The Treasure Map

We have put all the information from the story on the map below.

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		$$		n
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The square that the treasure is in is (3,3).

Noughts Solution

The first player can always win if she plays correctly. Call the first player, Player A and the second player, Player B. To win, Player A needs to put her first nought in the centre square of the board. Then, wherever Player B goes, Player A should copy that move but on the opposite side of the board. We show this in the picture below.

Player A has put the first nought in the centre (we have shown it as A1 to indicate that it was Player A’s first move). Then Player B has put a nought in the square marked B1. Player A has replied by putting her next nought in square A2, to match Player B’s move.

Now suppose that Player B has a move that will not mean that Player A can get three noughts in a row. Then there must be a square on the symmetrically opposite side of the board that is safe for Player A. If Player B doesn’t have a safe move, then Player A wins and doesn’t play symmetrically.