How many shapes?
Can you spot all the squares, rectangles, and triangles in these diagrams? These classic visual puzzles help develop spatial reasoning, geometry skills, and attention to detail. Perfect for primary students preparing for Maths Olympiads or challenges like the UKMT. Great for classroom warm-ups, enrichment activities, or home learning.
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Example: How Many Squares Are in a 4×4 Grid?
Learn the methodRead guide
Example: How Many Squares Are in a 4×4 Grid?
Let’s walk through how to solve one of the most classic shape-counting puzzles: How many total squares can you find in a 4×4 square grid?
✅ Step-by-Step Method:
We need to count all square shapes, not just the smallest ones.
A square can be any size: 1×1, 2×2, 3×3, or 4×4. Let’s count them by size:
🔹 Step 1: Count 1×1 Squares
Each small cell is a 1×1 square. There are 4 rows and 4 columns:
→ 4 × 4 = 16 squares
🔹 Step 2: Count 2×2 Squares
Each 2×2 square occupies a 2×2 block of cells. We can fit these starting from rows 1–3 and columns 1–3:
→ (4 − 1) × (4 − 1) = 3 × 3 = 9 squares
🔹 Step 3: Count 3×3 Squares
Each 3×3 square fits within a 3×3 portion of the grid. They can start from rows 1–2 and columns 1–2:
→ (4 − 2) × (4 − 2) = 2 × 2 = 4 squares
🔹 Step 4: Count 4×4 Squares
There’s only one 4×4 square — the whole grid itself:
→ 1 × 1 = 1 square
✅ Final Count:
16 + 9 + 4 + 1 = 30