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The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole. What is the maximum number of squares without a “hole in the interior” that can be formed within the 4 × 4 grid using the unit squares as building blocks?

The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole. What is the maximum number of squares without a “hole in the interior” that can be formed within the 4 × 4 grid using the unit squares as building blocks? Correct Answer 20

According to the question, 

Total number of squares = 16

Number of squares without hole,

4 × 4 - 1 = 16 - 1 = 15,

∴ the total number of 1 × 1 squares (without hole) = 15

Now,

the total number of 2 × 2 squares (without hole) = 5

Total number of squares = 15 + 5 = 20

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