World
Game
Of
Sprouts
Association
Strategy for N = 10, 16, …
Let's look at the game: n=2(3k+2), k=1,2,3... (10,16,22,28...spots)
n+
1) 1(n+1)1[2] 3(n+2)4 1(n+3)n+1[3,5]
2) 1(n+1)1[2] 1(n+2)3 n+1(n+3)n+2[3]
3) 1(n+1)1[2] 3(n+2)3 3(n+3)n+2[4,5]
4) 1(n+1)1[2] 3(n+2)3[4-m] m=2(3s+2), s=0,1,2…
4.1) n=m
3((n+3)@1)n+2
4.2) n>m
3(n+3)n+2[m+1]
5) 1(n+1)1[2] 3(n+2)3[4-m] m=6s+5, s=0,1,2…
3((n+3)@4)n+2
6) 1(n+1)1[2] 3(n+2)3[4-m] m=6s, s=1,2,3…
6.1) n-m=4
3(n+3)n+2[4]
6.2) n-m>4
3((n+3)@4)n+2
7) 1(n+1)1[2] 3(n+2)3[4-m] m=6s+1, s=1,2,3…
3(n+3)n+2[m+1]
8) 1(n+1)1[2] 3(n+2)3[4-m] m=2(3s+1), s=1,2,3…
3((n+3)@4)n+2
9) 1(n+1)1[2] 3(n+2)3[4-m] m=3(2s+1), s=1,2,3…
9.1) n=m+1
3(n+3)n+2[4]
9.2) n>m+1
3(n+3)n+2[m+1,m+2]