## Real MATHEMATICS – Game #10

Free the Oreos

Free the Oreos is a multiplayer game for everyone aged over 6. Here is what you need for the game:

• 9 identical squares drawn inside a bigger square:
• 24 matches in order to construct those 9 little squares:
• Placing an Oreo inside each little square:

Rules:

1. Players will remove matches in turns. A player will remove exactly one match whenever it is his/her turn.
2. In order to free an Oreo inside a square, all the matches of that square must be removed:

To free the Oreo sitting on top-left, all four sides of the square must be removed.
3. The player who removed the last side of a square is known as the one who freed the Oreo.

Goal is to free more Oreos than your opponent.

Defense vs. Attack

Attacking Strategy: You should remove the last match surrounding the Oreo in case you want to free it.

Defending Strategy: In case there are two matches around a specific Oreo, you should avoid removing either of those matches. Otherwise your opponent can and will free that Oreo in his/her turn.

Two experienced players will use the defending strategy as long as possible. But in the end the game will be in a position where defending won’t be possible:

In such situation, game can continue as follows:

At the end of this sample game first player freed 6 Oreos as the second freed only 3.

One wonders…

1. Can you find a winning strategy?
2. At most how many Oreos can a player free in a single turn? Show your answer with a sample game.

M. Serkan Kalaycıoğlu