Question 26
Let $n$, $k$ be positive integers. Julia and Florian play a game on a $2n \times 2n$ board. Julia has secretly tiled the entire board with invisible dominos. Florian now chooses $k$ cells. All dominos covering at least one of these cells then turn visible. Determine the minimal value of $k$ such that Florian has a strategy to always deduce the entire tiling.