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2004 Indonesia MO Problems/Problem 8

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Problem 8

A floor with an area of $3 \text{ m}^2$ will be covered by $5$ rugs with various shapes, each having an area of $1 \text{ m}^2$. Show that there exist $2$ overlapping rugs with the overlapped area at least $1/5 \text{ m}^2$.

Solution

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