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KPvk

3 pieces.

h#8.5
longest mate: h#6.5
deepest unique: 13
positions at that depth: h#7
deepest dual: h#3.5
deepest strict dual: 165,660
positions with a helpmate: 1,782
with a unique solution: 86,688
cells in the plane: 156,227 bytes
on disk

Deepest unique problems

h#6.5

6k1/8/8/8/8/8/4P3/2K5 w - - 0 1

e3 Kf7 e4 Ke6 e5 Kd5 e6 Kc4 e7 Kb3 e8=Q Ka2 Qa4#

set-play pure model ideal mirror promotion excelsior excelsior:white single-piece single-piece:white single-piece:black nocapture nocheck umnov

Published as Niemann (1947)

Niemann, John — Schachmatt, No. 427, 13/07/1947; Catalogue h# (CHM) avec 6 pieces, No. 61, 1995; Wenigsteiner im Hilfsmatt, No. 77, 1977; Problemista, No. 1569, 07-10/1981
Ban, Jenö — Magyar Sakkelet, 1961; Ideal-Mate Encyclopedia Vol.1, No. 12, 1999

h#6.5

8/8/7k/8/8/K7/P7/8 w - - 0 1

Kb3 Kg5 a4 Kf4 a5 Ke3 a6 Kd2 a7 Kc1 a8=Q Kb1 Qh1#

pure model ideal mirror promotion excelsior excelsior:white single-piece single-piece:black nocapture nocheck

h#6.5

8/8/8/K7/8/8/3P3k/8 w - - 0 1

d4 Kg3 d5 Kf4 d6 Ke5 d7 Kd6 Kb5 Kc7 Ka6 Kb8 d8=Q#

pure model ideal mirror promotion excelsior excelsior:white single-piece single-piece:black nocapture nocheck umnov

Deepest dual problems

Deepest dual with different first and last moves: h#3.5. The deepest dual overall is h#7, where the two solutions share a first or a last move.

h#3.5

8/2P5/8/8/8/8/8/2K1k3 w - - 0 1

Two solutions, with different first and last moves (2 starts, 2 ends).

c8=R Kf2 Kd2 Kf1 Ke3 Ke1 Rc1#
c8=Q Kf2 Kd2 Kf1 Ke3 Ke1 Qc1#

pure model ideal mirror promotion underpromotion closed-walk single-piece single-piece:black nocapture nocheck

h#3.5

8/3K4/5P2/3k4/8/8/8/8 w - - 0 1

Two solutions, with different first and last moves (2 starts, 2 ends).

Kc7 Ke6 f7 Ke7 Kc6 Kd8 f8=Q#
f7 Kc4 Kc6 Kb4 f8=Q+ Ka5 Qa3#

pure model ideal mirror promotion single-piece single-piece:black nocapture

h#3.5

3K4/2P5/8/4k3/8/8/8/8 w - - 0 1

Two solutions, with different first and last moves (2 starts, 2 ends).

Ke7 Kf4 Kf6 Kg4 c8=Q+ Kh5 Qh3#
Ke8 Kd6 Kf7 Kd7 Kf6 Ke8 c8=Q#

pure model ideal mirror promotion single-piece single-piece:black nocapture