A227437 Longest checkmate in king and 3 knights versus king endgame on an n X n chessboard.

10, 10, 16, 18, 21, 25, 29, 33, 36, 41, 45, 50, 55, 60, 66

Offset

4,1

Comments

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

Links

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

Example

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)

Crossrefs

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

Sequence in context: A175220 A272479 A167427 * A352314 A363328 A047879

Adjacent sequences: A227434 A227435 A227436 * A227438 A227439 A227440

Keyword

nonn,hard,more

Author

Vaclav Kotesovec, Jul 11 2013

Extensions

a(16) from Vaclav Kotesovec, Jan 07 2017

a(17) from Vaclav Kotesovec, Sep 05 2017

a(18) from Vaclav Kotesovec, Jan 24 2018

Status

approved