REPITITION

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raysands
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Real name: RAY SANDS

REPITITION

Post by raysands » Sun Mar 18, 2018 00:20

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

ildjarn
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Real name: Joost de Heer

Re: REPITITION

Post by ildjarn » Sun Mar 18, 2018 10:17

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.
Lasst die Maschinen verhungern, Ihr Narren...
Lasst sie verrecken!
Schlagt sie tot -- die Maschinen!

raysands
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Real name: RAY SANDS

Re: REPITITION

Post by raysands » Sun Mar 18, 2018 16:17

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
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Re: REPITITION

Post by TAILLE » Sun Mar 18, 2018 17:10

raysands wrote: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
Image

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
Gérard

raysands
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Real name: RAY SANDS

Re: REPITITION

Post by raysands » Sun Mar 18, 2018 20:31

many thanks.
nicely demonstrated

ildjarn
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Joined: Tue Aug 22, 2006 15:38
Real name: Joost de Heer

Re: REPITITION

Post by ildjarn » Sun Mar 18, 2018 21:15

I read the question wrong. I assumed it was in the same game. If you talk about different variations, then yes, of course.
Lasst die Maschinen verhungern, Ihr Narren...
Lasst sie verrecken!
Schlagt sie tot -- die Maschinen!

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