Die Schwalbe

19 problem(s) found in 3364 milliseconds (displaying 19 problem(s)). [COMMENTDATE>=20200919 AND NOT K='Hilfsrückzüger' AND A='Buchanan, Andrew' AND K='Miniatur'] [download as LaTeX]

1 - P1006923
Andrew Buchanan
H0657 StrateGems 07-09/2002
in memory of Wolfgang Pauly
P1006923
(3+3) C+
h#2
4 solutions
1) 1. Tf7 Dc1 2. Tce7 Dc8#
2) 1. Te7 Dg1 2. Tcd7 Dg8#
3) 1. Kd8 Dh1 2. Kc8 Da8#
4) 1. Ke7 Df1 2. Kd8 Df8#
play all play one stop play next play all
Suggested by P1001731.
Yuri Bilokin: h#1.5 1...Qf1 2.Kd8 Qf8# (MM) (2021-11-25)
more ...
comment
Keywords: black Bristol, Umnov, Model mate (4), Tempo Move, Echo (4), Miniature
Genre: h#
Computer test: (Popeye WINDOWS98-32Bit-Version 3.75 (2048 KB))
FEN: 4k3/2rr4/8/8/8/8/PK6/Q7
Input: hpr, 2003-01-19
Last update: A.Buchanan, 2021-01-21 more...
2 - P1294321
Andrew Buchanan
www.anselan.com 2001
P1294321
(1+2)
Black to move. Last move?
R: 1. Kb8xSa8
play all play one stop play next play all
Compare P0001033.
Gerald Ettl: steht der sLh5 vielleicht auf h2 ?? (2023-07-02)
SCHRECKE: Why not R: Kb8xLa8? (2023-07-03)
Mario Richter: Wie "SCHRECKE" mit seiner Frage schon illustriert hat: mit dem sL auf h2 wäre das Problem inkorrekt, da neben R: 1. Kb8xSa8 auch R: 1. Kb8xLa8 als letzter Zug möglich gewesen wäre. Grund sind die etwas verwirrenden Dead-Reckoning-Regeln: mit sLh5 kann zuletzt nicht Kb8xLa8 geschehen sein, da in der Stellung wKb8 - sKb6 sLh5 sLa8 wegen der unzureichendes-Material-zum-Mattsetzen-Regel das Spiel schon in dieser Position beendet gewesen wäre, der wK als gar nicht mehr zur Ausführung eines Zuges geommen wäre ... (2023-07-03)
Mario Richter: Dear James, I suggest that you undo last change and put the black bishop back on h5! (2023-07-03)
A.Buchanan: There are 17 valid squares for the wB. Got to be on a light square for reasons given. Also it can't occupy or attack c8. And can't be attacking a8 because BTM. I think h5 selection was random, but could argue for any. (2023-07-04)
A.Buchanan: Or maybe bBa4, with which White by his last move avoided a completely sound #12. (2023-07-04)
Gerald Ettl: Dann waere es vielleicht ganz sinnvoll man schreibt die Bedingung unter das Diagramm. (2023-07-04)
A.Buchanan: Hi Gerald, it's not a condition, it's a FIDE rule since 1997, invented by a problemist who is also a rules committee member (Igor Vereschchagin) and approved by the rules committee (headed by FIDE Head International Arbiter Stewart Reuben), backed up by a WFCC convention since 2015 (Kjell Widlert & Michel Caillaud, responding to a request from some endgame studiers who understood that it was a real thing. Like 50M rule, it applies by default for retro problems. And the PDB keywords here give the game away anyway. If it was a forward stipulation, then I would indeed add a stipulation, e.g. P1208623. Please enjoy the madness that is DP rule :) P.S. I have found recently that it was really invented by Shakespeare. (2023-07-04)
Gerald Ettl: Ich spiele nicht nach den FIDE-Regel. (2023-07-04)
Olaf Jenkner: Allright.
https://www.skat-online.com/regeln-hilfe/regelwerk/internationale-skatordnung.html (2023-07-05)
comment
Keywords: Type B, Last Move? (KxS), Dead Position, Economy record (Last Move? Type B), Rex solus (W), Aristocrat, Miniature, Minimal
Genre: Retro
FEN: K7/8/1k6/7b/8/8/8/8
Reprints: Retros mailing list 20/02/2007
Input: A.Buchanan, 2015-01-07
Last update: James Malcom, 2023-07-03 more...
3 - P1324999
Andrew Buchanan
9v Problemas 12, p. 285, 10/2015
after Hauke Reddmann
P1324999
(2+2)
Illegal position.
White to move.
How does the game end?

