdb.dieschwalbe.de/search.jsp?e ... 1399890%27

I also noticed that J.G. Island Chess Moremovers solved it quickly before I posted it, it seems that the engines get tripped up on this one because the White King must move in the way of the Black square White Bishop checking the Black King and then a Pawn must move in the way of the same Bishop before advancing to give check again and then then the white Rook and finally another pawn...it's like a quadruple Indian. I'm certain that Chest would solve it also if given enough time.

[towforce]

Indeed I do have a source for it, it's actually a mate in 15, but I started it on the 3rd move because that was where the engines were having problems with it, here is the PGN of the original:

[pgn][Event "Mate in 15"]
[Site "Columbus, Ohio"]
[Date "2021"]
[Round "?"]
[White "Bernard Courthiau"]
[Black "?"]
[Result "1-0"]
[Time "07:17:53"]
[TimeControl "0"]
[SetUp "1"]
[FEN "5B2/5R2/2p3K1/8/2P1P1PP/1p1BpPP1/prp1p3/bk1bR3 w - - 0 1"]
[Termination "normal"]
[PlyCount "29"]
[WhiteType "Human"]
[BlackType "Human"]

1. Bc5 Kc1 2. Bxe3+ Kb1 3. Bh6 c5 4. Kg5 Kc1 5. Kh5+ Kb1 6. g5 Kc1 7. g6+ Kb1 8. Rf4 Kc1 9. Rg4+ Kb1 10. f4 Kc1 11. f5+ Kb1 12. Rf4 Kc1 13.
Rff1+ Kb1 14. Rxd1+ exd1=Q+ 15. Rxd1# 1-0
[/pgn]

Bravo - wonderful mating sequence - and really difficult for most engines to find!

[peter]

I'm certain that Chest would solve it also if given enough time.

Chest with 2 King Squares:

8/5R2/2p3K1/8/2P1P1PP/1p1BBPP1/prp1p3/bk1bR3 w - -

Engine: ChestUCI Ver.5.2 (0 MB)
von Franz Huber

13.10 20:32 +M13 1.Lh6 3271

And Gustav with 1 Flight:

***** Gustav 4.2 h 64 Bit ***** Berechnung beendet am 15.12.2025 19:26

Matt in 13 Zügen, Weiß beginnt, ,

Lösung gefunden bei folgenden Parametern:
Fluchtfelder: 1
alle Lösungen suchen / keine Duale in Kurzvarianten anzeigen
Zugzahl unbekannt / Hashtabelle: 8192 MB

Lösezeit: 09 : 38,25 min Zaehler: 299.264013

1.Le3-h6 Bc6-c5 2.Kg6-g5 Kb1-c1 3.Kg5-h5 Kc1-b1 4.Bg4-g5 Kb1-c1 5.Bg5-g6 Kc1-b1 6.Tf7-f4 Kb1-c1 7.Tf4-g4 Kc1-b1 8.Bf3-f4 Kb1-c1 9.Bf4-f5 Kc1-b1 10.Tg4-f4 Kb1-c1 11.Tf4-f1 Kc1-b1 12.Te1xd1 e2xd1D 13.Tf1xd1#

[Joerg Oster]

I'm certain that Chest would solve it also if given enough time.

Chest with 2 King Squares:

8/5R2/2p3K1/8/2P1P1PP/1p1BBPP1/prp1p3/bk1bR3 w - -

Engine: ChestUCI Ver.5.2 (0 MB)
von Franz Huber

13.10 20:32 +M13 1.Lh6 3271

And Gustav with 1 Flight:

***** Gustav 4.2 h 64 Bit ***** Berechnung beendet am 15.12.2025 19:26

Matt in 13 Zügen, Weiß beginnt, ,

Lösung gefunden bei folgenden Parametern:
Fluchtfelder: 1
alle Lösungen suchen / keine Duale in Kurzvarianten anzeigen
Zugzahl unbekannt / Hashtabelle: 8192 MB

