World
Game
Of
Sprouts
Association


 

Strategy for N = 11, 17,

 

 

 

Let's look at the game: n=6k+5, k=1,2,3... (11,17,23,29...spots)

 

 

n+

 

1) n=6(2q+1)+5, q=0,1,2

 

1.1) 1(n+1)1[2-(n+1)/2)] 2(n+2)3 1(n+3)n+1[2,4]

 

1.2) 1(n+1)1[2-(n+1)/2)] 1(n+2)2 n+1(n+3)n+2[2]

 

1.3) 1(n+1)1[2-(n+1)/2)] 2(n+2)2 1(n+3)n+1[2]

 

1.4) 1(n+1)1[2-(n+1)/2)] 2(n+2)2[3-m] m=3(2s+1), s=0,1,2

2(n+3)n+2[m+1]

 

1.5) 1(n+1)1[2-(n+1)/2)] 2(n+2)2[3-m] m=2(3s+2), s=0,1,2

2((n+3)@3)n+2

 

1.6) 1(n+1)1[2-(n+1)/2)] 2(n+2)2[3-m] m=6s+5, s=0,1,2

 

1.6.1) (n-1)/2=m

2(n+3)n+2[3]

 

1.6.2) (n-1)/2>m

2(n+3)n+2[m+1,m+2]

 

1.7) 1(n+1)1[2-(n+1)/2)] 2(n+2)2[3-m] m=6s, s=1,2,3

 

1.7.1) (n+1)/2=m

2((n+3)@1)n+2

 

1.7.2) (n+1)/2>m

2(n+3)n+2[m+1]

 

1.8) 1(n+1)1[2-(n+1)/2)] 2(n+2)2[3-m] m=6s+1, s=1,2,3

2((n+3)@3)n+2

 

1.9) 1(n+1)1[2-(n+1)/2)] 2(n+2)2[3-m] m=2(3s+1), s=1,2,3

1.9.1) (n+1)/2=m+4

2(n+3)n+2[3]

 

1.9.2) (n+1)/2>m+4

2(n+3)n+2[(m+1)-(m+5)]

 

 

2) n=12q+5, q=1,2,3

 

2.1) 1(n+1)1[2-(n+1)/2)] 2(n+2)3 1(n+3)n+1[2,4]

 

2.2) 1(n+1)1[2-(n+1)/2)] 1(n+2)2 n+1(n+3)n+2[2]

 

2.3) 1(n+1)1[2-(n+1)/2)] 2(n+2)2 2(n+3)n+2[3,4]

 

2.4) 1(n+1)1[2-(n+1)/2)] 2(n+2)2[3-m] m=3(2s+1), s=0,1,2

 

2.4.1) (n+1)/2=m

2((n+3)@1)n+2

 

2.4.2) (n+1)/2>m

2(n+3)n+2[m+1]

 

2.5) 1(n+1)1[2-(n+1)/2)] 2(n+2)2[3-m] m=2(3s+2), s=0,1,2

2((n+3)@3)n+2

 

2.6) 1(n+1)1[2-(n+1)/2)] 2(n+2)2[3-m] m=6s+5, s=0,1,2

2.6.1) (n+1)/2=m+4

2(n+3)n+2[3]

 

2.6.2) (n+1)/2>m+4

2((n+3)@3)n+2

 

2.7) 1(n+1)1[2-(n+1)/2)] 2(n+2)2[3-m] m=6s, s=1,2,3

2(n+3)n+2[m+1]

 

2.8) 1(n+1)1[2-(n+1)/2)] 2(n+2)2[3-m] m=6s+1, s=1,2,3

2((n+3@3)n+2

 

2.9) 1(n+1)1[2-(n+1)/2)] 2(n+2)2[3-m] m=2(3s+1), s=1,2,3

 

2.9.1) (n-1)/2=m

2(n+3)n+2[3]

 

2.9.2) (n-1)/2>m

2(n+3)n+2[m+1,m+2]

 

 



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