Question 75
A $5 \times 5$ board, consisting of 25 unit squares, a positive integer $k \le 25$ and an unlimited supply of $L$-shapes are given. Two players, $A$ and $B$, play the following game: starting with $A$ they alternately mark a previously unmarked unit square until they mark a total of $k$ unit squares.
We say that a placement of $L$-shapes on unmarked unit squares is called good if the $L$-shapes do not overlap and each of them covers exactly three unmarked unit squares of the board. $B$ wins if every good placement of $L$-shapes leaves uncovered at least three unmarked unit squares. Determine the minimum value of $k$ for which $B$ has a winning strategy.
We say that a placement of $L$-shapes on unmarked unit squares is called good if the $L$-shapes do not overlap and each of them covers exactly three unmarked unit squares of the board. $B$ wins if every good placement of $L$-shapes leaves uncovered at least three unmarked unit squares. Determine the minimum value of $k$ for which $B$ has a winning strategy.