Question 20
Karlo and Lovro play the following game. Karlo cuts the paper of dimensions $9 \times 9$ into rectangles of integer dimensions having at least one side of length $1$. Lovro then chooses a positive integer $k \in \{1, \dots, 9\}$, after which Karlo gives him as many coins as the total area of $1 \times k$ and $k \times 1$ cut rectangles is. Lovro chooses $k$ so that he gets as many coins from Karlo as possible, while Karlo wants to give as few coins to Lovro as possible.
Find the minimum possible number of coins that Karlo gives to Lovro. (Ukraine 2013)
Find the minimum possible number of coins that Karlo gives to Lovro. (Ukraine 2013)