%I #32 Nov 03 2024 05:02:11
%S 10,10,16,18,21,25,29,33,36,41,45,50,55,60,66
%N Longest checkmate in king and 3 knights versus king endgame on an n X n chessboard.
%C With 16 GB of memory it was possible to explore this ending on boards up to 15 X 15. On these boards the ending is a general win. I think that from some greater n this ending is drawn (and the sequence is finite), but this is only conjecture. - _Vaclav Kotesovec_, Jul 19 2013
%H John Beasley, <a href="http://www.jsbeasley.co.uk/besn/s8.pdf">How many knights does a king require?</a>, British Endgame Study News, Special Number 8, p. 8, December 1997.
%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="http://problem64.beda.cz/silo/kotesovec_fairy_endgames_2008.pdf">Fairy chess endgames - new results 2008</a>, Electronic edition of chess booklets by Vaclav Kotesovec, Vol. 2, (2008)
%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, pp.52-64 (2013)
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Endgame_tablebase">Endgame tablebase</a>
%e Longest win on an 8 X 8 chessboard: Ka1 Sa2 Sb1 Sg1 - Kf2, 1.Sg1-h3! Kf2-g3! 2.Sh3-g5! Kg3-f4! 3.Sg5-f7! Kf4-g3 4.Ka1-b2 Kg3-f4 5.Kb2-c2 Kf4-g3 6.Kc2-d2 Kg3-f4 7.Sb1-a3 Kf4-f3 8.Kd2-d3 Kf3-f4! 9.Sa3-c4 Kf4-f5! 10.Sc4-e5 Kf5-f4 11.Sa2-b4 Kf4-f5! 12.Sb4-c6 Kf5-e6 13.Kd3-e4! Ke6-f6! 14.Sc6-d4! Kf6-e7 15.Ke4-f5! Ke7-f8! 16.Kf5-e6! Kf8-g7 17.Sd4-f5! Kg7-f8 18.Se5-g6! Kf8-g8! 19.Ke6-f6! Kg8-h7! 20.Sf7-g5! Kh7-g8! 21.Sf5-e7#, therefore a(8) = 21.
%e (In the above, 'S' (for "Springer" in German?) stands for knight moves.) - _M. F. Hasler_, Apr 22 2022
%Y Cf. A225551, A225552, A225553, A225554, A225555, A225556, A225557.
%K nonn,hard,more,changed
%O 4,1
%A _Vaclav Kotesovec_, Jul 11 2013
%E a(16) from _Vaclav Kotesovec_, Jan 07 2017
%E a(17) from _Vaclav Kotesovec_, Sep 05 2017
%E a(18) from _Vaclav Kotesovec_, Jan 24 2018