What is the number of lines that pass through the center of an n-dimensional tic-tac-toe grid?
closed as too localized by Robin Chapman, Andy Putman, Charles Siegel, François G. Dorais♦ Aug 21 '10 at 19:38
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The squares tic tac toe grid can be represented with $(x^1,x^2,...,x^n)$ where each can be 0, 1 or 2.
A line passing through the center can be identified Given any coordinate except $(0,0,...,0)$.
There are $3^n-1$ possible coordinates to start a line from.
For each line through center, there will be two endpoints. This should help you get your answer.