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.

3, 12, 16, 31, 21, 44, 3, 6

Offset: 0

Author

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

Keywords

• nonn

Comments

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.

Examples

			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
		

References

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