Author's "Solution" from Problemas magazine [edited]:
"White has no move, and is not in check. But for stalemate to apply, and end the game, it basically requires that the move producing the position was legal (see Law A5.2a). Not only is the position illegal, but no legal last move exists, even from a previously illegal position! So we are stuck in some kind of limbo. The result can perhaps be described as “nearly stalemate”.
Hauke Reddmann described a position like this as “dividing by zero”. It's an exception to the general observation that one can continue to play chess if the wrong player is in check. It seems odd to insist that only the final move in a game has to be legal, but that’s what the rules do. And I think that’s as far down the rabbit hole as we should go today."
Not Thema Null, because set play does not already achieve the stipulation.
A.Buchanan: The forward rules can apply perfectly well to illegal positions (e.g. set play, where we never concern ourselves with the position's legality). But a lacuna comes where a position with no precursor position is delivering mate, stalemate or DP. A #0 should work as well as a #2. In all cases, the FIDE Laws currently require that the prior move (and only that move) be legal. The Law is about catching errors/cheating otb, so I think the Codex should ensure it does not get carried over to problem chess. This problem will then lose its point, but it will have served its purpose and it can be retired to Golden Age, much to Henrik's relief :) (2023-12-15)
comment
Keywords: Lese Majeste, Illegal position, Dead Position, Miniature
Genre: Retro
FEN: 8/8/8/8/8/nk6/P7/K7
Input: A.Buchanan, 2016-09-06
Last update: A.Buchanan, 2019-12-09 more...
4 - P1359492
Andrew Buchanan
17464 Die Schwalbe 291, p. 492, 06/2018
to Torsten Linß
P1359492
(2+4) C+
h#6
1. f3 Kg4 2. f2 Kf3 3. c1=L Ke2 4. f1=L+ Kd1 5. Lc4 Kxc1 6. La2 Lc3#
play all play one stop play next play all
See P1316696 and P1359493
Henrik Juel: Pg2 prevents cooks ending 5... Kxc2 6.La2 Lc3# (2019-01-12)
A.Buchanan: I just realized I chose the dedications of these two problems the right way round luckily: L for Linß and S for Schnoebelen :D (2019-01-12)
VL: Reprint: (2) Problemas 37, p.1232, 01/2022 (2022-01-23)
comment
Keywords: Minimal, Schnoebelen Theme (l), Prentos Theme (l), Ceriani-Frolkin Theme (l), Miniature, Promotion (ll)
Genre: h#
Computer test: Popeye WINDOWS98-32Bit-Version 3.77 (8192KB)
FEN: 8/8/8/7K/5p2/8/2pB2p1/k7
Input: Felber, Volker, 2019-01-12
Last update: A.Buchanan, 2021-01-21 more...
5 - P1359493
Andrew Buchanan
17465 Die Schwalbe 291, p. 492, 06/2018
to Philippe Schnoebelen
P1359493
(2+4) C+
h#6
1. c1=S Lxe7 2. d3 Kf2 3. d2 Ke3 4. d1=L Kd2 5. Lb3 Kxc1 6. La2 Lf6#
play all play one stop play next play all
See P1316696 and P1359492
And see P1375440 for a fairy version
Mario Richter: Henrik wrote: "The term Schnoebelen theme first was used in proof games".

Even if it's like fighting against windmills, "Schnoebelen promotions" were *NOT* first used in proof games, but in orthodox retros. Ceriani invented the theme in 1948, maybe even before Philippe was born!
See my post in the Retros Mailig List:
https://pairlist1.pair.net/pipermail/retros/2008-December/002752.html (2019-01-13)
VL: Reprint: (3) Problemas 37, p.1232, 01/2022 (2022-01-23)
more ...
comment
Keywords: Minimal, Promotion key (s), Schnoebelen Theme (s), Prentos Theme (s), Ceriani-Frolkin Theme (s), Miniature, Promotion (sl)
Genre: h#
Computer test: Popeye WINDOWS98-32Bit-Version 3.77 (8192KB)
FEN: 8/4p3/5B2/8/3p4/8/2p5/k5K1
Input: Felber, Volker, 2019-01-12
Last update: A.Buchanan, 2021-01-21 more...
6 - P1368554
Andrew Buchanan
OzProblems.com 16/10/2019
P1368554
(4+3) C+
Gewinn
1. Sd3! Kf8 2. Se3 Sg6+ 3. Kd4 Td8+ 4. Kc3 Tc8+ 5. Sc4 Kg7 6. Sf2 Sh8 7. Tf1 Sf7 8. Se4 Td8 9. Sf6 Sg5 10. Se3 Ta8 11. Kb4 Tb8+ 12. Kc4 Tc8+ 13. Kb5 Tb8+ 14. Kc6 Ta8 15. Sfd5 Ta3 16. Kb5 Se4 17. Te1 Sg5 18. Kb4 Ta2 19. Tf1 Kg6 20. Tf6+ Kh5 21. Kb3 Ta7 22. Sf4+ Kh4 23. Se2 Tb7+ 24. Kc4 Sf7 25. Tf1 Kg5 26. Sd4 Se5+ 27. Kd5 Sd3 28. Se6+ Kg6 29. Sf8+ Kg5 30. Ke4 Sc5+ 31. Kd4 Sd7 32. Se6+ Kg6 33. Sd5 Ta7 34. Se7+ Kh5 35. Tg1 Ta4+ 36. Ke3 Tg4 37. Ta1 Sb6 38. Kf2 Sd7 39. Ta8 Tc4 40. Tg8 Tc2+ 41. Ke3 Tc3+ 42. Kf4 Tc4+ 43. Kf5 Kh4 44. Sf4 Sf6 45. Tg2 (thr 46.Sg6#) Tc5+ 46. Kxf6 Tc6+ 47. Kf5 Tc5+ 48. Sed5 (thr 49.Tg4#) Txd5+ 49. Sxd5 (switch to Syzygy DTM) Kh3 50. Sf4+ Kh4 51. Tg4#
Compare 44. ... Tc5+ which gives a longer DTM at the cost of a slightly sub-optimal DTZ. 45. Sed5 (thr 46.Tg4#) Txd5+ 46. Sxd5 (switch to Syzygy DTM) Kh3 47. Tc8 Kg3 48. Ke6 Sb6 49. Sxb6 Kf2 50. Sc4 Ke1 51. Td8 Ke2 52. Td2+ Ke1 53. Kd5 Kf1 54. Ke4 Kg1 55. Kf3 Kh1 56. Kg3 Kg1 57. Td1#
play all play one stop play next play all
According to the Syzygy tablebase, *any* move wins for White except the silly 1. Sa2??
However, the tablebase does not know about castling!
The quickest winning move 1. Sd3!? would be defeated by 1. ... 0-0-0!? which attacks Sd3 and threatens the skewer Re8+. After this, White can only draw - or even loses after 2. Sc1??
But by a simple retro argument, Black cannot castle.
Since this retro point is essential to the solution, we have a retro problem, and hence the 50 move rule, which by Codex default is disengaged, is switched on.
When working with the 50 move rule, the key concept is not the number of moves to mate, but the number of moves to the first capture, pawn move or checkmate, known as DTZ.
All the alternatives to 1. Sd3 take more than 50 moves to force the first capture. The closest are 1. Sc3 & Se3 which according to Syzygy require exactly 50.5 moves, so seem *just* too slow. (For positions close to the cut-off, one has to be careful about *rounding*, see https://syzygy-tables.info/metrics. The number of half-moves for DTZ can be n or n+1. In fact here, after 1. Sc3/Sf3, the zeroing move is at its earliest White's 52nd move, not 51st.)
By the retro property therefore *only* 1. Sd3!, which requires 45 moves to force the first capture, can win. So this removes all the cooks for the first White move.

