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

3,1

Comments

If n is odd then the bishop must be on a black square.

Links

Table of n, a(n) for n=3..24.

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.

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

Cf. A225551, A225552, A225553, A225554, A225555, A225557, A227437.

Sequence in context: A196178 A269161 A307964 * A064666 A269160 A286418

Adjacent sequences: A225553 A225554 A225555 * A225557 A225558 A225559

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