Faster Forced Mate

[MikeGL]

Hi!

For the mean time I think I saw an improvement on the above solution. Moves 10 to 16 of white is not necessary because white can directly play 10.Bc2+ then followed by 11.Kc1 or 11.Kd1 Δ 12.Kc1 depending on white whites replies. 88-6 = 82 moves

Had a little detour of that kind in my line at first too and deleted yesterdyay a posting about it again. 82 seems to be correct:

[pgn]
[Event "#82"]
[Site "Talkchess"]
[Date "2017.06.27"]
[Round "?"]
[White "Fabel, Karl"]
[Black "komodo0, Sting"]
[Result "1-0"]
[SetUp "1"]
[FEN "8/1p1p2p1/5p1p/5P1P/1p1p1P2/pP1P1P2/P1k1B3/4K3 w - - 0 1"]
[PlyCount "163"]
[EventDate "2017.??.??"]

1. Bf1 Kc1 2. Bh3 Kc2 3. Ke2 Kc1 4. Bg2 Kc2 5. Bf1 Kc1 6. Ke1 Kc2 7. Be2 Kc1 8.
Bd1 Kb2 9. Kd2 Kb1 10. Bc2+ Kb2 11. Kd1 Ka1 12. Kc1 Kxa2 13. Bd1 Ka1 14. Kc2
Ka2 15. Be2 Ka1 16. Bf1 Ka2 17. Bh3 Ka1 18. Bg2 Ka2 19. Bf1 Ka1 20. Be2 Ka2 21.
Bd1 Ka1 22. Kc1 Ka2 23. Bc2 Ka1 24. Bb1 d6 25. Bc2 Ka2 26. Bd1 Ka1 27. Kc2 Ka2
28. Be2 Ka1 29. Bf1 Ka2 30. Bg2 Ka1 31. Bh3 Ka2 32. Bf1 Ka1 33. Be2 Ka2 34. Bd1
Ka1 35. Kc1 Ka2 36. Bc2 Ka1 37. Bb1 d5 38. Bc2 Ka2 39. Bd1 Ka1 40. Kc2 Ka2 41.
Be2 Ka1 42. Bf1 Ka2 43. Bh3 Ka1 44. Bg2 Ka2 45. Bf1 Ka1 46. Be2 Ka2 47. Bd1 Ka1
48. Kc1 Ka2 49. Bc2 Ka1 50. Bb1 b6 51. Bc2 Ka2 52. Bd1 Ka1 53. Kc2 Ka2 54. Be2
Ka1 55. Bf1 Ka2 56. Bh3 Ka1 57. Bg2 Ka2 58. Bf1 Ka1 59. Be2 Ka2 60. Bd1 Ka1 61.
Kc1 Ka2 62. Bc2 Ka1 63. Bb1 b5 64. Bc2 Ka2 65. Bd1 Ka1 66. Kc2 Ka2 67. Be2 Ka1
68. Bf1 Ka2 69. Bg2 Ka1 70. Bh3 Ka2 71. Bf1 Ka1 72. Be2 Ka2 73. Bd1 Ka1 74. Kc1
Ka2 75. Bc2 Ka1 76. Bb1 g5 77. hxg6 h5 78. g7 a2 79. Bc2 h4 80. g8=Q h3 81.
Qxd5 h2 82. Qxd4# 1-0
[/pgn]

Best engine for (backward) solving this might be komodo with switched off nullmove.
According to YACPD it's a study from Karl Fabel (1951, #82).
Database gives only first move as solution, which is not so difficult to find anyhow.

Yet a great one from there onward, in German I'd say Fabel-haft

Very nice pun. Fabel-haft position indeed.