Lomonosov DTM #59: 1. Nd3!! Kf8!! 2. Ne3! Ng6+! 3. Kd5 Rd8+ 4. Kc4 Rc8+ 5. Kb5 Rb8+ 6. Ka6 Kf7 7. Nc5 Ne5 8. Nd5 Re8 9. Kb7 Nc4 10. Rf1+ Kg7 11. Kc6 Re5 12. Nd3 Re6+ 13. Kc5 Ne5 14. N3f4 Nd7+ 15. Kb5 Rd6 16. Nc7 Kf7 17. Nfd5+ Kg6 18. Ne7+ Kg5 19. Ncd5 Kg4 20. Rf4+ Kg5 21. Rf2 Kg4 22. Ne3+ Kg5 23. N7d5 Kg6 24. Rf1 Nf6 25. Nf4+ Kf7 26. Nc4 Rd8 27. Ne5+ Kg8 28. Rg1+ Kh7 29. Kc6 Rc8+ 30. Kd6 Re8 31. Re1 Ra8 32. Rh1+ Kg8 33. Ke7 Ra4 34. Rg1+ Kh7 35. Ne6 Nd5+ 36. Kd6 Nf4 37. Nc5 Rd4+ 38. Ke7 Rd2 39. Rg4 Rf2 40. Ncd7 Nd5+ 41. Ke6 Nf4+ 42. Kd6 Rd2+ 43. Ke7 Nd5+ 44. Kf8 Kh6 45. Rh4+ Kg5 46. Nf3+ Kf5 47. Nxd2 (zeroing 50M) Nc7 48. Re4 Ne6+ 49. Ke7 Nf4 50. Nf6 Ng6+ 51. Kf7 Ne5+ 52. Kg7 Kg5 53. Nf1 Kf5 54. Ne3+ Ke6 55. Nc4 Ke7 56. Rxe5+ Kd8 57. Rc5 Ke7 58. Rd5 Ke6 59. Re5# 1-0.
http://www.ozproblems.com/walkabout/walkabout2019#WA1610
https://www.chess.com/blog/Rocky64/a-heraldic-endgame-tablebase-composition

The school shield which inspired the problem:
http://www.calvert-trust.org.uk/images/colour.jpg
Henrik Juel: With White to move, last move was made with Ta8 or Ke8, so Black may not castle
An endgame connaisseur may supply the solution... (2019-10-25)
James Malcom: It is now supplied, Henrik. :) I worked through the Sygyzy tablebase, move by move, to get the computer recommended line. (2020-10-09)
A.Buchanan: Thanks James for this hard work to record a solution. Alas there is not just a single recommended line - White has a choice as early as W3. I wonder too if there is a DTM line which is faster than #57, and still clears the DTZ hurdle although maybe not as quickly as B45 as here. There is no DTM engines for 7 pieces yet.
What is certain is that the key works, and is unique. The exactly details of the best mating line remain to be revealed by improving technology. (2020-10-09)
A.Buchanan: For example, 2. Nc5 has DTZ 90, compared to the "superior" 2. Ne3 DTZ 88. However, if you keep picking the top move all the way through, then the final DTZ is in fact checkmate! I haven't all the Black choices though, but there aren't that many of them (2020-10-09)
A.Buchanan: The Lomonosov tablebase is DTM, and is available for free on Android. Today I found a PC app called Blue Stacks which emulates Android. According to Lomonosov, the position is #59, compared to Syzygy's DTZ offering #57 via zero at B45. When I run through the L. indicative solution (very quick to download and grab all of it), it is close to S.'s choices and all the mainline positions are safe from 50M. The zero is at W47, and the final mate is attractive in the middle of the board.
The real questions are:
(1) Is the #59 sound from 50M perspective? Or can Black force White to delay a few moves in order to avoid 50M trouble somewhere?
(2) How dualized is the solution? How does 50M play into pruning that?
What is clear is that both tablebases agree the solution begins 1. Nd3!! Kf8!! 2. Ne3! Ng6! (2020-10-10)
A.Buchanan: James' Syzygy solution had seemed a little odd, because it seemed to go against Syzygy's assertion that DTZ=n means that zeroing happens at n or n+1 ply (it's not exact because of Syzygy's rounding of the units bit of the integers, which apparently saves a vast amount of data, and is allegedly "safe"). But James's solution has zeroing at n-1. If Black was indeed forced to zero prematurely in this way, this would show a bug in Syzygy.

In no sense is this a criticism of James: for whose talent, hard work & existence I am incredibly grateful. But it turns out there is a tiny issue in the solution he posted, just before DTZ=0.

Quarantine lockdown in Hong Kong has given me a chance to look at the position after W44, https://syzygy-tables.info/?fen=6R1/3nN3/8/5K2/2r2N1k/8/8/8_b_-_-_0_1, Black has two choices Tc5+ & Sf6. James chose the first for simplicity, as sensibly he always did, but 45. Sed5 threatens 46. Tg4#. The only way to avoid this 45. ... Txd5+ prematurely zeroing. But Syzygy makes no promises about DTM - it just happens that the random path that James found has mate as the zeroing move! This is not typical, so a better illustrative solution has 44. ... Sf6. With best play by both sides, I think this results in mate at W51.

