

(1) Posted by Hauke Reddmann [Thursday, Apr 8, 2021 14:50] 
Maximum "unknotting" number What is the longest *nonunique* mate against a Rex Solus? (Not necessarily 16+1  first beat 33# of KBN/K ;) 

(2) Posted by seetharaman kalyan [Thursday, Apr 8, 2021 15:39] 
I don't think that 33 can be beaten 

(3) Posted by Rewan Demontay (Real Name: James Malcom) [Thursday, Apr 8, 2021 16:36] 
Since you didn't specify, I found 103. :)
Otto Titusz Bláthy, The Fairy Chess Review 08/1939
s#103, Maximummr
(= 1+16 )
1. Kc4 Qh8 2. Kb5 Qa1 3. Kc6 Qh8 4. Kb7 Qa1 5. Ka8 Qh8 6. Kb8 Qa1 7. Kb7 Qh8 8. Kc6 Qa1 9. Kb5 Qh8 10. Kc4 Qa1 11. Kb3 Qh8 12. Kxa2 Qa1+ 13. Kb3 Qh8 14. Kc4 Qa1 15. Kb5 Qh8 16. Kc6 Qa1 17. Kb7 Qh8 18. Ka8 Qa1 19. Kb8 Qh8 20. Kb7 Qa1 21. Kc6 Qh8 22. Kb5 Qa1 23. Kc4 Qh8 24. Kb3 Qa1 25. Kc2 Qh8 26. Kxd1 Qa1+ 27. Kc2 Qh8 28. Kb3 Qa1 29. Kc4 Qh8 30. Kxd5 Qa1 31. Kc4 Qh8 32. Kxb4 Qa1 33. Kb3 Qh8 34. Kc2 Qa1 35. Kd2 Qh8 36. Ke1 Qa1+ 37. Kf2 Qh8 38. Kg1 Qa1+ 39. Kh2 Qh8 40. Kxh3 Qa1 41. Kh2 Qh8 42. Kg1 Qa1+ 43. Kf2 Qh8 44. Ke1 Qa1+ 45. Kd2 Qh8 46. Kc2 Qa1 47. Kb3 Qh8 48. Kc4 Qa1 49. Kd5 Qh8 50. Kc6 Qa1 51. Kb7 Qh8 52. Kc8 Qa1 53. Kxd8 Qh8 54. Kc8 Qa1 55. Kb7 Qh8 56. Kc6 Qa1 57. Kb5 Qh8 58. Kc4 Qa1 59. Kb3 Qh8 60. Kc2 Qa1 61. Kd2 Qh8 62. Ke1 Qa1+ 63. Kf2 Qh8 64. Kg1 Qa1+ 65. Kh2 Qh8 66. Kh3 Qa1 67. Kh4 Qh8 68. Kxh5 Qa1 69. Kh4 Qh8 70. Kh3 Qa1 71. Kh2 Qh8 72. Kg1 Qa1+ 73. Kf2 Qh8 74. Ke1 Qa1+ 75. Kd2 Qh8 76. Kc2 Qa1 77. Kb3 Qh8 78. Kc4 Qa1 79. Kd5 Qh8 80. Kc6 Qa1 81. Kb7 Qh8 82. Kb8 Qa1 83. Kc8 Qh8 84. Kd8 Qa1 85. Kxe8 Qh8 86. Kf7 Qa1 87. Kxg8 Qh8+ 88. Kf7 Qa1 89. Ke7 Qh8 90. Kd6 Qa1 91. Kd5 Qh8 92. Kc4 Qa1 93. Kb3 Qh8 94. Kc2 Qa1 95. Kd2 Qh8 96. Ke1 Qa1+ 97. Kf2 Qh8 98. Kg1 Qa1+ 99. Kh2 Qh8 100. Kh3 Qa1 101. Kh4 Qh8 102. Kh5 Qa1 103. Kxh6 Qh8# 

(4) Posted by Jacques Rotenberg [Thursday, Apr 8, 2021 19:12] 
James, this is not a mate against a rex solus, it is a mate with a rex solus 

(5) Posted by Andrew Buchanan [Friday, Apr 9, 2021 10:25] 
Here's a position with KNNNvK, Black to move 1... Kf2 leaves DTM 41 for White.
(= 4+1 ) BTM
https://syzygytables.info/?fen=8/8/8/8/8/8/N7/NK2k1N1_b___0_1
I can't think how one could do better than this. 

(6) Posted by seetharaman kalyan [Friday, Apr 9, 2021 11:20] 
Oh 3 knights!. I didn't know it takes longer than BNK 

(7) Posted by Jacques Rotenberg [Friday, Apr 9, 2021 12:13] 
Andrew, Nalimov tables give after 1...Kf2 white mates in 21 moves 

(8) Posted by Andrew Buchanan [Friday, Apr 9, 2021 12:23] 
Hi Jacques,
Haha Syzygy counts in single moves, while Lemonosov is double moves! So KBNvK is indeed longer: 65 single moves from BTM e.g.
(= 3+1 )
Thanks,
Andrew 

(9) Posted by Joost de Heer [Friday, Apr 9, 2021 14:27] 
Syzygy uses DTZ as far as I know, so it doesn't find the shortest mate. 

(10) Posted by Andrew Buchanan [Friday, Apr 9, 2021 15:04] 
Yes Syzygy operates to DTZ rather than DTM, but there's no short cuts possible for KNNN or KBN because any sac will almost certainly render forced mate impossible.
In addition, Syzygy has a separate lookup for up to 5 pieces to show the DTM directly, so we are safe. Just the units were confusing, as I'd forgotten again that Lomonosov & Syzygy differ by a factor of 2.
If I was trying to be systematic in analyzing a problem exhaustively, I would begin with Lomonosov to find the absolute shortest DTM, and if this gives a problem with 50M, Syzygy can indicate whether a DTZ can help out. Syzygy runs in any browser so it's easier to check, although I do have Lomonosov running in BlueStacks on my PC, as I don't have an android phone. 

(11) Posted by Joost de Heer [Friday, Apr 9, 2021 18:43] 
https://syzygytables.info/?fen=8/8/8/1N6/B7/1Nk5/8/7K_b___0_1
Has a DTM of 67. 

(12) Posted by Andrew Buchanan [Friday, Apr 9, 2021 20:14] 
That's very nice Joost... :) 

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