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KNNvk

4 pieces.

h#8
longest mate: h#6.5
deepest unique: 9
positions at that depth: h#6.5
deepest dual: h#5
deepest strict dual: 1,572,652
positions with a helpmate: 20,936
with a unique solution: 1,892,352
cells in the plane: 1,421,837 bytes
on disk

Deepest unique problems

h#6.5

1k5N/8/8/8/8/8/7N/3K4 w - - 0 1

Ke2 Kc7 Kf3 Kd6 Kg4 Ke5 Kh5 Kf4 Ng6+ Kg3 Nf1+ Kh3 Nf4#

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

Published as Bebesi (1910)

Bebesi, Gyula — Diagramme und Figuren, No. 1910, 12/12/1966; Catalogue h# (CHM) avec 6 pieces, No. 624, 1995; Ideal-Mate Encyclopedia Vol.1, No. 930, 1999

h#6.5

5k2/8/8/8/8/7N/2K5/7N w - - 0 1

Kd3 Kg7 Ke4 Kh6 Kf5 Kh5 Ng3+ Kh4 Kg6 Kg4 Nf2+ Kh4 Nf5#

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

h#6.5

7k/8/8/8/8/8/3N4/2NK4 w - - 0 1

Ke2 Kg7 Kf3 Kf6 Kg4 Ke5 Kh5 Kf4 Nd3+ Kg3 Nf1+ Kh3 Nf4#

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

Deepest dual problems

Deepest dual with different first and last moves: h#5. The deepest dual overall is h#6.5, where the two solutions share a first or a last move.

Only 2 distinct ideas exist at this depth.

h#5

8/8/8/8/8/5N2/3K4/k6N b - - 0 1

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

Kb1 Kc3 Kc1 Ng3 Kd1 Ne4 Ke2 Kb2 Kd1 Nc3#
Kb2 Kd1 Kc3 Kc1 Kd3 Ne5+ Ke2 Ng3+ Ke1 Nd3#

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

h#5

8/8/8/k7/8/3K4/1N6/6N1 b - - 0 1

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

Kb4 Ne2 Ka3 Kc4 Ka2 Kb5 Kb3 Nc1+ Ka3 Nc4#
Kb5 Kc2 Kb4 Kb1 Kc3 Na4+ Kd2 Nf3+ Kd1 Nc3#

set-play pure model ideal mirror closed-walk single-piece single-piece:black nocapture