Just completed the Mate in 50 at ChestUCI.epd position 6314.
[d]8/7p/7p/7p/K4Q1p/p1p5/pbpr4/qrk5 w - - 0 1

+M50

[pgn]
[Event "Computer chess game"]
[Site "Talkchess"]
[Date "2017.06.27"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "1-0"]
[BlackElo "2400"]
[Time "16:59:52"]
[WhiteElo "2400"]
[TimeControl "0+2"]
[SetUp "1"]
[FEN "8/7p/7p/7p/K4Q1p/p1p5/pbpr4/qrk5 w - - 0 1"]
[Termination "normal"]
[PlyCount "99"]
[WhiteType "human"]
[BlackType "human"]

1. Kb4 h3 2. Kb3 h4 3. Qf1+ Rd1 4. Qf2 Rd2 5. Qf4 h5 6. Qf1+ Rd1 7. Qf2 Rd2
8. Qf4 h6 9. Qf1+ Rd1 10. Qf2 Rd2 11. Qf4 h2 12. Qf1+ Rd1 13. Qg2 Rd2 14.
Qh1+ Rd1 15. Qxh2 Rd2 16. Qf4 h3 17. Qf1+ Rd1 18. Qf2 Rd2 19. Qf4 h4 20.
Qf1+ Rd1 21. Qf2 Rd2 22. Qf4 h5 23. Qf1+ Rd1 24. Qf2 Rd2 25. Qf4 h2 26.
Qf1+ Rd1 27. Qg2 Rd2 28. Qh1+ Rd1 29. Qxh2 Rd2 30. Qf4 h3 31. Qf1+ Rd1 32.
Qf2 Rd2 33. Qf4 h4 34. Qf1+ Rd1 35. Qf2 Rd2 36. Qf4 h2 37. Qf1+ Rd1 38. Qg2
Rd2 39. Qh1+ Rd1 40. Qxh2 Rd2 41. Qf4 h3 42. Qf1+ Rd1 43. Qf2 Rd2 44. Qf4
h2 45. Qf1+ Rd1 46. Qg2 Rd2 47. Qh1+ Rd1 48. Qxh2 Rd2 49. Qf4 Kd1 50. Qf1#
1-0
[/pgn]

Not sure if there are some flaws on this Mate in 50 line I have manually tried, or maybe this is already optimum. Engines seems clueless due to a lot of zugzwangs.
Maybe the correct title for this puzzle is "The h2 sniper would also deliver checkmate".
All foot soldiers trying to invade h2 would be owned by the sniper.

[MikeGL]

Mate in #75

[d]2Q5/2pp1p1p/1N3p2/kPpK4/4n3/8/p4P1p/qrnB2bN w - - 0 1

This is a ChestUCI.epd position number 6365 "White to Play Mate in #75":

[pgn]

[Event "Computer chess game"]
[Site "Talkchess"]
[Date "2017.06.28"]
[Round "?"]
[White "McBrain_2017"]
[Black "McBrain_2017"]
[Result "1-0"]
[BlackElo "2400"]
[TimeControl "0+2"]
[SetUp "1"]
[FEN "2Q5/2pp1p1p/1N3p2/kPpK4/4n3/8/p4P1p/qrnB2bN w - - 0 1"]
[Termination "normal"]
[PlyCount "149"]
[WhiteType "human"]
[BlackType "human"]
[Comment "bm #75;"]

1. Qa6+ Kb4 2. Qa4+ Kc3 3. Qc2+ Kb4 4. Qc4+ Ka3 5. Qa4+ Kb2 6. Kxe4 cxb6 7.
Kd5 Kc3 8. Qc2+ Kb4 9. Qc4+ Ka3 10. Qa4+ Kb2 11. Kc4 h6 12. Kd5 Kc3 13.
Qc2+ Kb4 14. Qc4+ Ka3 15. Qa4+ Kb2 16. Kc4 h5 17. Kd5 Kc3 18. Qc2+ Kb4 19.
Qc4+ Ka3 20. Qa4+ Kb2 21. Kc4 h4 22. Kd5 Kc3 23. Qc2+ Kb4 24. Qc4+ Ka3 25.
Qa4+ Kb2 26. Kc4 h3 27. Kd5 Kc3 28. Qc2+ Kb4 29. Qc4+ Ka3 30. Qa4+ Kb2 31.
Kc4 f5 32. Kd5 Kc3 33. Qc2+ Kb4 34. Qc4+ Ka3 35. Qa4+ Kb2 36. Kc4 f4 37.
Kd5 Kc3 38. Qc2+ Kb4 39. Qc4+ Ka3 40. Qa4+ Kb2 41. Kc4 f3 42. Kd5 Kc3 43.
Qc2+ Kb4 44. Qc4+ Ka3 45. Qa4+ Kb2 46. Kc4 f6 47. Kd5 Kc3 48. Qc2+ Kb4 49.
Qc4+ Ka3 50. Qa4+ Kb2 51. Kc4 f5 52. Kd5 Kc3 53. Qc2+ Kb4 54. Qc4+ Ka3 55.
Qa4+ Kb2 56. Kc4 f4 57. Kd5 Kc3 58. Qc2+ Kb4 59. Qc4+ Ka3 60. Qa4+ Kb2 61.
Kc4 d6 62. Kd5 Kc3 63. Qc2+ Kb4 64. Qc4+ Ka3 65. Qa4+ Kb2 66. Kc4 d5+ 67.
Kxd5 Kc3 68. Qc2+ Kb4 69. Qc4+ Ka3 70. Qa4+ Kb2 71. Kc4 Bxf2 72. Nxf2 h1=Q
73. Nd3+ Nxd3 74. Qb3+ Kc1 75. Qc2# 1-0
[/pgn]

