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MatPlus.Net Forum General ABCD-DCBA

### ABCD-DCBA

Has this been done in #2 form? does anyone have an example either from set to key or try to key? (4 changed black defenses). In keeping with Cyclone terminology, has the threat form been shown with 3 defenses? A, BCD to D, CBA

Isn't this just a double reciprocal change [or reciprocal change + le Grand]?

ABCD - BADC is double reciprocal change.

This is the same: it is equal to AD-DA + BC-CB

You are right of course :)

silly me!! besides the 4th Pr. Problemist 1973 by Vukcevich, are there others that achieve this, perhaps without king flights?

(7) Posted by Peter Gvozdjak [Wednesday, Sep 7, 2011 17:40]

using the following kind of formula
phase i: K(T)MMMM… / phase ii: K(T)MMMM… etc,
where K=key, T=threat, M=mate,
we can simply come to several two-phase non-cyclic patterns:

this is a double reciprocal change of mates ()AB/()BA and ()CD/()DC (and is equal to eugene's question ()ABCD/()DCBA).
there are about 20 orthodox twomovers known to me.
yes, there are also examples without bK defences.
as an example, see CYCLONE 2, No. xlii (p18).

this is the le grand theme (A)B/(B)A combined with a reciprocal change ()CD/()DC.
only 3 such orthodox twomovers in existence so far!
see CYCLONE 2, No. xliii (p18).

there are also other possibilities, not mentioned in this thread, like using thematic keys and mates, or keys, threats and mates.
for those, see CYCLONE 2, Nos. xliv, xlv and xlvi (pp18-19).

f.y.i.: i am planning to start a series of articles exactly on this subject in "pat a mat" next year.
i believe it could be of help and of interest for the composers for two reasons:
1. such themes are quite a demanding challenge.
2. there are not many examples in majority of these themes.

correct me if I'm wrong, I believe a double-reciprocal can be relettered into a completely-reduced Ideal Rukhlis?!

It is indeed a special category of Ideal Rukhlis known by the more descriptive "Double Reciprocal change"

Aaron Hirschenson &
Peter Gvozdják
Pat a Mat 2012

#2

In Pat a Mat (from Slovakia) Peter Gvozdják has embarked on a series of articles surveying the
field of 4 recurrent white moves in the 2-moverwithout cyclic effects. Never one to mind about
offending the purists, Peter quotes, among some fineexamples, the 2-mover given above, with its
unprovided flights andflight-taking try and key:
1.Qc6? (-) Sc~/Sce6/Sg~/
Sge6 2.Sc4/Sd7/Sf7/Sg4
ABCD; 1…Kxf6! 1.Qg6!
(-) with 2.Sd7/Sc4/Sg4/Sf7 BADC after the samedefences (also 1…Kxd6,Ke6 2.e8Q)
: doublereciprocal change afterrandom and correctionmoves of the two bSs. (Source THE PROBLEMIST MAY 2012 Pg.no.355 )