How to compare this with the Lomonosov solution with mate at W59? How is it possible that Syzygy, with the extra constraint of avoiding 50M draw, has found a *shorter* mate? If you think about it, there is no issue here. Syzygy is only focusing on DTZ, and there are many points in the long solution at which there are choices of equal DTZ. What Lomonosov tells us is that Black can somehow force a Syzygy branch which gives #59 or longer. For 6 or 7 pieces, we just don't have the visibility in Syzygy to find that DTM path. That is the explanation. However for 5 pieces, Syzygy also gives us the DTM value, and as long as one has escaped 50M range, it makes case to switch to that as soon as 5 pieces are reached. (2022-08-05)
A.Buchanan: As problemists, what we would really like to know is the minimum number of moves to mate, while not falling foul of 50M. Even with both DTZ & DTM values known, this is not easy to find. Here is a toy example to show one difficulty: https://syzygy-tables.info/?fen=7k/8/7K/4P2R/8/8/8/8_b_-_-_0_1 Black's forced move leads to DTZ=1 DTM=3, but White must choose which he wants to achieve, as they are mutually exclusive. If the 50M clock is low, 1.e6 gives DTM=16. But otherwise 1.Rf5 gives DTM=2. Now White will know which he wants, but Black is usually free to decide whether to defend the DTZ or the DTM or potentially to delay the commitment. The tactical richness of a position is not captured by simply the DTZ & DTM values (2022-08-05)
A.Buchanan: OK it turns out that what I'd been arguing for already exists to some extent: it's called DTM50 - see http://galen.metapath.org/egtb50/ (2022-08-05)
comment
Keywords: Cant Castler, Aristocrat, 50 move rule, Miniature
Genre: Retro, Studies
Computer test: www.syzygy.com
FEN: r3k2n/8/8/4K3/8/8/8/2NNR3
Reprints: www.chess.com 17/10/2019
Input: A.Buchanan, 2019-10-25
Last update: A.Buchanan, 2022-08-05 more...
7 - P1375440
Andrew Buchanan
17465v Die Schwalbe 291, p. 492, 06/2018
to Rewan Demontay
P1375440
(3+4) C+
h#6
White Dummy f2
1. c1=DU Lxe7 2. d3 Kf1 3. d2 Ke2 4. d1=L Kd2 5. Lb3 Kxc1 6. La2 Lf6#
play all play one stop play next play all
Added 1 Dummy to P1359493, and changed the dedicatee. My luck with this little series continues to hold: the dedicatee's surname begins with a D!
James Malcom: Andrew, I just found this today-I thank you very much, but perhaps it holds no more, for my true name is known now! (2020-10-28)
comment
Keywords: Miniature, Promotion key (du), Schnoebelen Theme (du), Prentos Theme (du), Ceriani-Frolkin Theme (du), Promotion (du,l)
Pieces: i = Dummy (DU)
Genre: h#, Fairies
Computer test: Popeye 4.81
FEN: 8/4p3/5B2/8/3p4/8/2p2I2/k5K1
Input: A.Buchanan, 2020-05-03
Last update: A.Buchanan, 2021-05-01 more...
8 - P1379502
Andrew Buchanan
1127 Julias Fairies 19/09/2016
P1379502
(2+2) C+
h=3
Chess4E71
1. h1 Kf2 2. Kh3 Sf7 3. Kh2 Sg5=
play all play one stop play next play all
Author's solution: Schema problem to show the idea. At first glance, h=3 seems completely impossible, even without the confusing fact that Black to move is apparently checking White. But this absurdity is what renders the problem solvable.

Law A1.2 tells us that if the player to move is already apparently checking or even checkmating the opposing king, then he is not allowed to capture that king, and must make another move. The assessment whether the opponent is actually checked or mated is made only when the opponent has the move. In normal chess, such a position is illegal, but it is no more and no less illegal than say wBa1 wPb2. Law A1.2, tells us that we can still play chess. (See Lese Majeste)

In Chess4E71 such "illegal" checks can clearly occur, but only in the starting position. Therefore no moves have been made in the game so far. In particular, bPh3 has never moved. Now Article 3.7b of the Laws of Chess says: "on its first move the pawn [...] may advance two squares along the same file, provided that both squares are unoccupied. So 1. h3-h1! is legal.

Now what happens to the pawn when it arrives on h1? Again we consult the Laws. Article 3.7e says: "When a player, having the move, plays a pawn to the rank furthest from its starting position, he must exchange that pawn as part of the same move for a new queen, rook, bishop or knight of the same colour on the intended square of arrival." The pawn began on the 3rd rank, so it would only promote when it reaches the furthest rank, namely the 8th rank (which it never can attain, under orthodox rules, but that's irrelevant). When it arrives on the 1st rank, it merely remains a pawn. I can almost hear the groans :-)

The rest of the problem solves itself. Or an engine does.

