GATE 2022 MN – Question 4

General Aptitude · Spatial Aptitude: Spatial Reasoning and Visualization · 1 mark · Multiple choice

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 $4\times4$ grid using the unit squares as building blocks?

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Show answer and explanation

Correct answer: (B) 20

Explanation

A $4\times4$ grid contains $16+9+4+1=30$ squares in all. The hole is the second cell in the second row. The squares that contain it are the hole itself (1), the $2\times2$ squares containing it (4), the $3\times3$ squares containing it (4) and the whole $4\times4$ square (1), making 10. So $30-10=20$ squares have no hole inside.

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