Tic Tac Toe 1

If $X$ puts his sign in either of the two ways shown above (the yellow $X$ is the move), he will force $O$ to block his three-in-a-row and the game will be a draw.

If $X$ puts his sign in any of the following positions, he will loose because $O$ can put his sign in a way that he can make a three-in-a-row no matter what could be $X$ 's third move:

In the image above the yellow $X$ represents $X$ 's second move and the rede $O$ represents $O$ 's third move. The red lines shows where $O$ will be able to make a three-in-a-row in his fourth move.

If X put in 1 , O can put in 3 or 5 and then O will in his next turn, because O will have 2 ways to win in this case.

It is symmetric , so also if X puts in 3 , X will lose .

If X put in 4 , O will put in 2 and then O will in his next turn, because O will have 2 ways to win in this case.

It is symmetric , so also if X puts in 6 , X will lose .

If X put in 2 , O will put in 4 then X will put in 3 then O will put in 1 or 6 to have an opporunity to win , then X will put in the other choice of "1 or 6" and then O will put in 5 (last box) so it is draw .

It is symmetric , so also if X puts in 5 the game will end as draw .

So the answer is 1+3+4+6=14

If X goes at 1, then O can go at 5, and O will win at either 2 or 3 on his next turn (whatever X does not block), so X will lose.

If X goes at 2, then O must block at 4, and then X must block at 3, and this will eventually result in a draw.

If X goes at 4, then O can go at 2 to block X's two in a row, and O will win at either 1 or 5 on his next turn (whatever X does not block), so X will lose.

By symmetry, if X goes at 3 it will be same result as X going at 1 (X will lose), if X goes at 5 it will be the same result as X going at 2 (a draw), and if X goes at 6 it will be the same result as X going at 4 (X will lose).

Therefore, X will lose if he goes at 1, 4, 3, and 6, and 1 + 3 + 4 + 6 = 14 .

X can only win if he places at 2 or 5 , at every other position O can win by forming two ways to win of which X can block only one

If $X$ puts in 1, $O$ will put in 5 and has two chances to make 3 in a diagonal or column. $X$ loses .

If $X$ puts in 2, $O$ must put 4, then $X$ must put in 3, $O$ can put in 1, 5 and 6 . Lets say he puts in 1. $X$ must put in 6, $O$ puts in 5 and it is a draw.

If $X$ puts in 3, $O$ will put in 2 and has two chances to make 3 in a diagonal or row. $X$ loses .

If $X$ puts in 4, $O$ must put in 2 has two chances to make 3 in a diagonal or column. $X$ loses .

If $X$ puts in 5, $O$ must put in 6, $X$ must put in 1, $O$ can put in 2, 3 and 4. Lets say he puts in 3, $X$ must put in 4 and $O$ only has the space to put in 2. And it's a draw.

If $X$ puts in 6, $O$ must put in 5 and has two chances to make 3 in a diagonal or column. $X$ loses .

1 + 3 + 4 + 6 = 14