The recognition that BTM is delivering check in what must be the starting position is hardly retro reasoning, so the Article 17A bell does not sound to awake the demon of the Dead Position rule from his slumbers. Hence with a forward stipulation, we don't worry that there is no mate possible after B1 move.
Henrik Juel: groan (2020-08-30)
A.Buchanan: Hark, what’s that I hear? :-) (2020-08-31)
James Malcom: Hark, I hear the angels groan! Oh snark, I head their echos spawn!:-) (2020-08-31)
A.Buchanan: Jacobi does not yet support dummy pawns, alas (2021-05-11)
more ...
comment
Keywords: Chess4E71, Lese Majeste, Dummy Pawn, Minimal, Miniature, Dead Position (not!), Golden Age (Dummy Pawn)
Genre: Fairies
Computer test: HC+ Popeye v4.87. No solution in diagram position for h#3 & 1 solution after key as h#2.5. Only other solution might be if B2 or B3 is h1 without promotion. But bK can only be without a move if in corner or adjacent to bP, which cannot happen after 1. Kg5,Kh5?
FEN: 8/8/7N/8/7k/7p/6K1/8
Input: A.Buchanan, 2020-08-30
Last update: A.Buchanan, 2023-08-04 more...
9 - P1384899
Andrew Buchanan
Facebook 03/01/2021
motto = "God save the queen!"
P1384899
(2+3) C+
h#3.5
1. ... Lc8 2. Ke8 Kf5 3. Df8+ Ke6 4. Ld8 Ld7#
play all play one stop play next play all
After I posted the meme https://knowyourmeme.com/photos/1459595-queen-elizabeth-chess-moves in Chess Studies and Composition group in Facebook, I was asked to augment it with a composition. So I added three pieces, but kept the spatial relationship between Her Majesty and some (arch)bishop I don't recognize. However an earlier version https://knowyourmeme.com/photos/1459589-queen-elizabeth-chess-moves shows that someone j'adoubed the board! (It's probably treason to j'adoube the queen herself.)
Henrik Juel: C+ Popeye 4.61 (2021-01-03)
comment
Keywords: Aristocrat, Minimal (L), Miniature, Ideal mate, Parody (QE2)
Genre: h#
Computer test: C+ Popeye 4.61
FEN: 8/4k3/3q4/5Bb1/4K3/8/8/8
Input: A.Buchanan, 2021-01-03
Last update: A.Buchanan, 2022-01-31 more...
10 - P1389166
Andrew Buchanan
Retros mailing list 12/12/2012
P1389166
(2+1) C+
#3
b) Capture the King: win in 2 moves
a) 1. Kf6 Kh7 2. f8=T Kh6 3. Th8#
b) 1. Kg6 Kg8 2. fxg8=D,T,L,S
1. ... Kg7,Kh7 2. Kxg7,Kxh7
play all play one stop play next play all

Duplicate Diagram: P1013439

zu a) s. z.B. P1133499
Henrik Juel: part a) is C+ Popeye 4.61
1.Kf6 Kh7 2.f8=T Kh6 3.Th8#
part b) is damaged by a promotion dual...
1.Kg6 Kg8 2.fxg8=DTLS, 1... Kg7,Kh7 2.KxK (2021-05-02)
A.Buchanan: The point about promotion dual hadn't occurred to me: interesting! On reflection, I think it's like the tolerated dual in regular chess, where if the mating move is =Q/R or =Q/B that's ok, because it would be unreasonable to exclude from soundness all promotion mates where the mated king is not very near to the promoted unit. Similarly here, the promotion captures the opposing king, so the promotion choice is academic. Nevertheless, we would not wish to render unsound *all* king-capturing promotion moves, so we need a tolerated dual! Ground-breaking! :D Thanks so much (2021-05-02)
SP: Herr Buchanan: You are not claiming to have composed part (a), are you?
It has been published by several others. (2023-01-08)
A.Buchanan: The contrast between the two win conditions is the entire point. However this must be represented using the a)&b) notation, which gives the impression that each twin is separate. The composition was just a self-published schema anyway, so who cares? (2023-01-09)
comment
Keywords: Capture the King, Kindergarten Problem, Minimal, Miniature, Tolerated dual promotion (DTLS)
Genre: 2#, 3#, Fairies
Computer test: HC+ Popeye 4.61 part a ok part b has "tolerated dual" for Capture the King stip :-)
FEN: 7k/5P2/8/5K2/8/8/8/8
Reprints: chess.stackexchange.com 2/5/2018
Discord Chess Problems & Studies Server 2/5/2021
Input: A.Buchanan, 2021-05-02
Last update: Mario Richter, 2023-01-09 more...
11 - P1394484
Andrew Buchanan
A The Problemist Supplement 174, p. 182, 09/2021
Motto="U for Uplex"
P1394484
(4+3) C+
h#2.5 Duplex
w) 1. a2 a6 2. Ka3 Ta5#
s) 1. b2 Td5 2. b1=D Td3 3. Db2#
play all play one stop play next play all
BTM in both twins.
Numerous retro tries but none distinct in the retro twin w).
AB: Duplex means that there is a twin where B/W roles are reversed. If we can deduce who must have the move then, e.g. in a helpmate, one of those twins will lose the first single move. So here it's Black to move, and the twins are BWBWB# (Black checkmating White) and BWBW# (White checkmating Black). "Uplex" is not a Fairy Condition - it's just an identifier of an obvious idea for retro-active compositions, which curiously hasn't been explored before, as far as Geoff Foster and I can see.
Henrik Juel: Thanks for the explanation, Andrew
Here Black has no last move, so he has the move
1.b2 Td5 2.b1=D Td3 3.Db2#
1.a2 a6 2.Ka3 Ta5#
C+ Popeye 4.61 (using 'sti h#2.5 opt hal' and 'sti h#2') (2021-10-09)
comment
Keywords: No legal last move for Black, Miniature, Character problem (U)
Genre: h#, Retro
Computer test: HC+ Last move analysis + Popeye 4.61
FEN: 8/8/8/P1R5/k1P5/ppK5/8/8
Input: A.Buchanan, 2021-10-08
Last update: A.Buchanan, 2023-12-06 more...
12 - P1394490
Ayrton Twigg
Andrew Buchanan

