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:


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.