REPITITION

[raysands]

is it possible to have the same board position with a different side to move in 8x8 draughts ?

[ildjarn]

If you mean checkers: no.

Let p be the number of plies (half-moves), NUMPIECES the number of pieces on the board and ROW(X) be the row number of each piece.
Let F(p)=[p+sum(ROW(piece[n]),n=1..NUMPIECES)] MOD 2. This number is either 0 or 1. After a white or black move, p increased by one, and one of the ROW(X) numbers increased or decreased by one. This leads to an increase of 0 or 2. Modulo 2 this means that F(p+1)=F(p). In order to change the colour to move, F(p) must change from odd to even or from even to odd. Contradiction.

[raysands]

thanks for your answer (very nice). i emailed ed gilbert who says it is possible to have the same board position with a different side to move. the variation i am talking about is 8x8 english draughts.

thanks

[TAILLE]

is it possible to have the same board position with a different side to move in 8x8 draughts ?

Hi,
Let's take the following position you can also put an a 8x8 board


After 1.33-29 23x34 2.44-40 35x44 3.49x29 25-30 it is white to move
and after 1.44-40 35x44 2.49x40 25-30 3.33-29 23x34 4.40x29 it is blaxk to move

[raysands]

many thanks.
nicely demonstrated

[ildjarn]

I read the question wrong. I assumed it was in the same game. If you talk about different variations, then yes, of course.