[MikeGL]

Mate in #62 but I can find only Mate in #64, two move improvement needed.

[d]5Q2/p1p5/p1p5/6rp/7k/6p1/p1p3P1/rbK5 w - - 0 1
Mate in #62 (Source: ChestUCI.epd position 6338)

[pgn]
[Event "Computer chess game"]
[Site "Talkchess"]
[Date "2017.06.28"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "1-0"]
[BlackElo "2400"]
[WhiteElo "2400"]
[TimeControl "0+2"]
[SetUp "1"]
[FEN "5Q2/p1p5/p1p5/6rp/7k/6p1/p1p3P1/rbK5 w - - 0 1"]
[Termination "normal"]
[PlyCount "127"]
[WhiteType "human"]
[BlackType "human"]
[Comment "bm #62;"]

1. Qf4+ Rg4 2. Qf6+ Rg5 3. Qe7 c5 4. Qf6 Kg4 5. Qf3+ Kh4 6. Qf4+ Rg4 7.
Qf6+ Rg5 8. Qe7 c4 9. Qf6 Kg4 10. Qf3+ Kh4 11. Qf4+ Rg4 12. Qf6+ Rg5 13.
Qe7 c3 14. Qf6 Kg4 15. Qf3+ Kh4 16. Qf4+ Rg4 17. Qf6+ Rg5 18. Qe7 c6 19.
Qf6 Kg4 20. Qf3+ Kh4 21. Qf4+ Rg4 22. Qf6+ Rg5 23. Qe7 c5 24. Qf6 Kg4 25.
Qf3+ Kh4 26. Qf4+ Rg4 27. Qf6+ Rg5 28. Qe7 c4 29. Qf6 Kg4 30. Qf3+ Kh4 31.
Qf4+ Rg4 32. Qf6+ Rg5 33. Qe7 a5 34. Qf6 Kg4 35. Qf3+ Kh4 36. Qf4+ Rg4 37.
Qf6+ Rg5 38. Qe7 a4 39. Qf6 Kg4 40. Qf3+ Kh4 41. Qf4+ Rg4 42. Qf6+ Rg5 43.
Qe7 a3 44. Qf6 Kg4 45. Qf3+ Kh4 46. Qf4+ Rg4 47. Qf6+ Rg5 48. Qe7 a6 49.
Qf6 Kg4 50. Qf3+ Kh4 51. Qf4+ Rg4 52. Qf6+ Rg5 53. Qe7 a5 54. Qf6 Kg4 55.
Qf3+ Kh4 56. Qf4+ Rg4 57. Qf6+ Rg5 58. Qe7 a4 59. Qf6 Kg4 60. Qf3+ Kh4 61.
Qf4+ Rg4 62. Qf6+ Rg5 63. Qe7 Kg4 64. Qe4# 1-0
[/pgn]

[MikeGL]

Triangulation square is g6 or h1. White to Play Mate in #50

[d]1K6/3p4/3p4/8/p3n3/1p1N3p/rp2N1br/bR3n1k w - - 0 1
Mate in #50 from ChestUCI.epd position 6316

The mate can be delivered faster if there are many white squares where
white king can perform triangulation to capture the Ra3. Unfortunately,
there is only one white square where the King can occupy without
receiving a deadly check from the Ne4 of black and thereby untangling blacks position.
The only white square is g6, but the h1 square also becomes a
triangulation point once d6-d5 is forcibly pushed by black which blocks the Bg7 discovery check after Ne4 hops. So partly h1 and
most of triangulation is done at g6 as shown on the game below to deliver Mate in 50.

