Alice and Bob play a game together as a team on a 100×100 board with all unit squares initially white. Alice sets up the game by coloring exactly k of the unit squares red at the beginning. After that, a legal move for Bob is to choose a row or column with at least 10 red squares and color all of the remaining squares in it red. What is the
smallest k such that Alice can set up a game in such a way that Bob can color the entire board red after finitely many moves?Proposed by Nikola Velov, Macedonia JuniorBalkanshortlist2021combinatoricsColoringboard