GATE CS 2024 Set 1 Q10 — General Aptitude

To make the line $AB$ a line of symmetry, every shaded square on one side of the diagonal $AB$ must have a corresponding mirrored shaded square on the other side.

Let us represent the grid cells by their coordinates $(row, column)$ from $1$ to $6$ starting from the bottom-left:

• The square at $(1, 3)$ is shaded, but its reflection at $(3, 1)$ is empty. → Add 1
• The square at $(2, 5)$ is shaded, but its reflection at $(5, 2)$ is empty. → Add 2
• The square at $(3, 6)$ is shaded, but its reflection at $(6, 3)$ is empty. → Add 3
• The square at $(4, 1)$ is shaded, but its reflection at $(1, 4)$ is empty. → Add 4
• The square at $(5, 3)$ is shaded, but its reflection at $(3, 5)$ is empty. → Add 5
• The square at $(6, 2)$ is shaded, but its reflection at $(2, 6)$ is empty. → Add 6

Since there are exactly $6$ asymmetric shaded squares without their corresponding reflections, we must add at least $6$ squares to make the figure perfectly symmetric about $AB$.