Author: Bruce Moreland
Date: 10:24:28 09/20/00
KBN vs K is a win in the general case, like it is on an 8 x 8 board. The
longest mate with white to move is 64. Unless I made a visual mistake, the
black king went more or less straight across the board to the "wrong" corner,
then straight up the side to the right one. You'd think it would try for the
center, but perhaps that allows white to push more straight back into the right
corner.
[FEN "12/12/12/12/12/12/12/12/12/12/2k9/K1N1B7 w"]
{
a b c d e f g h i j k l
+---+---+---+---+---+---+---+---+---+---+---+---+
12| |///| |///| |///| |///| |///| |///|12
+---+---+---+---+---+---+---+---+---+---+---+---+
11|///| |///| |///| |///| |///| |///| |11
+---+---+---+---+---+---+---+---+---+---+---+---+
10| |///| |///| |///| |///| |///| |///|10
+---+---+---+---+---+---+---+---+---+---+---+---+
9 |///| |///| |///| |///| |///| |///| | 9
+---+---+---+---+---+---+---+---+---+---+---+---+
8 | |///| |///| |///| |///| |///| |///| 8
+---+---+---+---+---+---+---+---+---+---+---+---+
7 |///| |///| |///| |///| |///| |///| | 7
+---+---+---+---+---+---+---+---+---+---+---+---+
6 | |///| |///| |///| |///| |///| |///| 6
+---+---+---+---+---+---+---+---+---+---+---+---+
5 |///| |///| |///| |///| |///| |///| | 5
+---+---+---+---+---+---+---+---+---+---+---+---+
4 | |///| |///| |///| |///| |///| |///| 4
+---+---+---+---+---+---+---+---+---+---+---+---+
3 |///| |///| |///| |///| |///| |///| | 3
+---+---+---+---+---+---+---+---+---+---+---+---+
2 | |///| k |///| |///| |///| |///| |///| 2
+---+---+---+---+---+---+---+---+---+---+---+---+
1 |/K/| |/N/| |/B/| |///| |///| |///| | 1
+---+---+---+---+---+---+---+---+---+---+---+---+
a b c d e f g h i j k l
}
1. Na2! Kd1 2. Bc3 { Bb4, Ba5, Bf2, Bg3, Bh4, Bi5, Bj6, Bk7, Bl8 } Kc2 3. Be5
{ Bf6, Bg7, Bh8, Bi9, Bj10, Bk11, Bl12 } Kb3 { Kd3 } 4. Nc3 { Kb1 } Kc2 { Ka3 }
5. Ne4 { Nd5, Nb5, Ka2 } Kb3 { Kd3 } 6. Nf6 { Nd6, Kb1 } Kc2 { Ka4, Kc4, Ka3 }
7. Ka2 Kd2 8. Kb3 { Ka3, Kb2 } Kd3 9. Bd6 { Bc7, Bb8, Ba9, Kb4 } Kd4 10. Kb4
Ke3 { Kd3 } 11. Kc3 { Kc5, Kc4 } Kf2 { Ke2, Kf3 } 12. Kd4 Kf3 { Kg2 } 13. Ke5
Kg2 { Kg3 } 14. Kf4 { Kf5 } Kh3 { Kh2 } 15. Kg5 Ki4 { Ki3 } 16. Bf8 Kh3 { Kj3,
Ki3 } 17. Nh5 Ki2 { Ki4 } 18. Nj4+ { Kh4 } Ki3 { Kj2 } 19. Kh5 Kj3 20. Kh4 Kj2
21. Ki4 Kk1 22. Kj3 Kl1 23. Kj2 Kl2 24. Bg7 { Bh6, Bi5, Be9, Bd10, Bc11, Bb12 }
Kl1 25. Kj1 Kl2 26. Nl5+ Kl1 27. Nk3+ Kl2 28. Ni4+ Kl3 29. Nj6 Kl4 30. Bj4 Kl3
31. Kj2 Kl4 32. Kj3 Kl3 33. Nl7 { Ni4, Bi5 } Kl4 34. Bi5 Kl3 { Kl5 } 35. Nk5+
Kl4 36. Kj4 Kl5 37. Kj5 Kl4 38. Bh6 { Bg7, Bf8, Be9, Bd10 } Kl5 39. Bg5 { Bf4 }
