Explanation

In this question, we want to know the number of circles that fit inside a 5-by-5 box in the coordinate plane. We can consider the circles of different radii in turn. The smallest circles have a radius of 1. They can exist at (1, 1), or any combination of integers in the interior of this space apart from the edges. That's a total of possible centers. When the radius is 2, there are fewer possibilities; the outer rectangle of points allowed for circles of radius 1 are removed, leaving possibilities. No circle of radius 3 fits in the space if it is centered on integer coordinates, so we have considered all possible cases, which total .

The correct answer is (B).