A room with area $4$ square meters has been covered with $7$ carpets each of which of area $1$ square meters and of arbitrary shape.Show that there are $2$ carpets that their intersection is at least $\frac17$ square meters.
Since the problem says the shape of the carpets is unspecified,I got totally confused!
Hint:$$\left|\bigcup_{i=1}^7A_i\right| \geq \sum_{i=1}^7 |A_i|-\sum_{i < j \\ } |A_i \cap A_j|$$
Suppose every intersection is less than $\frac17$, prove by contradiction.