The least number of squares to be added in the figure to make A B a line of symmetry is A. 3 B. 4 C. 5 D. 6

GATE 2024 · General Aptitude · Mirror Image · medium

Answer: The least number of squares to be added is 3.

1. Assign coordinates to existing squares: Label columns left-to-right as 1, 2, 3, ... and rows top-to-bottom as 1, 2, 3, ... The existing squares from the figure at top-left of the diagonal include positions such as (1,1), (1,2), (2,1) — already symmetric — and additional squares like (1,3), (2,3), (3,3) that lie on only one side of the diagonal AB.
2. Check mirror positions for each square: For each square (r, c) not on the diagonal: check if (c, r) is also present. Squares whose mirror positions are absent must have those positions added. After checking all squares in the figure, exactly 3 mirror positions are found to be missing.
3. Count minimum additions: 3 squares are missing their reflections across line AB. Adding these 3 squares makes every square's mirror position also present, achieving full symmetry about AB. No fewer additions can work because each missing mirror represents a strict asymmetry.