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A115229 Number of ways in chess to force mate in n moves for a single knight against a single pawn, without duals, without short mates and excluding rotations, mirroring and color reversing. 0
3, 12, 16, 31, 21, 44, 3, 6 (list; graph; refs; listen; history; text; internal format)



The mate is only possible against a pawn on a border line (a-line or h-line).

No non-dual (single solution) mates are possible beyond n = 7 (cf. Springerzauber, page 178).

Obviously the positions with the higher number of moves lead via a unique chain of positions with the lower numbers.


John Selman and Harrie Grondijs, Springerzauber, 1998, chapter 16.


Table of n, a(n) for n=0..7.


Example: The three positions with 0 moves (checkmate) are:

a) White: Kc2, Nb3, Black: Ka1, Pawn a2

b) White: Kc1, Nb3, Black: Ka1, Pawn a2

c) White: Kc1, Nc2, Black: Ka1, pawn a2


Sequence in context: A277738 A064106 A022411 * A224924 A136047 A082965

Adjacent sequences: A115226 A115227 A115228 * A115230 A115231 A115232




N. J. A. Sloane, based on email from Harrie Grondijs, Mar 06 2006



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Last modified December 9 18:21 EST 2022. Contains 358703 sequences. (Running on oeis4.)