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]