World

Game

Of

Sprouts

Association

n - number of spots (from which 3 lines can emerge)

n<1> - this formula means, that we have a number "n" of spots and one more spot from which only one line can emerge (it already has two lines)

Let

n=3(2k+1), k=0,1,2,3…

Then

In game n<1>+ or, which is the same, 3(2k+1)<1>+ the first player wins, for his first move should be next one:

n<1>+ 1 (n+1) 1 [2-n] = 1 (2(3k+2)) 1 [2-(3(2k+1))] k=0,1,2,3…

Example 1:

n=3 (k=0)

3<1>+

3<1>+ 1(4)1[2,3]

1st player wins

Example 2:

n=9 (k=1) 9<1>+

9<1>+ 1(10)1[2-9]

1st player wins

And so on (etc.)

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