CEMC Fermat

Geometry Difficulty 2.5 Junior Find the answer

What is the largest number of squares with side length 2 that can be arranged, without overlapping, inside a square with side length 8?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

By arranging 4 rows of 4 squares of side length 2, a square of side length 8 can be formed. Thus, $4 \cdot 4=16$ squares can be arranged in this way. Since these smaller squares completely cover the larger square, it is impossible to use more $2 \times 2$ squares, so 16 is the largest possible number.

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