An easy question on counting shapes for P2–P3, with a step-by-step solution, diagrams and the answer. Every year of the Hua Xia Cup, P1 to P6, has shape-counting questions. The hard part is counting each shape once and missing none.
The question
A window is divided by wooden bars into 2 rows of 3 panes, every pane the same size of square, as shown.
How many squares are there in the picture? (Count squares of every size.)
Show the hints (2)
💡Hint 1: Count the smallest squares first, then those made of 2 × 2, and so on. How many cells wide is the biggest square?
💡Hint 2: A square 2 cells wide fits in 2 places across and 1 place down.
Worked solution
Have a go first, then read the solution step by step.
1.Squares 1 cell wide: the top-left corner can go on any blue dot. There are 2 rows of 3 dots: 2 × 3 = 6.
2.Squares 2 cells wide: the top-left corner can go on any blue dot. There are 1 row of 2 dots: 1 × 2 = 2.
3.6 + 2 = 8 squares in all.
⚠️Common mistake: counting only the 6 small cells, or taking a 1 × 2 rectangle for a square.
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