Tri-Hex is a topological variant of Tic-Tac-Toe. A player wins by placing three of their pieces in a row. However, unlike standard Tic-Tac-Toe, the first player of Tri-Hex has a guaranteed win. Therefore Tri-Hex offers the following additional challenge:

For each initial move, find the sequence of moves that guarantees a win.

In addition to its topological and combinatorial properties, the board has an unusual structure. Every line of three is divided by its middle spot into segments with lengths in the golden ratio.

Tri-Hex was devised by Thomas H. O'Beirne of Glasgow, author of Puzzles and Paradoxes (Oxford 1965). He experimented with all topologically distinct patterns of nine rows to see if any were suitable for Tic-Tac-Toe play. He found trivial wins for the first player on all configurations except for this one.

This game is featured in Martin Gardner's "Mathematical Games" column of the November 1967 issue of "Scientific American". There, the following question is posed: If both payers make their best moves, is the game a win for the first player or the second, or is it a draw as in Tic-Tac-Toe?
Note that the Axiom game engine has proved that it is a win for the first player.