World
Game
Of
Sprouts
Association

Pivot Table Periodicity

January 23, 2007

From normal games we know:

From normal games we know:

 

 

6n

6n+1

6n+2

6n+3

6n+4

6n+5

6m

0

1

1

1

0

0

6m+1

1

1

1

0

0

0

6m+2

1

1

1

0

0

0

6m+3

1

0

0

0

1

1

6m+4

0

0

0

1

1

1

6m+5

0

0

0

1

1

1

 

 

 

 

 

 

 

 

Remark:

n>=0,m>=0

 

Exception:

2P2=G0 (n=0,m=0)

 

 

In misere games it will look like this:

 

 

6n

6n+1

6n+2

6n+3

6n+4

6n+5

6m

0

0

1

1

1

0

6m+1

0

1

1

1

0

0

6m+2

1

1

1

0

0

0

6m+3

1

1

0

0

0

1

6m+4

1

0

0

0

1

1

6m+5

0

0

0

1

1

1

 

 

(!!!)Remark:

The given table only applies to iPj for which i=6n,6n+1, 6n+3, 6n+4 n>=0; i=6n+2, i=6n+5 n>0;

j=6m, 6m+1, 6m+2, 6m+3, 6m+4, 6m+5 m>0!

For m=0,n=0 the table will change.

For instance 3P5=G3, 0P5=G1 and so on.

 



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