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MathNet 2009-part-01 — 175 problems (EN–VI) Question 20

Math Olympiad Vault · MathNet 2009-part-01 — 175 problems (EN–VI)

Question 20

Pablo has a certain number of rectangles whose areas add up to $3$ and whose sides are all less than or equal to $1$. Prove that with these rectangles it is possible to cover a square of side $1$ in such a way that the sides of the rectangles are parallel to the sides of the square.

**Note:** The rectangles may overlap and may stick out of the square.