Lösezeit: 09 : 38,25 min Zaehler: 299.264013

1.Le3-h6 Bc6-c5 2.Kg6-g5 Kb1-c1 3.Kg5-h5 Kc1-b1 4.Bg4-g5 Kb1-c1 5.Bg5-g6 Kc1-b1 6.Tf7-f4 Kb1-c1 7.Tf4-g4 Kc1-b1 8.Bf3-f4 Kb1-c1 9.Bf4-f5 Kc1-b1 10.Tg4-f4 Kb1-c1 11.Tf4-f1 Kc1-b1 12.Te1xd1 e2xd1D 13.Tf1xd1#

Matefish's Proof-Number Search is really quick at this one

Code: Select all

setoption name Hash value 2048
setoption name ProofNumberSearch value true
position fen 8/5R2/2p3K1/8/2P1P1PP/1p1BBPP1/prp1p3/bk1bR3 w - - 0 1
go mate 13
info string Starting Proof-Number Search ...
info time 572 multipv 1 depth 8 seldepth 25 nodes 1586752 nps 2774041 hashfull 0 tbhits 0 score cp 0 pv e3h6
info time 772 multipv 1 depth 12 seldepth 25 nodes 3097305 nps 4012053 hashfull 0 tbhits 0 score cp 0 pv e3h6
info time 972 multipv 1 depth 12 seldepth 25 nodes 4673861 nps 4808498 hashfull 0 tbhits 0 score cp 0 pv e3h6
info time 1172 multipv 1 depth 12 seldepth 25 nodes 6246886 nps 5330107 hashfull 0 tbhits 0 score cp 0 pv e3h6
info time 1372 multipv 1 depth 12 seldepth 25 nodes 7833956 nps 5709880 hashfull 0 tbhits 0 score cp 0 pv e3h6
info time 1572 multipv 1 depth 12 seldepth 25 nodes 9425133 nps 5995631 hashfull 0 tbhits 0 score cp 0 pv e3h6
info time 1772 multipv 1 depth 12 seldepth 25 nodes 11016562 nps 6217021 hashfull 0 tbhits 0 score cp 0 pv e3h6
info time 1972 multipv 1 depth 13 seldepth 25 nodes 12550701 nps 6364452 hashfull 0 tbhits 0 score cp 0 pv e3h6
info string Nodes statistics:   Total 5876393   Solved 307802   Proven 66   Disproven 307736   Recycled 138993
info string Success! Mate in 13 found!
info time 2376 multipv 1 depth 13 seldepth 25 nodes 15609465 nps 6569640 hashfull 0 tbhits 0 score mate 13 pv e3h6 c6c5 g6g5 b1c1 g5h5 c1b1 g4g5 b1c1 g5g6 c1b1 f7f4 b1c1 f4g4 c1b1 f3f4 b1c1 f4f5 c1b1 g4f4 b1c1 f4f1 c1b1 e1d1 e2d1n f1d1
bestmove e3h6 ponder c6c5

[F.Huber]

Chest with 2 King Squares:

8/5R2/2p3K1/8/2P1P1PP/1p1BBPP1/prp1p3/bk1bR3 w - -

Engine: ChestUCI Ver.5.2 (0 MB)
von Franz Huber

13.10 20:32 +M13 1.Lh6 3271

Much faster (9 sec) with XPK order:

