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?
- A15
- B20
- C21
- D26
Solution & Step-by-step Explanation
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
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