login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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)
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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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