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]