## Solution to: Tick-Tack-Toe

It is clear that if we know who made the sixth move, we also know who can make the seventh move and wins.

If Angela (circles) has made the sixth move, there are three possibilities for the situation after five moves:

Possibility 1: Possibility 2: Possibility 3:
 O O X X X
 O O X X X
 O O X X X

Based on the rules of the game, only possibility 1 could have resulted in the situation after six moves. In that case, there are three possibilities for the situation after four moves:

Possibility 1: Possibility 2: Possibility 3:
 O O X X
 O O X X
 O O X X

Based on the rules of the game, David (crosses) would have made the winning move, which however did not happen. From this, we can conclude that David did not make the fifth move and Angela did not make the sixth move. Therefore, David must have made the sixth move and Angela can make the seventh, winning move!

To check that David could indeed have made the sixth move, we look at the following three possibilities after five moves:

Possibility 1: Possibility 2: Possibility 3:
 O O O X X
 O O O X X
 O O O X X

Based on the rules of the game, only possibility 3 can result in the situation after six moves. Therefore, David could indeed have made the sixth move.

Conclusion: David has made the sixth move, and Angela will make the seventh move and win.

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