

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
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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. 105107 (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.5264 (2013)
Wikipedia, Endgame tablebase


EXAMPLE

Longest win on an 8 X 8 chessboard: Ka1 Sa2 Sb1 Sg1  Kf2, 1.Sg1h3! Kf2g3! 2.Sh3g5! Kg3f4! 3.Sg5f7! Kf4g3 4.Ka1b2 Kg3f4 5.Kb2c2 Kf4g3 6.Kc2d2 Kg3f4 7.Sb1a3 Kf4f3 8.Kd2d3 Kf3f4! 9.Sa3c4 Kf4f5! 10.Sc4e5 Kf5f4 11.Sa2b4 Kf4f5! 12.Sb4c6 Kf5e6 13.Kd3e4! Ke6f6! 14.Sc6d4! Kf6e7 15.Ke4f5! Ke7f8! 16.Kf5e6! Kf8g7 17.Sd4f5! Kg7f8 18.Se5g6! Kf8g8! 19.Ke6f6! Kg8h7! 20.Sf7g5! Kh7g8! 21.Sf5e7#, 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 A047879 A344336
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



