No.575 by Petko A. Petkov – Author has sent this problem to illustrate some important moments of a play in Disparate-problems, in particular, how to create tries and anti-duals. (JV)
Definitions:
Disparate: If one side makes a move with a piece of type “x” (black, white, neutral, half-neutral, etc., King included), the other side cannot answer immediately by moving a piece of the same type “x”. (For example: white Qc1, black Ka8,Qa7 – mate in 1 move. After 1.Qc8#, Black is mated because 1…Qb8? is illegal. The mate is possible also with the neutral nQc1 – after 1.nQc8#. Black cannot move the same neutral Queen.) Every Pawn’s promotion is a Pawn’s move, therefore after such promotion (into any possible piece) the other side cannot answer immediately with its Pawn. We can say that after the move of the figure of type “x” any enemy figure of type “x” falls under Half-moving paralysis. This paralysis disappears immediately on the next half-move, if the opponent plays with another piece of type “y”. (This way it is implemented in Popeye. Another implementation of Disparate you can find in WinChloe, but it is based on the different rules. )
PAO(PA): (0,1) Chinese. Chinese piece operating along Rook lines: moves as Rook, but captures only by hopping over a hurdle to any square beyond.
VAO(VA): (1,1) Chinese. Chinese piece operating along Bishop lines: moves as Bishop, but captures only by hopping over a hurdle to any square beyond.
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No.575 Petko A. Petkov
Bulgaria
original – 23.07.2014
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Hints: (click to show/hide)
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white Kf1
black kh8 qd8 sd4 sh4 bg8 vac8 pae8 pa3 pb7 pf2 pg3
neutral vac1 pag1
h#2 2 solutions (1+11+2)
Disparate (Py)
PAOs: e8, g1; VAOs: c1, c8
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Preliminary notes:
In my opinion this problem has some logical elements. Without the VAc8 is possible mate in 1 after 1.nVAb2 nPAh1# (PAe8 is paralyzed). But with VAc8 this attempt is false because 2.VAh3! Analogical: without PAe8 is possible 1.nPAh1 nVAb2# (VAc8 is paralyzed) but with PAe8 this short plan is again not correct – 2.PAe5!
Therefore the main goal is to eliminate the control of black VAO/PAO to squares h3/e5. There are two ways for realization.
Thematical tries with black Grimshaw PA /VA on e6:
1. PAe6!? – but now it is impossible to make the tempo-move 1…nPAg2? because nPAg1 is paralyzed for White! No tempo-move is also 1…nVAd2? and 2.nVAc3 is impossible because paralyze of nVAd2 for Black!
1.VAe6!? – – but now it is impossible to make the tempo-move 1…nVAd2? because nVAb1 is paralyzed for White! No tempo-move is also 1…nPAg2? and 2.nPAh2 is impossible because paralyze of nPAg2 for Black!
Solutions: (click to show/hide)
1.Qd8-d7 nPAg1-g2{!! (Tempo-move! Here is only a try 1...nVAd2!?
because the nVAd2 is paralyzed for Black and it is impossible 2.nVAc3??)
} 2.nVAc1-b2 nPAg2-h2 #{! (because PA e8 is paralyzed 3.PAe5??
with idea to paralyze nPAh2 is impossible!).}
1.Qd8-e7 nVAc1-d2{!! (Tempo-move! Here is only a try 1...nPAg2!?
because the nPAg1 is paralyzed for Black and it is impossible 2.nPAh2??)
} 2.nPAg1-h1 nVAd2-c3 #{! (because VAc8 is paralyzed 3.VAh3??
with idea to paralyze nVAc3 is impossible!)
(C+ by Popeye 4.67)}
1. Creation of two special neutral batteries: nPAg2/nVAb2 (I sol) and nVAc3/nPAh1 ( 2 sol). It's interesting that in these batteries the both neutral pieces stand on 4 different squares!
2. In my opinion, here we have 4 combined duos of thematic pieces with reciprocal interchange of functions: a) nVAc1/nPAg1; b) VAc8/PAe8; c) PAe8/nPAg1 - because in the solution (I) nPA paralyses PA but in the try 1.PAe6? - PA paralyzes nPA!; d) VAc8/nVAc1 - because in the solution (II) nVA paralyses VA but in the try 1.VAe6? - VA paralyzes nVA!;
3. Dual-avoidance effects. Model mates.
Some other important moments will be shown in the second part of my article about Disparate, which is almost ready and will be published soon! (Author)
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No.575 
Very nice effects. I like it that though the mating move is only a single check, black cant defeat it moving neither nPao or NVao!