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How many squares of all sizes can be traced along the lines of the $5 \times 4$ grid of unit squares shown?

Competition practicePermutations & Combinations

A40
B20
C60
D38

Step-by-Step Solution

1 \times 1 : 5 \times 4 = 20

;

2 \times 2 : 4 \times 3 = 12

;

3 \times 3 : 3 \times 2 = 6

;

4 \times 4 : 2 \times 1 = 2

. Total

20 + 12 + 6 + 2 = 40

. (20 counts only the unit squares.)

Answer: A) 40

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