Discord Chess Problems & Studies Server 10/05/2021
P1394490
(4+3) C+
h#4
1. La4 Lh7 2. Ld1 Tg6 3. Ke4 e3 4. Lf3 Te6#
play all play one stop play next play all
Henrik Juel: C+ Popeye 4.61
1.La4 Lh7 2.Ld1 Tg6 3.Ke4 e3 4.Lf3 Te6#
Very nice (2021-10-09)
comment
Keywords: Miniature, Tempo Move (l), Indian, Model mate
Genre: h#
Computer test: C+ Popeye 4.61
FEN: K7/8/4R3/3p4/5k2/1b6/4P3/1B6
Input: A.Buchanan, 2021-10-09
Last update: A.Buchanan, 2023-05-08 more...
13 - P1398666
James Malcom
Michael Schreckenbach
Andrew Buchanan

PDB Website 26/01/2022
P1398666
(4+3) C+
h#2 (-:
1. g1=B Lf3 2. e1=B Te2#
play all play one stop play next play all
AB: economy record for 2 Dummy Pawns in h#. Miniature. Aimless promotion.
Henrik Juel: wPg3 prevents cooks like 1.Kg1 Kg3 2.e1=DTLSB Txe1# (2022-01-27)
more ...
comment
Keywords: Dummy Pawn, Golden Age (Dummy Pawn), Miniature, Tempo Move (Promotion)
Genre: h#
Computer test: C+ Popeye 4.79
FEN: 8/8/8/8/4R2K/6P1/4p1pk/7B
Input: A.Buchanan, 2022-01-27
Last update: A.Buchanan, 2023-08-04 more...
14 - P1399588
Andrew Buchanan
12625 feenschach 246, p. 184, 07-09/2021
to Erich Bartel
P1399588
(3+2) C+
Illegal position.
White to move and #3*
*) Null-Satz!
1. Ke7+ Ke5 2. De3 Kd5/Kf5 3. Dc5/Dg5#
play all play one stop play next play all
Henrik Juel: There may be some lazy slobs, who cannot be bothered to read and understand the general descriptions of these weird themes
They would appreciate it, if you would explain everything in plain language in the context of this rather simple-looking problem, Andrew (2022-03-02)
A.Buchanan: Thank you for your interest in Lese Majeste, Henrik :)
(1) In an illegal position, the usual forward rules of chess usually still work.
(2) Under the Codex, illegality of position does not prevent a position from being sound.
(3) Capturing the king is never a legal move.
(4) Popeye & Jacobi engines support this.
(5) Such problems are not unsound, fairy, joke or retro.
So go for it! :) (2022-03-03)
Henrik Juel: I spent all morning trying to install Popeye 4.87
Finally it works, I had forgotten 'begin' in the input file...
1.Ke7+ Ke5 2.De3 Kd5/Kf5 3.Dc5/Dg5#
Once you see the solution, it is so obvious; you even provided the Oneliner hint
The diagram position is an ideal mate, but the two solution mates are not even model mates (2022-03-03)
A.Buchanan: Yes I couldn't get these mates model. (2022-03-04)
more ...
comment
Keywords: Lese Majeste, Illegal position, Aristocrat, Miniature, Minimal, Thema Null, Model mate (1), Ideal mate (1), Oneliner (Delayed)
Genre: 3#
Computer test: C+ Popeye 4.87
FEN: 8/8/4NK2/8/3kb3/1Q6/8/8
Reprints: Discord Chess Problems & Studies Server 02/03/2022
Input: A.Buchanan, 2022-03-02
Last update: A.Buchanan, 2022-03-04 more...
15 - P1401567
Andrew Buchanan
Discord Chess Problems & Studies Server 31/05/2022
P1401567
(4+1)
ser-h#n
How many solutions, including all shorter ones!
(ignore draw by repetition & 50 move rule)
1. Kh8 Dh6#
1. Kf8 2. Ke8 Tg8#
1. Kf8 2. Ke8 3. Kd8 Tg8#
1. Kf8 2. Ke8 3. Kd8,Kf8 4. Ke8 Tg8#

play all play one stop play next play all
Solutions in exactly:
1,1,1,2,3,5…
Solutions in up to n:
1,2,3,5,8,13…
and both sequences seem to be more-or-less Fibonacci. What’s going on?

Let's look at something apparently irrelevant: Peg Solitaire (aka Conway's Soldiers). https://en.wikipedia.org/wiki/Peg_solitaire

In this, a peg hops 2 squares orthogonally, capturing the mandatory hurdle. (Is there a fairy chess piece with this movement?) Imagine a long line of them. e.g.
.1234567890abcde.

(We put a space at each end to show the termination.) Split them conceptually into two alternating lines:
.1.3.5.7.9.a.c.e.
&
..2.4.6.8.0.b.d..

No captures can be made, but if we "borrow" one additional peg on the left of each line:
*1.3.5.7.9.a.c.e.
&
.*2.4.6.8.0.b.d..

then these two pegs can hop over all the other pegs in their lines:
................f
&
...............e.

Then combining them again, e can capture f:
.................g

Fibonacci numbers behave exactly the same way when you add them! There is a capturing rule: f(n) = f(n-1) + f(n-2). Then:
sum(k=1...n-1)f(k) = f(n+1) - f(0) - f(1)

The two correction terms correspond to the "*" terms that we added on the left in order to get the cascade started!

So back to chess. Ignoring for now the odd solution with n=1, the number of ser-h#n in EXACTLY n moves is f(n-1), where f(k) is the kth fibonacci number 1,1,2,3,5,8,13,21,34...

[This comes from bK being able to occupy just 4 squares.
A(n) is the number of ways to reach d8 or e8 in n moves, B(n) is the number of ways to reach c8 or f8.
A(n+1) = A(n)+B(n)
B(n+1) = A(n)
You can see that this formula is just the "capturing rule" again.
And to get started: A(1)=0,B(1)=1.
So A(n)=B(n+1)=f(n-1).]

To find all the solutions in UP TO n moves, we need to sum them together:
sum(k=1...n-1)f(k) = f(n+1) - f(0) - f(1)

f(0)+f(1) is just 0+1=1. So this is why we need the extra solution with bKh8.

