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Longest checkmate in king and two bishops versus king endgame on an n X n chessboard.
7

%I #14 Jun 22 2017 15:18:20

%S 1,9,11,13,16,19,21,24,26,29,32,35,38,40,44,46,49,52,55,58

%N Longest checkmate in king and two bishops versus king endgame on an n X n chessboard.

%H V. Kotesovec, <a href="http://problem64.beda.cz/silo/kotesovec_icga_2001.pdf">King and Two Generalised Knights against King</a>, ICGA Journal, Vol. 24, No. 2, pp. 105-107 (2001)

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Fairy chess endings on an n x n chessboard</a>, Electronic edition of chess booklets by Vaclav Kotesovec, vol. 8, p.225 and 236 (2013)

%F Conjecture: a(n) ~ 11*n/4.

%e Longest win on an 8x8 chessboard: Ka1 Bd1 Bb4 - Kc4, 1.Bb4-d6 Kc4-d5! 2.Bd6-g3 Kd5-c6 3.Ka1-b1 Kc6-d5 4.Kb1-c1 Kd5-c6 5.Kc1-c2 Kc6-d5 6.Kc2-d3! Kd5-e6 7.Kd3-e4! Ke6-e7 8.Ke4-e5 Ke7-d7! 9.Ke5-d5 Kd7-e8 10.Bd1-h5 Ke8-e7 11.Bg3-e5! Ke7-d8 12.Kd5-d6! Kd8-c8! 13.Kd6-c6! Kc8-d8! 14.Be5-f6 Kd8-c8! 15.Bh5-g6 Kc8-b8! 16.Kc6-b6! Kb8-a8 17.Bg6-f5 Ka8-b8! 18.Bf6-e5! Kb8-a8! 19.Bf5-e4#, therefore a(8) = 19.

%Y Cf. A225551, A225552, A225553, A225554, A225555, A225556, A227437.

%K nonn,hard,more

%O 3,2

%A _Vaclav Kotesovec_, May 10 2013

%E a(21)-a(22) from _Vaclav Kotesovec_, Jan 11 2017