ChestUCI Ver.5.2:
FEN: 8/5R2/2p3K1/8/2P1P1PP/1p1BBPP1/prp1p3/bk1bR3 w - - (11+9)
Stellungs-Analyse: C0/R0/K1/P1/X1 W:10/41
Problem im Clipboard gefunden: #13;
AutoTurbo-Suche nach Spezial-Matt [C1/R0/K0/P0/X0] in 13 ... (Hash=256MB)
AutoTurbo-Suche nach Spezial-Matt [C0/R1/K0/P0/X0] in 13 ... (Hash=256MB)
AutoTurbo-Suche nach Spezial-Matt [C0/R2/K0/P0/X0] in 13 ... (Hash=256MB)
AutoTurbo-Suche nach Spezial-Matt [C0/R-2/K0/P0/X0] in 13 ... (Hash=256MB)
AutoTurbo-Suche nach Spezial-Matt [C0/R3/K0/P0/X0] in 13 ... (Hash=256MB)
AutoTurbo-Suche nach Spezial-Matt [C0/R-3/K0/P0/X0] in 13 ... (Hash=256MB)
AutoTurbo-Suche nach Spezial-Matt [C0/R0/K0/P0/X1] in 13 ... (Hash=256MB)
AutoTurbo-Suche nach Spezial-Matt [C0/R0/K0/P0/X2] in 13 ... (Hash=256MB)
AutoTurbo-Suche nach Spezial-Matt [C0/R0/K0/P0/X3] in 13 ... (Hash=256MB)
AutoTurbo-Suche nach Spezial-Matt [C0/R0/K0/P0/X4] in 13 ... (Hash=256MB)
13/13 00:08 4.171.566 1.397.977 +M13 1.Bh6
13/13 00:08 4.920.624 1.387.263 +M13 1.Bh6 c5 2.Kg5 Kc1 3.Kh5+ Kb1 4.g5 Kc1 5.g6+ Kb1 6.Rf4 Kc1 7.Rg4+ Kb1 8.f4 Kc1 9.f5+ Kb1 10.Rf4 Kc1 11.Rff1+ Kb1 12.Rxd1+ exd1Q+ 13.Rxd1+
AutoTurbo-Suche nach Spezial-Matt [C0/R0/K0/P1/X4] in 13 ... (Hash=256MB)
13/13 00:09 4.920.624 1.387.263 +M13 1.Bh6
13/13 00:09 261.721 1.530.532 +M13 1.Bh6 c5 2.Kg5 Kc1 3.Kh5+ Kb1 4.g5 Kc1 5.g6+ Kb1 6.Rf4 Kc1 7.Rg4+ Kb1 8.f4 Kc1 9.f5+ Kb1 10.Rf4 Kc1 11.Rff1+ Kb1 12.Rxd1+ exd1Q+ 13.Rxd1+
AutoTurbo-Suche nach Spezial-Matt [C0/R0/K2/P1/X4] in 13 ... (Hash=256MB)
13/13 00:09 261.721 1.530.532 +M13 1.Bh6
13/13 00:09 242.930 1.420.643 +M13 1.Bh6 c5 2.Kg5 Kc1 3.Kh5+ Kb1 4.g5 Kc1 5.g6+ Kb1 6.Rf4 Kc1 7.Rg4+ Kb1 8.f4 Kc1 9.f5+ Kb1 10.Rf4 Kc1 11.Rff1+ Kb1 12.Rxd1+ exd1Q+ 13.Rxd1+
Matt in 13 gefunden ! (1 Lösung in 00:00)
13/13 00:09 242.930 1.420.643 +M13 1.Bh6 c5 2.Kg5 Kc1 3.Kh5+ Kb1 4.g5 Kc1 5.g6+ Kb1 6.Rf4 Kc1 7.Rg4+ Kb1 8.f4 Kc1 9.f5+ Kb1 10.Rf4 Kc1 11.Rff1+ Kb1 12.Rxd1+ exd1Q+ 13.Rxd1+
Best move: Bh6, Value: +Mate in 13, Depth: 13/13, Time: 00:09,402, 242.930 Nodes, 1.420.643 N/sec

[Ajedrecista]

Hello Andrew:

Chest 5.2 with K1/P1/X1 parameters was not able to find a checkmate in 13 moves from the position of the OP. Surprisingly, I randomly found some parameters that worked for Chest!

Code: Select all

FEN: 8/5R2/2p3K1/8/2P1P1PP/1p1BBPP1/prp1p3/bk1bR3 w - - 0 1

ChestUCI:
FEN: 8/5R2/2p3K1/8/2P1P1PP/1p1BBPP1/prp1p3/bk1bR3 w - -   (11+9)
Stellungs-Analyse:  C0/R0/K1/P1/X1   W:10/41
Suche nach Spezial-Matt [C0/R0/K2/P3/X4] in 13 ...  (Hash=64MB)
  13	00:00	           0	0	+M13	Be3h6
Suche abgeschlossen ...  (Zeit=0.80s)
Matt in 13 gefunden !  (1 Lösung in 00:00)
 13/13	00:01	     981.249	1.231.178	+M13	Be3h6 c6c5 Kg6g5 Kb1c1 Kg5h5+ Kc1b1 g4g5 Kb1c1 g5g6+ Kc1b1 Rf7f4 Kb1c1 Rf4g4+ Kc1b1 f3f4 Kb1c1 f4f5+ Kc1b1 Rg4f4 Kb1c1 Rf4f1+ Kc1b1 Re1xd1+ e2xd1Q+ Rf1xd1+

