2 problem(s) found in 3406 milliseconds (displaying 2 problem(s)). [COMMENTDATE>=20200919 AND NOT K='Hilfsrückzüger' AND K='50-Züge-Regel']

1. cxb6 d6 2. bxc5 Txb8#

1. La7 Lxa7 2. 0-0-0? Tb8#

Castling is impossible because, if black can still castle, the diagram position is draw due to the 50-move rule!

White captures: axb, bxc, exf. Black captures: hxg, gxf, exd, dxc. Promotions: a1=T, b1=T, h8=X. The position can only be unblocked by unpromoting White piece on h8. This can only be wRb5. wK must go to c6 to unpin wR. The journey is via g3, h2, e1, b2, & a3.The 50 white moves are: 34 by wK (screens on c8 [with careful step on a2 to let bB pass] then g8), 11 by wB6 (to e3 to exchange place with bB then screen on a7), 3 by wR (promotion on h8), 2 by wBa4.

1. La7 Lxa7 2. 0-0-0? Tb8#

Castling is impossible because, if black can still castle, the diagram position is draw due to the 50-move rule!

White captures: axb, bxc, exf. Black captures: hxg, gxf, exd, dxc. Promotions: a1=T, b1=T, h8=X. The position can only be unblocked by unpromoting White piece on h8. This can only be wRb5. wK must go to c6 to unpin wR. The journey is via g3, h2, e1, b2, & a3.The 50 white moves are: 34 by wK (screens on c8 [with careful step on a2 to let bB pass] then g8), 11 by wB6 (to e3 to exchange place with bB then screen on a7), 3 by wR (promotion on h8), 2 by wBa4.

**Keywords:**Non-standard material (tt), 50 move rule, Cant Castler

**Genre:**Retro, h#

**Computer test:**Popeye WINDOWS-32Bit-Version 3.65 (2048 KB) Popeye 4.61 (also)

**FEN:**rb2k3/2p2p1K/1B6/1RPP1PP1/B1Prbrp1/1Prp1p2/2p2P2/N7

**Reprints:**Probleemblad , p. 220-227, 12/2010

**Input:**Gerd Wilts, 2001-02-11

**Last update:**A.Buchanan, 2020-10-10 more...

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 Tc5+ 45. Sed5 Txd5+ 46. Sxd5 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#

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.

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

An endgame connaisseur may supply the solution... (2019-10-25)

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)

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)

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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 castleAn 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)

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**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, 2020-10-10 more...

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The problems of this query have been registered by the following contributors:

Gerd Wilts (1)A.Buchanan (1)

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