[pgn]
[Event "Computer chess game"]
[Site "Talkchess"]
[Date "2017.06.28"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "1-0"]
[BlackElo "2400"]
[WhiteElo "2400"]
[TimeControl "0+2"]
[SetUp "1"]
[FEN "1K6/3p4/3p4/8/p3n3/1p1N3p/rp2N1br/bR3n1k w - - 0 1"]
[Termination "normal"]
[WhiteType "human"]
[BlackType "human"]

1. Kc7 Ra3 2. Kd8 Ra2 3. Ke7 Ra3 4. Kf8 Ra2 5. Kg7 Ra3 6. Kh6 Ra2 7. Kg6
Ra3 8. Kg7 Ra2 9. Kf8 Ra3 10. Ke7 Ra2 11. Kd8 Ra3 12. Kc7 Ra2 13. Kb6 Ra3
14. Ka5 Ra2 15. Kb4 d5 16. Ka5 Ra3 17. Kb6 Ra2 18. Ka7 d4 19. Kb6 Ra3 20.
Ka5 Ra2 21. Kb4 d6 22. Ka5 Ra3 23. Kb6 Ra2 24. Kc7 Ra3 25. Kd8 Ra2 26. Ke7
Ra3 27. Kf8 Ra2 28. Kg7 Ra3 29. Kh6 Ra2 30. Kg6 Ra3 31. Kg7 Ra2 32. Kf8 Ra3
33. Ke7 Ra2 34. Kd8 Ra3 35. Kc7 Ra2 36. Kb6 Ra3 37. Ka5 Ra2 38. Kb4 d5 39.
Ka5 Ra3 40. Kb6 Ra2 41. Ka7 Ra3 42. Ka8 Ra2 43. Kb8 Ra3 44. Ka7 Ra2 45. Kb6
Ra3 46. Ka5 Ra2 47. Kb4 Ra3 (47. .. a3 48. Ka5 Bf3 49. Rxf1+ Kg2 50. Rg1#)
48. Kxa3 Bf3 49. Rxf1+ Kg2 50. Rg1# 1-0
[/pgn]

[peter]

This one I found in YACPDB again, it's from Béla Bakay 1950.
Didn't find the one with #64, neither a shorter way to mate than you showed

[peter]

[d]1K6/3p4/3p4/8/p3n3/1p1N3p/rp2N1br/bR3n1k w - - 0 1
Mate in #50 from ChestUCI.epd position 6316

The mate can be delivered faster if there are many white squares where
white king can perform triangulation to capture the Ra3. Unfortunately,
there is only one white square where the King can occupy without
receiving a deadly check from the Ne4 of black and thereby untangling blacks position.
The only white square is g6, but the h1 square also becomes a
triangulation point once d6-d5 is forcibly pushed by black which blocks the Bg7 discovery check after Ne4 hops. So partly h1 and
most of triangulation is done at g6 as shown on the game below to deliver Mate in 50.

[pgn]
[Event "Computer chess game"]
[Site "Talkchess"]
[Date "2017.06.28"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "1-0"]
[BlackElo "2400"]
[WhiteElo "2400"]
[TimeControl "0+2"]
[SetUp "1"]
[FEN "1K6/3p4/3p4/8/p3n3/1p1N3p/rp2N1br/bR3n1k w - - 0 1"]
[Termination "normal"]
[WhiteType "human"]
[BlackType "human"]

