Source: Shared by Alok Mittal (Cannan Partners)
Problem:A 3x3 tic tac toe has 8 "winning lines" (3 horizontal, 3 vertical and 2 diagonals). How many "winning lines" does the 3x3x3 3D tictactoe have? There is a brute force solution, and then there is the aha! solution.
Update (23 Oct 2014)
Solution: Posted in comments by Anti, Taz, Javier, Shubham Gupta, Leela. Detailed solution and much more advanced problems in the document http://library.msri.org/books/Book42/files/golomb.pdf