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A227437 Longest checkmate in king and 3 knights versus king endgame on an n X n chessboard. 7
10, 10, 16, 18, 21, 25, 29, 33, 36, 41, 45, 50, 55, 60, 66 (list; graph; refs; listen; history; text; internal format)



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


Table of n, a(n) for n=4..18.

John Beasley, How many knights does a king require?, British Endgame Study News, Special Number 8, p. 8, December 1997.

V. Kotesovec, King and Two Generalised Knights against King, ICGA Journal, Vol. 24, No. 2, pp. 105-107 (2001)

V. Kotesovec, Fairy chess endgames - new results 2008, Electronic edition of chess booklets by Vaclav Kotesovec, Vol. 2, (2008)

V. Kotesovec, Fairy chess endings on an n x n chessboard, Electronic edition of chess booklets by Vaclav Kotesovec, vol. 8, pp.52-64 (2013)

Wikipedia, Endgame tablebase


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.

(In the above, 'S' (for "Springer" in German?) stands for knight moves.) - M. F. Hasler, Apr 22 2022)


Cf. A225551, A225552, A225553, A225554, A225555, A225556, A225557.

Sequence in context: A175220 A272479 A167427 * A352314 A047879 A344336

Adjacent sequences: A227434 A227435 A227436 * A227438 A227439 A227440




Vaclav Kotesovec, Jul 11 2013


a(16) from Vaclav Kotesovec, Jan 07 2017

a(17) from Vaclav Kotesovec, Sep 05 2017

a(18) from Vaclav Kotesovec, Jan 24 2018



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Last modified November 29 18:13 EST 2022. Contains 358431 sequences. (Running on oeis4.)