1. Kc7 Ra3 2. Kd8 Ra2 3. Ke7 Ra3 4. Kf8 Ra2 5. Kg7 Ra3 6. Kh6 Ra2 7. Kg6
Ra3 8. Kg7 Ra2 9. Kf8 Ra3 10. Ke7 Ra2 11. Kd8 Ra3 12. Kc7 Ra2 13. Kb6 Ra3
14. Ka5 Ra2 15. Kb4 d5 16. Ka5 Ra3 17. Kb6 Ra2 18. Ka7 d4 19. Kb6 Ra3 20.
Ka5 Ra2 21. Kb4 d6 22. Ka5 Ra3 23. Kb6 Ra2 24. Kc7 Ra3 25. Kd8 Ra2 26. Ke7
Ra3 27. Kf8 Ra2 28. Kg7 Ra3 29. Kh6 Ra2 30. Kg6 Ra3 31. Kg7 Ra2 32. Kf8 Ra3
33. Ke7 Ra2 34. Kd8 Ra3 35. Kc7 Ra2 36. Kb6 Ra3 37. Ka5 Ra2 38. Kb4 d5 39.
Ka5 Ra3 40. Kb6 Ra2 41. Ka7 Ra3 42. Ka8 Ra2 43. Kb8 Ra3 44. Ka7 Ra2 45. Kb6
Ra3 46. Ka5 Ra2 47. Kb4 Ra3 (47. .. a3 48. Ka5 Bf3 49. Rxf1+ Kg2 50. Rg1#)
48. Kxa3 Bf3 49. Rxf1+ Kg2 50. Rg1# 1-0
[/pgn]

Here your line isn't quite correct, I guess.
After 18...d4 (?!) White has a shorter way than in 50 moves:


8/K2p4/8/8/p2pn3/1p1N3p/rp2N1br/bR3n1k w - - 0 1

Analysis by Komodo 11.01 64-bit:

19.Kb6 Ra3 20.Ka5 Ra2 21.Kb4 d6 22.Ka5 Ra3 23.Kb6 Ra2 24.Kc7 Ra3 25.Kc8 Ra2 26.Kb8 Ra3 27.Ka7 Ra2 28.Kb6 Ra3 29.Ka5 Ra2 30.Kb4 d5 31.Ka5 Ra3 32.Kb6 Ra2 33.Kc7 Ra3 34.Kc6 Ra2 35.Kb6 Ra3 36.Ka5 Ra2 37.Kb4 a3 38.Ka5 Bf3 39.Rxf1+ Kg2 40.Rg1#
+- (#22) Depth: 49 00:02:51 4241MN


Yet Black isn't already forced to make the next pawn move already.
Didn't find this one in YACPDB

[MikeGL]

[d]1K6/3p4/3p4/8/p3n3/1p1N3p/rp2N1br/bR3n1k w - - 0 1
Mate in #50 from ChestUCI.epd position 6316

The mate can be delivered faster if there are many white squares where
white king can perform triangulation to capture the Ra3. Unfortunately,
there is only one white square where the King can occupy without
receiving a deadly check from the Ne4 of black and thereby untangling blacks position.
The only white square is g6, but the h1 square also becomes a
triangulation point once d6-d5 is forcibly pushed by black which blocks the Bg7 discovery check after Ne4 hops. So partly h1 and
most of triangulation is done at g6 as shown on the game below to deliver Mate in 50.

[pgn]
[Event "Computer chess game"]
[Site "Talkchess"]
[Date "2017.06.28"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "1-0"]
[BlackElo "2400"]
[WhiteElo "2400"]
[TimeControl "0+2"]
[SetUp "1"]
[FEN "1K6/3p4/3p4/8/p3n3/1p1N3p/rp2N1br/bR3n1k w - - 0 1"]
[Termination "normal"]
[WhiteType "human"]
[BlackType "human"]

1. Kc7 Ra3 2. Kd8 Ra2 3. Ke7 Ra3 4. Kf8 Ra2 5. Kg7 Ra3 6. Kh6 Ra2 7. Kg6
Ra3 8. Kg7 Ra2 9. Kf8 Ra3 10. Ke7 Ra2 11. Kd8 Ra3 12. Kc7 Ra2 13. Kb6 Ra3
14. Ka5 Ra2 15. Kb4 d5 16. Ka5 Ra3 17. Kb6 Ra2 18. Ka7 d4 19. Kb6 Ra3 20.
Ka5 Ra2 21. Kb4 d6 22. Ka5 Ra3 23. Kb6 Ra2 24. Kc7 Ra3 25. Kd8 Ra2 26. Ke7
Ra3 27. Kf8 Ra2 28. Kg7 Ra3 29. Kh6 Ra2 30. Kg6 Ra3 31. Kg7 Ra2 32. Kf8 Ra3
33. Ke7 Ra2 34. Kd8 Ra3 35. Kc7 Ra2 36. Kb6 Ra3 37. Ka5 Ra2 38. Kb4 d5 39.
Ka5 Ra3 40. Kb6 Ra2 41. Ka7 Ra3 42. Ka8 Ra2 43. Kb8 Ra3 44. Ka7 Ra2 45. Kb6
Ra3 46. Ka5 Ra2 47. Kb4 Ra3 (47. .. a3 48. Ka5 Bf3 49. Rxf1+ Kg2 50. Rg1#)
48. Kxa3 Bf3 49. Rxf1+ Kg2 50. Rg1# 1-0
[/pgn]

