Question 151
We have a $5 \times 5$ chessboard and a supply of $\{L\}$-shaped triominoes, i.e. $2 \times 2$ squares with one corner missing. Two players $A$ and $B$ play the following game: A positive integer $k \leq 25$ is chosen. Starting with $A$, the players take alternating turns marking squares of the chessboard until they mark a total of $k$ squares. (In each turn a player has to mark exactly one new square.)
At the end of the process, player $A$ wins if he can cover without overlapping all but at most 2 unmarked squares with $\{L\}$-shaped triominoes, otherwise player $\boldsymbol{B}$ wins. It is not permitted any marked squares to be covered.
Find the smallest $\boldsymbol{k}$, if it exists, such that player $\boldsymbol{B}$ has a winning strategy.
At the end of the process, player $A$ wins if he can cover without overlapping all but at most 2 unmarked squares with $\{L\}$-shaped triominoes, otherwise player $\boldsymbol{B}$ wins. It is not permitted any marked squares to be covered.
Find the smallest $\boldsymbol{k}$, if it exists, such that player $\boldsymbol{B}$ has a winning strategy.