There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?
Answer & explanation
Answer: (c) 36
Every rectangle, squares included, is fixed by choosing 2 of the 4 horizontal lines and 2 of the 4 vertical lines. That gives 6 × 6 = 36.
- Ways to choose 2 horizontal lines from 4 = 4C2 = 6.
- Ways to choose 2 vertical lines from 4 = 6.
- Each pair of choices gives one rectangle: 6 × 6 = 36 (squares included).
- Check: the grid has 3 × 3 unit cells; squares = 9 + 4 + 1 = 14 and non-square rectangles = 22; 14 + 22 = 36.
Remember · Rectangles in a grid of m horizontal and n vertical lines = mC2 × nC2; the squares are already included.
Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·