"Summing it all up", the number of ser-h#n is just f(n+1).

Noam's earlier setting https://pdb.dieschwalbe.de/P1243505 is the first afaik to show the whole Fibonacci sequence, and is one of two he published with the 4-chain (see also P1243525). This problem also uses a 4-chain as the easiest way to get Fib going, but (1) concentrates the mates onto just 2 of the 4 squares in the chain, (2) tots up the cumulative sum from 1 to n, and (3) exploits the curious diversion to h8. And is a seriesmover, as there's not much interest in the two-sided play.

The earlier https://pdb.dieschwalbe.de/P1259074 was the first I think to show a Fibonacci number.

What happens if the BK has more than the 4 free squares? There is a sneaky trick to get the answer quickly: instead of an n-chain, consider a (2n+2)-cycle:

x-x-x-x-x-x =>

x-x-x-x-x-x
|...............|
x..............x
|...............|
x-x-x-x-x-x

n-cycles are more symmetric than n-chains, so easier to analyze.

Counting paths in a graph systematically involves finding the "resonances", termed eigenvalues, which for a graph are always real numbers. The long-term growth rate in the number of paths is dominated by the eigenvalues with largest magnitude. It turns out that the eigenvalues of n-chain & (2n+2)-cycle are mostly the same! The dominant eigenvalues of the (2n+2)-cycle are +-1, but those are the only ones which *don't* carry over to the n-chain. The other eigenvalues are 2*cos(j*pi/(n+1)) for j=1..n, and they *do* carry over. The largest are where j=1 or n, and have opposite sign. We can ignore the sign from the perspective of the overall growth rate, but it's this sign that gives the "parity" in the n-chain paths: they either have odd or even length.

So the growth rate of an n-chain is 2*cos(pi/(n+1)). This "explains" why the golden ratio (which contains _/5) is the growth rate when n=4, which doesn't seem to have anything to do with 5.

Here's a few values of growth rates from n=1 upwards:
1-chain: 0 (no movement can happen)
2-chain: 1 (just deterministic pendulum)
3-chain: _/2 ~= 1.4142
4-chain: golden ratio = (1+_/5)/2 ~= 1.618
5-chain: _/3 ~= 1.7321
6-chain: ~= 1.8019
7-chain: ~= 1.8477
etc.

Some other random observations. As n increases, so does the growth rate, but it will always be less than 2 because the n-chain is a subgraph of the n-cycle (just missing 1 edge), and the n-cycle always has a growth rate of 2. The growth rate increases with n, because the missing edge is increasingly negligible. There is also a recursive formula for the polynomial of degree n, p_n(t) which contain the eigenvalues as roots:
p_n = - t*p_(n-1) - p_(n-2)
which is reminiscent of both Fibonacci & Pascal, although is more general.
Previous problems of this kind were "exact", excluding short solutions. Here's one where, for a given n, you need to tot up *all* the solutions with m less than or equal to n into a nice sum.
Henrik Juel: n=1, 1.Kh8 Dh6#, total t=1
n=2, 1.Kf8 2.Ke8 Tg8#, t=2
n=3, 1.Kf8 2.Ke8 3.Kd8 Tg8#, t=3
n=4, t=5
After this it gets a little hairy, but Andrew will give the nice sum next week... (2022-06-03)
A.Buchanan: Nice sum supplied :) (2022-06-08)
Henrik Juel: Thanks, Andrew
So the nice sum is t=f(n+1), where f are the Fibonacci numbers given by
f(1)=f(2)=1, f(n)=f(n-1)+f(n-2) for n=3,4,..
n 1 2 3 4 5 6
f 1 1 2 3 5 8
t 1 2 3 5 8 (2022-06-08)
more ...
comment
Keywords: Path enumeration (Fibonacci), Aristocrat, Miniature, Rex solus (s)
Genre: Fairies, Mathematics
FEN: 6k1/6R1/N3K3/8/8/4Q3/8/8
Reprints: MatPlus.net Forum 31/05/2022
Input: A.Buchanan, 2022-06-02
Last update: A.Buchanan, 2022-06-08 more...
16 - P1401711
Andrew Buchanan
OP008 The Hopper Magazine I01 24/12/2021
"Ak ja, retten, retten; hvad hjælper det, at du har retten, når du ikke har nogen magt?"
P1401711
(3+3) C+
h#2.5 (2 solutions)
Position after Black's 5,696th move
1. ... Se6 2. Th2 Ta8 3. Th7 Txe8#
1. ... Txa2 2. Lg6 Tg2 3. Lh7 Sf7#
not 1. ... 0-0-0 2. Lg6 Tg1 3. Lh7 Sf7#?? (game just ended by 50M)
play all play one stop play next play all
A full solution is really too big for PDB, but it is available at https://www.thehoppermagazine.com/AA084
Henrik Juel: solutions
1...Sg5-e6 2.Ra2-h2 Ra1-a8 3.Rh2-h7 Ra8*e8 #
1...Ra1*a2 2.Be8-g6 Ra2-g2 3.Bg6-h7 Sg5-f7 #
not 1...0-0-0? 2.Be8-g6 Rd1-g1 3.Bg6-h7 Sg5-f7 #
because White has lost his right to castle, as Andrew will explain, I hope... (2023-07-29)
A.Buchanan: White has not necessarily lost the right to castle, but if he can castle then the 50M rule triggers before the mate can be executed. It is pretty complicated, sorry. (2023-07-29)
A.Buchanan: We don't do mottoes much these days. Mrs Baird was a big fan. On page 301 of the July 1916 Chess Amateur P.H. Williams wrote:
"I think it was Mrs Baird who did more to search Shakespeare for accidental (or deliberate) reference to chess, since all her retractors had Shakespearean mottoes, and her knowledge of the Avonian bard was obviously extensive. Her example was followed by other composers of retractors, who considered such positions would be incomplete without some reference to the poet."
But there are other great playwrights, and Asteroid 5696 was named after one such, whose bitter quotation accurately states this problem's theme. (2023-07-31)
Henrik Juel: The citation is by danish philosopher Søren Kierkegaard (1813-1855) and means something like
Oh yes, to be right, to be right; it does not help much that you are right, when you have no power. (2023-07-31)
Henrik Juel: Asteroid 5696 is named Ibsen after the norwegian playwright Henrik Ibsen (1828-1906), who must have borrowed the citation from Søren Kierkegaard (2023-07-31)
A.Buchanan: Thanks for this Henrik - I resolved the question here: https://philosophy.stackexchange.com/questions/101229/did-ibsen-originate-this-statement
Beyond the castling try, the other innovation here is in the solution beginning 1...Se6. Castling convention and 50M I think are trying to combine by Retro Strategy (being optimistic about 50M rights like we are with castling, rather than pessimistic like we are with ep). (2023-08-04)
more ...
comment
Keywords: Aristocrat, Miniature, 50 move rule, Castling, Exchange of roles (T/S, Guard/Mate), Chumakov theme (l/t, simplified), Retro Strategy (RS), Model mate (2), Constrained problem
Genre: h#, Retro
Computer test: HC+ Popeye 4.61 and analysis
FEN: 4b2k/8/8/6N1/8/8/r7/R3K3
Reprints: AA084 The Hopper Magazine I04 13/07/2023
Input: A.Buchanan, 2022-06-09
Last update: A.Buchanan, 2023-08-27 more...
17 - P1407481
ChatGPT
Andrew Buchanan

