Lesson eLearning

In a 3×3 grid, the central square is removed. How many squares of all sizes can be formed using the remaining squares?

hard 3 marks Class 5 · Mathematics · How Many Squares
Answer
8 squares

The correct answer is 8 squares — Hence 8 squares remain.

Step-by-step solution

  1. Compute the total squares in a full 3×3 grid: .
  2. Determine which squares used the removed central unit:
  3. - 1×1 square: 1 lost.
  4. - 2×2 squares: 4 lost (each 2×2 square contains the center).
  5. - 3×3 square: 1 lost (the whole grid).
  6. Total lost squares: .
  7. Subtract from the full total: .
  8. Hence 8 squares remain.
Common mistake: Not accounting for all 2×2 squares that include the centre

Concept tested: Counting squares after removal

Published · How this solution was prepared and checked

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