Math competition

This week I returned from a math competition called Exeter. It’s in (wouldn’t you know it) Exeter Massachusetts. It was about a 5 hour drive. So I ended up riding in a car for 10 hours in the space of 24. The competition  itself was very fun. It was also very difficult. I only got a few questions right. But even the winning team got less then half the questions right. Here’s a fun one which I managed to figure out: player A and player B are playing a game. Each player has their own color. The game is played on a 9×9 grid. On player A’s turn they must make an uncolored 1×1 square their color. On player B’s turn they must color in an uncolored 2×2 square (if they can) of their color. If player b can’t make a move, the game ends and player a gets to fill in all the remaining squares. Assuming player A goes first, and both players are trying to maximize the amount of squares in their color. What is the maximum amount of squares that player A can color in?


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