How many rectangles, squares included, can be traced along the lines of a grid of 2 rows and 3 columns? The figure is a rectangle divided into a grid of 2 rows and 3 columns of equal squares.

How many rectangles, squares included, can be…

How many rectangles, squares included, can be traced along the lines of a grid of 2 rows and 3 columns?

MediumOriginal question

How many rectangles, squares included, can be traced along the lines of a grid of 2 rows and 3 columns?

16Correct answerYour answer18Correct answerYour answer19Correct answerYour answer21Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

A rectangle is fixed by choosing 2 of the 4 vertical lines and 2 of the 3 horizontal lines.
Vertical pairs: $\binom{4}{2} = 6$ . Horizontal pairs: $\binom{3}{2} = 3$ .
Rectangles $= 6 \times 3 = 18$ .

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.