JBMO 2015 Problem 4

An $L$-figure is one of the following four pieces, each consisting of three unit squares:

A $5 \times 5$ board, consisting of 25 unit squares, a positive integer $k \leq 25$ and an unlimited supply $L$-figures are given. Two players, $\boldsymbol{A}$ and $\boldsymbol{B}$, play the following game: starting with $\boldsymbol{A}$ they alternatively mark a previously unmarked unit square until they marked a total of $k$ unit squares.

We say that a placement of $L$-figures on unmarked unit squares is called good if the $L$-figure do not overlap and each of them covers exactly three unmarked unit squares of the board. $\boldsymbol{B}$ wins if every $\boldsymbol{g o o d}$ placement of $L$-figures leaves uncovered at least three unmarked unit squares. Determine the minimum value of $k$ for which $\boldsymbol{B}$ has a winning strategy.