[Retros] Sets of illegal positions. Yefim 02/06/2006

[TregerYefim at aol.com]

Hello, from Yefim.
Still working on the book about Math and Chess I found an illegal position 
which forms illegal set of positions.
Thus, the first position
k7/BRp5/KpP1p3/1P1b4/4p3/1P1P4/8/8 w - - 0 1
forms cycle set with four illegal positions (if sides moves by Bishops 
without captures).
The second position
k7/BRp5/KpP1p3/1P1b1p2/8/1P1P1p2/8/8 w - - 0 1
forms an illegal set with 6 positions (also only Bishops move) and so on...
I have proved that if all positions in a set are mutual reached and one of 
them is illegal then all positions of the set are illegal.
There are illegal sets in chess... Chess players risk to enter illegal 
position and not noticing about this, continue to play creating new illegal 
positions... Unreal World?! 
Please use this idea only for fantastic book, not for Math (just kidding!; 
but if you
have some interesting thoughts about it, they will be appreciated in the 
book).

Yefim. 02/06/2006
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