OFFSET
3,1
COMMENTS
If n is odd then the bishop must be on a black square.
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).
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.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Vaclav Kotesovec, May 10 2013
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
STATUS
approved