[Solved]: Is this NIM game tree correct?

Problem Detail: 

I have an assignment to construct a game of Nim (a game in which two players must divide a pile of tokens into two unequal sizes; 6 can be divided into 2 & 4 but not 3 & 3). I was provided a game tree (the same one I find on Google), but I am confused. Shouldn't the first turn of the second player have access to S6, S5, and S4 and S3 since 7 can be divided into 4 & 3?

Asked By : David B

Answered By : yatima2975

No, the game tree is not correct for the description you gave.

If you look a few levels downward, there's the position F(2), which by your description should be a dead end: you can't make a move, since splitting a pile of 2 into non-equal parts is not possible. Yet, the tree gives two options. Your observation that you should be able to move from 7 to 5, 6, or 3+4 is also correct.

I think Hendrik Jan is right, and this tree describes the game where you either take one or two tokens from a pile, and the player who takes the last token wins.

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Question Source : http://cs.stackexchange.com/questions/10787