REPITITION

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raysands
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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 ?

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ildjarn
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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.
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raysands
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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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Re: REPITITION

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

many thanks.
nicely demonstrated

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ildjarn
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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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