Question 13
Mike and Harry play a game on an $8 \times 8$ board. For some positive integer $k$, Mike chooses $k$ squares and writes an $M$ in each of them. Harry then chooses $k+1$ squares and writes an $H$ in each of them. After Harry is done, Mike wins if there is a sequence of letters forming "$H M M$" or "$M M H$", when read either horizontally or vertically, and Harry wins otherwise. Determine the smallest value of $k$ for which Mike has a winning strategy.