Kl4 40. Bj2+ Kl5 41. Ni6 Kl6 42. Bg5 Kl5 43. Nj4+ Kl6 44. Kj6 Kl7 45. Kj7 Kl6
46. Bi7 Kl7 47. Bj8 Kl8 48. Nl3 { Nl5, Nh5, Ni6 } Kl7 { Kl9 } 49. Nk5+ Kl8 50.
Ki8 Kk8 51. Ki9 Kl8 52. Kj9 Kl9 53. Nl7 { Bi7, Bh6, Bg5, Bf4, Be3, Bd2, Bh10 }
Kl8 54. Nk9 Kl9 55. Bk7 Kl10 56. Ni10 Kl9 57. Nk11+ { Nj8+ } Kl10 58. Kj10 Kl11
59. Nj9 { Bj8, Bh10, Kj11 } Kk12 { Kl12 } 60. Bh10 Kl11 61. Kj11 Kl12 62. Kk10
Kk12 63. Nl10+ Kl12 64. Bi9# 1-0
KQ vs KR is also won for white, mate in 85 with white to move. KQ vs K is a
mate in 15 in 12 x 12 chess, so it's proven that this position is a draw given
the 50-move rule. Note that the rook stays on until move 83 here. It doesn't
appear to stay near the king, so this is another case where that might be a
sub-optimal strategy (the first being 8 x 8 chess).
[FEN "r11/12/12/12/12/12/12/12/12/5k6/12/K1Q w"]
{
a b c d e f g h i j k l
+---+---+---+---+---+---+---+---+---+---+---+---+
12| r |///| |///| |///| |///| |///| |///|12
+---+---+---+---+---+---+---+---+---+---+---+---+
11|///| |///| |///| |///| |///| |///| |11
+---+---+---+---+---+---+---+---+---+---+---+---+
10| |///| |///| |///| |///| |///| |///|10
+---+---+---+---+---+---+---+---+---+---+---+---+
9 |///| |///| |///| |///| |///| |///| | 9
+---+---+---+---+---+---+---+---+---+---+---+---+
8 | |///| |///| |///| |///| |///| |///| 8
+---+---+---+---+---+---+---+---+---+---+---+---+
7 |///| |///| |///| |///| |///| |///| | 7
+---+---+---+---+---+---+---+---+---+---+---+---+
6 | |///| |///| |///| |///| |///| |///| 6
+---+---+---+---+---+---+---+---+---+---+---+---+
5 |///| |///| |///| |///| |///| |///| | 5
+---+---+---+---+---+---+---+---+---+---+---+---+
4 | |///| |///| |///| |///| |///| |///| 4
+---+---+---+---+---+---+---+---+---+---+---+---+
3 |///| |///| |///| k |///| |///| |///| | 3
+---+---+---+---+---+---+---+---+---+---+---+---+
2 | |///| |///| |///| |///| |///| |///| 2
+---+---+---+---+---+---+---+---+---+---+---+---+
1 |/K/| |/Q/| |///| |///| |///| |///| | 1
+---+---+---+---+---+---+---+---+---+---+---+---+
a b c d e f g h i j k l
}
1. Kb2 Rb12+ 2. Ka3 Ra12+ 3. Kb4 Rb12+ 4. Ka5 Ra12+ 5. Kb6 Rb12+ 6. Ka7 Ra12+
7. Kb8 Rb12+ 8. Ka9 Ra12+ 9. Kb10 Rb12+ 10. Ka11 { Kc11 } Re12 { Rg12 } 11. Qi7
Re5 { Re4 } 12. Kb10 { Ka10 } Ke4 { Kg4 } 13. Kc9 { Kb9 } Kf5 14. Qf7+ { Kd8,
Kc8 } Kg4 { Kg5 } 15. Kd8 Rf5 { Rg5, Rh5, Kg5 } 16. Qe6 { Qg6+, Qi4+, Qi7,
Qj7+ } Kg5 { Kf4 } 17. Ke7 Rf3 18. Qg8+ { Qi6, Qj6, Qk6, Ql6 } Kh6 19. Qd5
{ Qh9+, Qa8, Qh8+ } Rf4 20. Qd2 Kg5 21. Ke6 Kg4 22. Qc1 { Qh2 } Rf3 { Kg3 } 23.
