GATE CS 2024 Set 1 — Question 10

To make the line AB a line of symmetry, every shaded square on one side of the line must have a corresponding shaded square on the other side at the same distance from the line.Let's analyze the positions of the existing squares relative to the line AB:

• One square at column 3, 2 units above.
• One square at column 4, 1 unit above.

2. Below the line:

• One square at column 2, 1 unit below.
• One square at column 4, 1 unit below.
• A $2 \times 2$ block of squares at columns 5 and 6, spanning 1 and 2 units below (total 4 squares).

Symmetry Check:

• The square at (column 4, 1 unit above) and the square at (column 4, 1 unit below) are already symmetric to each other. No squares need to be added here.
• The square at (column 3, 2 units above) needs a reflection at (column 3, 2 units below). (+1 square)
• The square at (column 2, 1 unit below) needs a reflection at (column 2, 1 unit above). (+1 square)
• The $2 \times 2$ block at (columns 5-6, 1-2 units below) needs a reflection at (columns 5-6, 1-2 units above). (+4 squares)

Total squares to be added = $1 + 1 + 4 = 6$.