[Retros] Ortho-reconstructions

Valery Liskovets liskov at im.bas-net.by
Tue Mar 30 04:52:51 EDT 2010

Counting maximal 3d-repetition-avoiding routes as a retro-theme was
by N.Plaksin and me more than 25 years ago in several Proca-retractors,
and also in
long AP Keym-type problems. In simplest cases we are only to make
between 4x13>50 and 4x12<50, but there are subtler situations. See, in
PDB's P0008501 (-293&#1) with a 42-move Bishops's "waltz", P0000045
with the most sophisticated solution (including a longest Knight's
route) and P0000594 (#150 AP).

Similar combinatorics lies in the core of Pr.16 (b)
("Ortho-reconstructions") by M.Caillaud
(R199, Probleemblad, Mar. 2003; P1007324). I found this twin to be unsound:
there exists a 3d-repetition-avoiding proof-game which is 103
single-moves long
(and which can easily be transformed into an exact 100-move draw game).
we start from the diagram modified to wKd2, wBc8, bNe6 (for convenince I
mark by "!"
the moves resulting in the 2nd repetition):

1.Kd3 Nf8 2.Be6 Nh7 3.Bc8 Nf6 4.Be6 Nh5 5.Bc8 Ng7 6.Be6 Ne8
7.Bc8 Nc7 8.Be6 Na8 9.Bc8 Nc7! 10.Be6!Ne8! 11.Bc8!Ng7! 12.Be6!Nh5!
13.Bc8!Nf6! 14.Be6!Nh7! 15.Bc8!Nf8! 16.Be6!Ng6 17.Bc8 Nh8 18.Be6 Ng6!
19.Bc8!Ne7 20.Be6 Ng8 21.Bc8 Nh6 22.Be6 Ng8! 23.Bc8!Ne7! 24.Be6!Nc6
25.Bc8 Na7 26.Be6 Nc6! 27.Bc8!Na7! 28.Bd7+ Nc6 29.Be6 Ne7 30.Bc8 Ng6
31.Be6 Nh8 32.Bc8 Ng6! 33.Be6!Nf8 34.Bc8 Nh7 35.Be6 Nf6 36.Bc8 Nh5
37.Be6 Ng7 38.Bc8 Ne8 39.Be6 Nc7 40.Bc8 Na8 41.Be6 Nc7! 42.Bc8!Ne8!
43.Be6!Ng7! 44.Bc8!Nh5! 45.Be6!Nf6! 46.Bc8!Ng8 47.Be6 Nh6 48.Bc8 Ng8!
49.Be6!Ne7! 50.Bc8!Nc6! 51.Be6!Na7 52.Bd7+!

Valery Liskovets

Guus Rol wrote:

> I named this phenomenon "premature repetition". It makes an

> interesting study to compare the repetition convention and the 50-M

> convention regarding "possible draws" which occur fully in the past or

> partly in the present / future as well. It is baffling that

> FIDEX uses such diverse descriptions for such similar administrative laws.


> Guus.





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