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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?

A number or a short expression. Spacing and $ signs are ignored.

Solution

By arranging 4 rows of 4 squares of side length 2, a square of side length 8 can be formed. Thus, 44=164 \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 2×22 \times 2 squares, so 16 is the largest possible number.

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