Qd1 { Qj1+ } Kf4 24. Qd2+ Kg4 25. Qe2 Kg3 { Kf4 } 26. Ke5 Ra3 27. Qb5 { Qe1+ }
Re3+ { Rf3 } 28. Kf5 Rf3+ 29. Kg5 Re3 30. Qb8+ { Qc5, Qd5 } Kf3 31. Qf4+
{ Qb7+, Kf5 } Ke2 32. Qc4+ { Qa4, Kg4 } Kf2 33. Qd4 Ke2 34. Kf4 Rf3+ 35. Ke4
{ Kg4 } Rg3 36. Qb2+ Kf1 37. Kf4 Rh3 38. Qk2 Rc3 { Kg1 } 39. Qf7 Ke2 40. Qe6+
{ Qa2+ } Kd2 41. Qd5+ { Qe5 } Rd3 { Ke2 } 42. Qc5 { Qe5, Qg5 } Rd12 { Rc3 } 43.
Qe3+ Kc2 44. Qe11 Rd4+ 45. Ke3 Rd3+ 46. Ke4 Rl3 47. Qd12 { Qc11+ } Rk3 48. Qd11
{ Qd9, Qd8, Qc12+, Qa12 } Rb3 49. Qa8 { Qd9, Qd5 } Rb4+ 50. Kd5 Rl4 51. Qh8 Rl2
{ Rb4 } 52. Qh7+ { Kc4 } Kb3 53. Qd3+ Kb2 54. Qk3 Ri2 { Rg2, Rf2, Re2, Rd2+,
Rc2 } 55. Kc4 { Kd4 } Rc2+ 56. Kb4 Kc1 57. Qf3 { Kb3 } Rb2+ 58. Kc3 { Kc4 }
Rc2+ 59. Kd3 Rd2+ 60. Ke3 Rc2 61. Qf1+ Kb2 62. Qf6+ Kb3 63. Kd3 Rc1 64. Qf7+
Ka3 65. Qf5 { Qf4, Qf3, Qf9 } Kb3 66. Qb5+ Ka3 67. Qb8 Ka2 68. Kd2 Rb1 69. Qe5
{ Qa8+ } Rb12 { Kb3 } 70. Qe6+ Kb2 71. Qf6+ Kb1 72. Qg6+ Ka2 73. Qg8+ Kb1 74.
Kc3 Rb2 75. Qg1+ Ka2 76. Qd1 Rl2 77. Qb3+ { Qa4+ } Ka1 78. Qb12 Ra2 79. Qf8
{ Qb11, Qb10, Qj12 } Rj2 80. Qe7 { Qa8+ } Rj3+ 81. Kc2 Ka2 82. Qd8 { Qa11+,
Qa7+ } Rj2+ { Rh3, Rg3, Rf3, Re3, Rc3+, Rb3, Ra3, Rk3, Rl3 } 83. Qxj2 Ka3 84.
Qh4 { Ql4, Qj4 } Ka2 85. Qa11# { Qa4# } 1-0
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Last modified: Thu, 15 Apr 21 08:11:13 -0700
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