A225556 Longest checkmate in king, bishop and knight versus king endgame on an n X n chessboard.
7, 14, 13, 22, 21, 33, 29, 47, 39, 64, 50, 78, 63, 93, 76, 112, 90, 131, 105, 151, 121, 171
Offset: 3
Examples
Longest win on an 8 X 8 chessboard: Ka1 Bc1 Sb1 - Kc2, 1.Bc1-d2 Kc2-b3! 2.Bd2-f4 Kb3-c2! 3.Ka1-a2! Kc2-d3! 4.Ka2-b3! Kd3-e4 5.Bf4-h2 Ke4-d5 6.Kb3-c3 Kd5-e4 7.Sb1-d2! Ke4-d5! 8.Kc3-d3! Kd5-c5! 9.Sd2-c4! Kc5-b5 10.Kd3-d4 Kb5-c6! 11.Bh2-g3 Kc6-b7! 12.Kd4-d5 Kb7-a7! 13.Kd5-c6! Ka7-a6 14.Bg3-h2 Ka6-a7! 15.Sc4-b6! Ka7-a6! 16.Bh2-b8! Ka6-a5! 17.Sb6-d5! Ka5-a4! 18.Kc6-c5 Ka4-b3! 19.Sd5-b4! Kb3-b2! 20.Bb8-f4! Kb2-c3! 21.Bf4-g5 Kc3-b3! 22.Bg5-f6 Kb3-a4 23.Kc5-c4! Ka4-a5! 24.Bf6-d8! Ka5-a4! 25.Sb4-d3! Ka4-a3! 26.Bd8-e7 Ka3-a4! 27.Sd3-c5! Ka4-a3! 28.Kc4-c3! Ka3-a2! 29.Sc5-d3! Ka2-b1! 30.Kc3-b3! Kb1-a1! 31.Kb3-c2! Ka1-a2! 32.Sd3-c1! Ka2-a1! 33.Be7-f6#, therefore a(8) = 33.
Links
- Julius Telesin, Can B + S give checkmate on 1000 x 1000 chessboard?, EG 73, 1983, p. 190.
- Vaclav Kotesovec, King and Two Generalised Knights against King, ICGA Journal, Vol. 24, No. 2, pp. 105-107 (2001).
- Vaclav Kotesovec, Fairy chess endings on an n x n chessboard, Electronic edition of chess booklets by Vaclav Kotesovec, vol. 8, p. 224 and 231 (2013), p. 349 and 362 (second edition, 2017).
- Chess Stackexchange, Mate with Bishop and Knight, 2018.
- Johan Wästlund, The bishop and knight checkmate on a large chessboard, arXiv:2405.04421 [math.CO], 2024. See p. 13.
Formula
Conjecture: a(n) ~ n^2/6 + 3*n if n is even and a(n) ~ n^2/6 + 2*n if n is odd.
Extensions
a(21) from Vaclav Kotesovec, Jan 11 2017
a(22) from Vaclav Kotesovec, Jan 15 2017
a(23) from Vaclav Kotesovec, Jun 22 2017
a(24) from Vaclav Kotesovec, Jun 30 2017
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