The original checkmate in 15 moves is also solved with the same K2/P3/X4 parameters:

Code: Select all

FEN: 5B2/5R2/2p3K1/8/2P1P1PP/1p1BpPP1/prp1p3/bk1bR3 w - - 0 1

ChestUCI:
FEN: 5B2/5R2/2p3K1/8/2P1P1PP/1p1BpPP1/prp1p3/bk1bR3 w - -   (11+10)
Stellungs-Analyse:  C0/R0/K2/P2/X2   W:10/36
Suche nach Spezial-Matt [C0/R0/K2/P3/X4] in 15 ...  (Hash=64MB)
  15	00:01	           0	0	+M15	Bf8c5
Suche abgeschlossen ...  (Zeit=0.94s)
Matt in 15 gefunden !  (1 Lösung in 00:00)
 15/15	00:01	   1.122.500	1.192.879	+M15	Bf8c5 Kb1c1 Bc5xe3+ Kc1b1 Be3h6 c6c5 Kg6g5 Kb1c1 Kg5h5+ Kc1b1 g4g5 Kb1c1 g5g6+ Kc1b1 Rf7f4 Kb1c1 Rf4g4+ Kc1b1 f3f4 Kb1c1 f4f5+ Kc1b1 Rg4f4 Kb1c1 Rf4f1+ Kc1b1 Re1xd1+ e2xd1Q+ Rf1xd1+

I see that some people found working parameters for Chest while I was writing, so this is a kind of shared, independent solutions. My parameters are with default KXP SearchOrder; the solving time was less than 1 second using 64 MB of hash in a CPU of year 2010 if I am not wrong.

------------

Thank you for the source. I replayed the solution at PDB and my head is still burning... wow!

Phénix site has links to many issues, including the one given in PDB:

Inédits - Phénix 325 (Décembre 2021)

The study is the No. 9181 at page 12681 and solution in French at page 12692. The author noted that the key ideas are the same than in other problems, for example one of his own:

Inédits - Phénix 312 (Novembre 2020)

The study No. 8889 at page 12168 and solution in French at page 12181. The author noted that No. 8889 was an Indian theme linked with Herlin, Zabunov and Klasinc themes, where each of the last three is explained in the solution. Chest 5.2 succeeded again with K2/P3/X4 parameters:

Code: Select all

FEN: 6R1/8/2p5/2p2P2/2P3PP/p1pB2P1/rpp1PK2/bk4B1 w - - 0 1

ChestUCI:
FEN: 6R1/8/2p5/2p2P2/2P3PP/p1pB2P1/rpp1PK2/bk4B1 w - -   (10+9)
Stellungs-Analyse:  C0/R0/K2/P1/X1   W:8/23
Suche nach Spezial-Matt [C0/R0/K2/P3/X4] in 14 ...  (Hash=64MB)
  14	00:01	           0	0	+M14	Kf2e1
Suche abgeschlossen ...  (Zeit=0.10s)
Matt in 14 gefunden !  (1 Lösung in 00:00)
 14/14	00:01	     121.947	1.270.281	+M14	Kf2e1 Kb1c1 Bg1e3+ Kc1b1 Be3xc5 Kb1c1 Bc5e3+ Kc1b1 Be3h6 c6c5 Rg8g5 Kb1c1 Rg5h5+ Kc1b1 g4g5 Kb1c1 g5g6+ Kc1b1 Rh5g5 Kb1c1 Rg5g4+ Kc1b1 Rg4f4 Kb1c1 Rf4f1+ Kc1b1 Ke1f2+

Regards from Spain.

Ajedrecista.

[acase]

Bravo - wonderful mating sequence - and really difficult for most engines to find!

Glad you liked it Paul, I thought the mating sequence was pretty neat myself.