BTW, I actually see 6 squares in the arrangement. That led me to think of the question: how can you take away 2 toothpicks to leave 3 squares?

Some other extensions: what are the least numbers of toothpicks you can take away to leave n squares (0, 1, 2, 3, 4, 5)?

How do you maximize squares remaining and toothpicks taken? For example, what is the max of (remaining squares) * (toothpicks removed)?

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