A 3 × 3 grid of cells is drawn. In addition, one small square is drawn inside the top-left cell and one inside the middle cell. H…

Question

A 3 × 3 grid of cells is drawn. In addition, one small square is drawn inside the top-left cell and one inside the middle cell. How many squares are present in the following figure?

1. A. 16 (Correct answer)
2. B. 18
3. C. 12
4. D. 14

Correct Answer

Option A — 16

Detailed Solution & Explanation

The correct answer is 16.

Key Points

• Count the squares formed by the 3 × 3 grid itself:
  • 1 × 1: nine · 2 × 2: four · 3 × 3: one
  • subtotal = 9 + 4 + 1 = 14
• Add the small squares drawn inside cells — one in the top-left cell and one in the middle cell = 2.
• Total = 14 + 2 = 16.

Additional Information

• The grid contributes 14 regardless of what is drawn inside it, so these questions reduce to "14 plus however many extra squares are shown" — worth recognising, since a 3 × 3 grid appears constantly.
• Use 1² + 2² + 3² = 14, the standard sum-of-squares result, rather than counting by hand.
• Compare this with the other counting question in the same paper, which places five extra squares instead of two and therefore totals 19 — the grid is identical and only the additions differ.
• Count in a fixed order — grid squares by size first, then the extras — so nothing is counted twice.