Question 93
Let $m \geq n$ be positive integers. Frieder is given $mn$ posters of Linus with different integer dimensions $k \times l$ with $1 \leq k \leq m$ and $1 \leq l \leq n$. He must put them all up one by one on his bedroom wall without rotating them. Every time he puts up a poster, he can either put it on an empty spot on the wall, or on a spot where it entirely covers a single visible poster and does not overlap any other visible poster. Determine the minimal area of the wall that will be covered by posters.
Remark: a wall is a structure often made of bricks and concrete (or cardboard if you live in Winterthur) commonly found in houses.
Remark: a wall is a structure often made of bricks and concrete (or cardboard if you live in Winterthur) commonly found in houses.