Counting squares as rectangles, find the total number of rectangles in a 3 × 3 grid of equal squares. The figure is a rectangle divided into a grid of 3 rows and 3 columns of equal squares.

Counting squares as rectangles, find the total…

Counting squares as rectangles, find the total number of rectangles in a 3 × 3 grid of equal squares.

HardOriginal question

Counting squares as rectangles, find the total number of rectangles in a $3 \times 3$ grid of equal squares.

16Correct answerYour answer27Correct answerYour answer34Correct answerYour answer36Correct answerYour answer

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CorrectNot quiteAnswer D

Correct answer: D

A rectangle is fixed by choosing 2 of the 4 vertical lines and 2 of the 4 horizontal lines.
Vertical pairs: $\binom{4}{2} = 6$ . Horizontal pairs: $\binom{4}{2} = 6$ .
Rectangles $= 6 \times 6 = 36$ .

Worth noting

Counting only the small squares, or only the squares, misses the long thin rectangles. The line-pair method counts every rectangle exactly once.

Ten questions from Non-verbal Reasoning, at your own pace.

Ten questions from Non-verbal Reasoning, at your own pace.