No.415 
Pierre Tritten (France)

 

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Original Problems, Julia’s Fairies – 2013 (III): September- December

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Please send your original fairy problems to: julia@juliasfairies.com


No.415 by Pierre Tritten – Excellent activity of the white King and Queen! (JV)


Definitions:

Anti-Circe Clone: A capturing piece (including King) takes the nature of the captured piece and then goes to its Circe rebirth square. The checking/mating piece do not take the nature of the King and its returning square is according its own nature. 

Circe:  Captured units (not Ks) reappear on their game-array squares, of the same color in the case of pieces, on the file of capture in the case of pawns, and on the promotion square of the file of capture in the case of fairy pieces. If the rebirth square is occupied the capture is normal.


No.415 Pierre Tritten
France
original – 07.11.2013
 
415-h#2-pt
h#2                                              (2+8)
b) Sh4→g4; c) Sh4→f2
Anti-Circe Clone
 
 
Solutions: (click to show/hide)
 

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seetharaman
seetharaman
November 8, 2013 07:52

Very nice problem. But where is the ‘cycle’? Three different black pieces sacrifice to the white king – very neat! Does it mean there is a cyclic effect?

Pierre Tritten
Pierre Tritten
November 8, 2013 20:52

Thank you, seetharaman!
The black pieces having the same role in each solution, I think I can call that a cycle, but I may be wrong…

Nikola Predrag
Nikola Predrag
November 8, 2013 22:12

Pierre,
cycle needs the links which connect 1st point with 2nd, 2nd with 3rd, … so on to the last point and finally the last point with the 1st. There is usually some relation between the elements of 2 sets, for instance in 3 phases (3×2):
(A+B+C)x(1+2)=(A1+B2)+(B1+C2)+(C1+A2)
or “incomplete” in 2 phases (3×3):
(A+B+C)x(1+2+3)=(A1+B2+C3)+(B1+C2+A3) +missing phase (C1+A2+B3) which would make a full cycle.

Full 3×3 cycle can be organized to show three cycles 3×2:
(A1+B2)+(B1+C2)+(C1+A2)
(B2+C3)+(C2+A3)+(A2+B3)
(A1+C3)+(C1+B3)+(B1+A3)
e.g. A,B,C may be particular pieces and 1,2,3 particular functions (or squares). Of course, any relation might cyclically connect the pairs of the elements into a cycle.

In your No.260 (Kobulchess), 3 white pieces cyclically exchange the functions:
1=W1-capture for sacrifice to bK
2=W2-capture for mate
3=passive flight-guard
That is a complete 3×3 cycle in 3 phases.

Pierre Tritten
Pierre Tritten
November 9, 2013 09:22

It’s surely a cycle that doesn’t turn round 😉