It’s time to take out paper and a pencil.
One of the ways in which we can think about this problem is to find where the three empty spots need to go instead of the six ones with an X.
The middle spot has to be empty because it is part of too many potential lines. If it had an X, then only four other spots (two corner and two sides) could have Xs as well, for a total of five.
At least one corner has to be empty because otherwise no sides could be filled, which would mean that there would only be four Xs.
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If three corners were filled, it wouldn’t work either because at least one of the sides between the filled corners would have to have an X, and this would create a line of three. So, only two corners can have Xs.
That leaves two options: diagonally opposite corners or corners on the same side.
If we try for corners on the same side, we can’t fill the spot between them because that would make a line of three. So, that doesn’t work.
Thus, the three empty spots have to be the center, and two diagonally opposing corners.