Here your line isn't quite correct, I guess.
After 18...d4 (?!) White has a shorter way than in 50 moves:


8/K2p4/8/8/p2pn3/1p1N3p/rp2N1br/bR3n1k w - - 0 1

Analysis by Komodo 11.01 64-bit:

19.Kb6 Ra3 20.Ka5 Ra2 21.Kb4 d6 22.Ka5 Ra3 23.Kb6 Ra2 24.Kc7 Ra3 25.Kc8 Ra2 26.Kb8 Ra3 27.Ka7 Ra2 28.Kb6 Ra3 29.Ka5 Ra2 30.Kb4 d5 31.Ka5 Ra3 32.Kb6 Ra2 33.Kc7 Ra3 34.Kc6 Ra2 35.Kb6 Ra3 36.Ka5 Ra2 37.Kb4 a3 38.Ka5 Bf3 39.Rxf1+ Kg2 40.Rg1#
+- (#22) Depth: 49 00:02:51 4241MN


Yet Black isn't already forced to make the next pawn move already.
Didn't find this one in YACPDB

Thanks for pointing that error Peter. I noticed the c8 white square is available for triangulation when the d6 is occupied by a black pawn because the Ne4 cannot deliver a check while K is at c8. Here's the corrected variation making use of the c8 square everytime black occupies the d6 square with a pawn.

[pgn]

[Event "Computer chess game"]
[Site "Talkchess"]
[Date "2017.06.28"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "1-0"]
[BlackElo "2400"]
[WhiteElo "2400"]
[TimeControl "0+2"]
[SetUp "1"]
[FEN "1K6/3p4/3p4/8/p3n3/1p1N3p/rp2N1br/bR3n1k w - - 0 1"]
[Termination "normal"]
[PlyCount "99"]
[WhiteType "human"]
[BlackType "human"]

1. Kc8 Ra3 2. Kc7 Ra2 3. Kb6 Ra3 4. Ka5 Ra2 5. Kb4 d5 6. Ka5 Ra3 7. Kb6 Ra2
8. Ka7 Ra3 9. Ka8 Ra2 10. Kb8 Ra3 11. Ka7 Ra2 12. Kb6 Ra3 13. Ka5 Ra2 14.
Kb4 d4 15. Ka5 Ra3 16. Kb6 Ra2 17. Kc7 Ra3 18. Kd8 Ra2 19. Ke7 Ra3 20. Kf8
Ra2 21. Kg7 Ra3 22. Kh6 Ra2 23. Kg6 Ra3 24. Kg7 Ra2 25. Kf8 Ra3 26. Ke7 Ra2
27. Kd8 Ra3 28. Kc7 Ra2 29. Kb6 Ra3 30. Ka5 Ra2 31. Kb4 d6 32. Ka5 Ra3 33.
Kb6 Ra2 34. Kc7 Ra3 35. Kc8 Ra2 36. Kb8 Ra3 37. Kc7 Ra2 38. Kb6 Ra3 39. Ka5
Ra2 40. Kb4 d5 41. Ka5 Ra3 42. Kb6 Ra2 43. Kc7 Ra3 44. Kc6 Ra2 45. Kb6 Ra3
46. Ka5 Ra2 47. Kb4 a3 (47. .. Ra3 48. Kxa3 Bf3 49. Rxf1+ Kg2 50. Rg1#) 48.
Ka5 Bf3 49. Rxf1+ Kg2 50. Rg1# 1-0
[/pgn]

Also I was referring to a8 square instead of h1. The K now can triangulate at a8, c8 and g6 depending on the position. Once d5 is blocked then a8 is available, if d6 is blocked then c8 is available. Else, there's g6 for last recourse.

[Nordlandia]

Here is two PDF files of Otto Blathy's compositions.

