Helpmate tablebases Every solution to every position, precomputed.

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KNvkr

4 pieces.

h#9.5
longest mate
h#8
deepest unique
9
positions at that depth
h#8
deepest dual
h#6.5
deepest strict dual
2,913,057
positions with a helpmate
16,580
with a unique solution
1,892,352
cells in the plane
1,167,965 bytes
on disk

Deepest unique problems

h#8

8/8/8/8/8/7k/5r1N/K7 b - - 0 1

  1. Kg2 Nf3 Kf1 Kb1 Ke2 Kb2 Kd3+ Kc1 Kc3 Kd1 Kb2 Nd4 Ka1 Kc1 Ra2 Nb3#

pure model ideal switchback self-block nocapture

Published as Elkies (1995)

  • Elkies, Noam D. — Variantim, No. 546, 11/1995
  • Mertes, Helmut — feenschach, 01/1977; Ideal-Mate Encyclopedia Vol.1, No. 400, 1999

Deepest dual problems

Deepest dual with different first and last moves: h#6.5. The deepest dual overall is h#8, where the two solutions share a first or a last move.

Only 2 distinct ideas exist at this depth.

h#6.5

8/8/8/4k3/8/2N5/1r6/K7 w - - 0 1

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

  1. Ne4 Ra2+ Kb1 Kf4 Kc1 Kf3 Kd1 Kg2 Ke1 Kh1 Kf1 Rh2 Ng3#
  2. Nd5 Rb1+ Ka2 Kd6 Ka3 Kc6 Ka4 Kb7 Ka5 Ka8 Ka6 Rb8 Nc7#

pure model ideal self-block nocapture

h#6.5

8/8/8/8/8/8/1rK1k3/N7 w - - 0 1

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

  1. Kc1 Kd3 Nc2 Kc4 Kd2 Kb3 Kd1 Ka2 Nd4 Ka1 Kc1 Ra2 Nb3#
  2. Kc3 Ke1 Nb3 Kd1 Kb4 Kc2 Ka4 Kb1 Nd4 Ka1 Ka3 Rb1 Nc2#

pure model ideal closed-walk self-block nocapture nocheck

Note: the side to move is in check in the diagram.