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Anti-symmetri by Pavlos Moutecidis, International master in composition 1984

Anti-symmetry is a term in chess compositions with explicit reference to the following:

It clearly sounds like a Greek word, yet I was not able to find the exact meaning when I searched in the dictionary. It is in fact a Greek-made composite word, from the words ANTI (anti) and ΣYMMETPIA (symmetry). I copy from the ancient Greek dictionary:
Anti: As a prefix, it negates the meaning of the second part of a word.
Symmetry: The harmony occurring from ordinary analogy.

I do not know who established the term; he probably had good knowledge of the ancient Greek language. He was aware of the term "a-symmetry" (A-ΣYMMETPIA), which means the lack of analogy, and he excluded it on purpose. Instead, he introduced the term "anti-symmetry" that identifies the break of ordinary analogy in a chess problem, which while it has a symmetric setting across a certain axis, there is only a single solution (a unique key). The alternative solution with the symmetric key fails for some reason.
In the following four examples, both aspects required by the anti-symmetry are fulfilled, i.e. the positions are symmetric across an axis and the alternative key is only a try for a single reason.

Diagram 1
Thomas R: Dawson
Eskilstuna Kuriren 1920
S#5 Max. C+ 2+3



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Diagram 2
Herbert Hultberg
Springaren 1987
#3 C+ 5+2



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Diagram 3
Wilhelm Massmann
Problem 1953
S#5 Max. C+ 2+2



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Diagram 4
Gyögy Bakcsi & Lásló Zoltán
1 PR DSK's 58 TT
Serie-H#5 2 solutions C+ 4+6



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I also quote a sketch (in 4x8 board) that apparently meets both of the requirements, but it is not a true anti-symmetric. The initial diagram is indeed symmetric and the key is only 1 Rab4+! and not 1 Rcb4+? However, if we check carefully the position after the 4th black move, we notice that the position is still symmetric, yet there is no alternative to 5 Rd4. In my opinion, only half of the anti-symmetry pre-requisites is fulfilled and this sketch cannot be considered anti-symmetric.

Diagram 5
Pavlos Moutecidis
Sketch
S#7 C+ 4+3
Diagram 6
Position after
black's 4th move



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