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Problem 47

Combinatorics Difficulty 1.1 Multiple choice CEMC Fermat · Canada · 2022

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

Pick one

Official solution

By arranging 4 rows of 4 squares of side length 2, a square of
side length 8 can be formed.

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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.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.