[Retros] Castling and repetition

[TregerYefim at aol.com]

I have read suggestions about genetic ideas for castling with a big pleasure.
They are probably good for chess composition, but they have little 
connections with
mathematics, which we have discussed before (below).
 
Each position (as diagram) has to have unique properties of castling rights 
which may be recorded by binary system (corresponds to EPD-FEN notation)
There are 16 of them.
0000 = no games (from the position) with any castling;
0001= q: games with Black Queen side castling;
0010 = k: games with Black King side castling;
0011= kq: games with Black King or Queen side castling;
0100 = Q: games with White Queen side castling;
0101 = Qq: games with White Queen side or Black Queen side castling;
0110 =Qk: games with White Queen side or Black King side castling;
0111=games with White Queen side or Black King side or Queen side castling;
1000=K: games with White King side castling;
1001=Kq: games with White King side or Black Queen side castling;
1010=Kk: games with White King or Black King side castling;
1011=Kkq: games with White King side or Black King or Queen side castling;
1100=KQ: games with White King side or Queen side castling;
1101=KQq: games with White King side or Queen side or Black Queen side 
castling;
1110=KQk: games with White King or Queen side and Black King side castling;
1111= KQkq games with all castling possible.

"Equal positions must have the same Binary Word for castling". If you add 
this sentence to the FIDE rules (about repetition) you do not need wierd phrases 
about permanent or temporary rights of castlings...

Of course, there are situations where defining the right castling Binary type 
is very difficult, but that is caused by complexity of Chess, not by the math 
classification above. There are positions with King and Rook have not been 
moved before, but no games from them, so they have 0000 castle type. If an 
arbiter decides by his judgment that castling is possible, we may accept it, but it 
is not math point of view.

Problem.
Create a position (White to move) with all castling rights (1111=KQkq), where 
after White's move all castling right will be lost (0000).

Yefim 10/23/2007




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