Otto Blathy.rar
http://www23.zippyshare.com/v/I1ZXltq5/file.html

[peter]

Thanks for pointing that error Peter. I noticed the c8 white square is available for triangulation when the d6 is occupied by a black pawn because the Ne4 cannot deliver a check while K is at c8. Here's the corrected variation making use of the c8 square everytime black occupies the d6 square with a pawn.

[pgn]

[Event "Computer chess game"]
[Site "Talkchess"]
[Date "2017.06.28"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "1-0"]
[BlackElo "2400"]
[WhiteElo "2400"]
[TimeControl "0+2"]
[SetUp "1"]
[FEN "1K6/3p4/3p4/8/p3n3/1p1N3p/rp2N1br/bR3n1k w - - 0 1"]
[Termination "normal"]
[PlyCount "99"]
[WhiteType "human"]
[BlackType "human"]

1. Kc8 Ra3 2. Kc7 Ra2 3. Kb6 Ra3 4. Ka5 Ra2 5. Kb4 d5 6. Ka5 Ra3 7. Kb6 Ra2
8. Ka7 Ra3 9. Ka8 Ra2 10. Kb8 Ra3 11. Ka7 Ra2 12. Kb6 Ra3 13. Ka5 Ra2 14.
Kb4 d4 15. Ka5 Ra3 16. Kb6 Ra2 17. Kc7 Ra3 18. Kd8 Ra2 19. Ke7 Ra3 20. Kf8
Ra2 21. Kg7 Ra3 22. Kh6 Ra2 23. Kg6 Ra3 24. Kg7 Ra2 25. Kf8 Ra3 26. Ke7 Ra2
27. Kd8 Ra3 28. Kc7 Ra2 29. Kb6 Ra3 30. Ka5 Ra2 31. Kb4 d6 32. Ka5 Ra3 33.
Kb6 Ra2 34. Kc7 Ra3 35. Kc8 Ra2 36. Kb8 Ra3 37. Kc7 Ra2 38. Kb6 Ra3 39. Ka5
Ra2 40. Kb4 d5 41. Ka5 Ra3 42. Kb6 Ra2 43. Kc7 Ra3 44. Kc6 Ra2 45. Kb6 Ra3
46. Ka5 Ra2 47. Kb4 a3 (47. .. Ra3 48. Kxa3 Bf3 49. Rxf1+ Kg2 50. Rg1#) 48.
Ka5 Bf3 49. Rxf1+ Kg2 50. Rg1# 1-0
[/pgn]

Had a posting just before I deleted again not being quite sure about it, but yes, I think so too.
With black pawn on d4, White can use a8 for triangle too.

An Ipman- SF can get switched off nullmove really fully (I guess other UCI- parameters of that kind rather raise verification only?):

1K6/3p4/3p4/8/p3n3/1p1N3p/rp2N1br/bR3n1k w - - 0 1

Analysis by SF 171114IPx 64 POPCNTe:

1.Kc8 Ra3 2.Kc7 Ra2 3.Kb6 Ra3 4.Ka5 Ra2 5.Kb4 d5 6.Ka5 Ra3 7.Kb6 Ra2 8.Kc7 Ra3 9.Kb8 Ra2 10.Ka8 Ra3 11.Ka7 Ra2 12.Kb6 Ra3 13.Ka5 Ra2 14.Kb4 d4 15.Ka5 Ra3 16.Kb6 Ra2 17.Kc7 Ra3 18.Kd8 Ra2 19.Ke7 Ra3 20.Kf8 Ra2 21.Kg7 Ra3
+- (#50) Depth: 42/42 00:03:32 4003MN

[MikeGL]

This one I found in YACPDB again, it's from Béla Bakay 1950.
Didn't find the one with #64, neither a shorter way to mate than you showed

That one I have figured out the 1st and 2nd move can be bypassed and just play 1.Qe7 directly. So the 3rd move is actualy the first move of the puzzles which makes it Mate in #62. Was eager to find the Queen-move pattern and missed the direct 1.Qe7 which forces Mate in 62.

Here is two PDF files of Otto Blathy's compositions.

Otto Blathy.rar
http://www23.zippyshare.com/v/I1ZXltq5/file.html

Thanks for this Blathy PDF file Jon, looks like I was very lucky to chose Mate position which are not on that PDF file. Have not seen that file before, so thanks a lot for those puzzles and solutions.