Discord Chess Problems & Studies Server 29/01/2023
P1407481
(2+2)
#2
1. bxa3+ Kd4 2. Kb2#
play all play one stop play next play all
Chess problem by AI program ChatGPT

Q: Can you give an example of a chess retrograde analysis problem?

A: A retrograde analysis problem in chess is a problem where the goal is to determine the sequence of moves that led to a given position. For example:

White to move and mate in 2
[FEN "8/8/1p6/1P6/3k4/8/8/K7 w - - 0 1"]

In this problem, the goal is to determine the two moves (one for white and one for black) that led to the position shown. The solution is 1. bxa3+ Kd4 2. Kb2#
Henrik Juel: I do not understand this at all
It seems that ChatGPT is worthless for retro problems (2023-01-29)
A.Buchanan: Generally ChatGPT is amazing. We have entered a new age. Interacting with it reminds me of the first time I sent emails, or used a browser: we have crossed a frontier into engage with a function that will soon be commonplace. I already use it as a work tool for the last week. However it has limited skills and I was surprised it even attempted to construct a chess problem. It’s failure is humorous and kind of dreamlike (2023-01-30)
Henrik Juel: Thanks for your clarification, Andrew
ChatGPT is so amazing that it will give you a grade of B on some university exams; using it is obviously cheating, but do you enforce it?
In my youth calculators were developing fast; initially I banned the use of calculators in my OR exam, but the students were unhappy about it, saying that they were allowed in high school; I was forced to allow calculators, but then the poor students pointed out that the rich students had an unfair advantage; I then bought a few hundred cheap calculators and let the students borrow one for the exam (the rich students were still mad, but had to accept their lot in the social-democratic society of Danmark) (2023-01-30)
comment
Keywords: Joke, Kindergarten Problem, Minimal, Miniature
Genre: 2#, Retro
FEN: 8/8/1p6/1P6/3k4/8/8/K7
Reprints: Facebook 05/07/2023
Input: A.Buchanan, 2023-01-29
Last update: A.Buchanan, 2023-07-05 more...
18 - P1411220
Andrew Buchanan
chess.stackexchange.com 25/07/2023
P1411220
(3+3)
Draw
(White is in desperate time trouble, see FIDE Law 6.9)
1. g8=L+! & Dg7+ 2. Dxg7# is forced
1. g8=D+? & Dg7+ & can have 2. Dgxg7+ Ke6 & Black can still win
(1.g8=T+,g8=S+,Df8+ are also uncertain)
play all play one stop play next play all
Henrik Juel: White seems to win easily with 1.g8=S+ Ke6,Kf7 2.Sxe7 (2023-07-25)
Joost de Heer: Henrik, white loses on time in that try.
The only way to force an draw is 1. g8=B! and even if white can't finish the forced moves 1... Qg7 2. Qg7# he at least has a draw since black can't possibly win anymore.
1. g8=Q? doesn't lead to a half-dead position (1... Qg7 2. Qgxg7 and black still has moves), so white would lose on time.

@Andrew: Shouldn't the stipulation be 'at least draw'? (2023-07-26)
A.Buchanan: @Joost - could be. Can also think that the stip asks for the minimum White can guarantee (2023-08-09)
comment
Keywords: Dead Position (half-dead), Miniature
Genre: Studies
FEN: 7Q/4q1P1/5k1K/5r2/8/8/8/8
Input: A.Buchanan, 2023-07-25
Last update: A.Buchanan, 2023-08-09 more...
19 - P1411234
Andrew Buchanan
GG004 Discord Chess Problems & Studies Server 24/09/2022
P1411234
(2+2) C+
h=DP in 1.0
1. c1=S g8=D+ (dp) 2. Kxg8=
play all play one stop play next play all
more ...
comment
Keywords: Dead Position, Help Dead Position, Kindergarten Problem, Minimal, Miniature
Genre: Fairies
Computer test: C+ deadpos v2.1 8-Jan-2024
FEN: 8/6Pk/8/6K1/8/8/2p5/8
Reprints: GG004 The Hopper Magazine I04 13/07/2023
Input: A.Buchanan, 2023-07-26
Last update: A.Buchanan, 2024-01-08 more...
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