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## Answers to 3D Tic-Tac-Toe

How many different 3-in-a-rows are there?

__Answer:__
49. There are eight 3-in-a-rows on each level, as well as twenty-five
3-in-a-rows using all three levels. Nine of these are vertical
3-in-a-rows where the spaces are directly on top of each other.
The other sixteen come from taking a 3-in-a-row within one level and
spreading it out between the three levels -- for example:

OR

By doing this, we get two 3-in-a-rows from each of the 3-in-a-rows
within a level, for a total of sixteen. This gives the total of
8 + 8 + 8 + 9 + 16 = 49.