MathDB

Alice and Bob play a game together as a team on a

100 \times 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

Problem Statement