Problem

Source: Kyiv mathematical festival 2016

Tags: Kyiv mathematical festival, combinatorics, games



Two players in turn paint cells of the $7\times7$ table each using own color. A player can't paint a cell if its row or its column contains a cell painted by the other player. The game stops when one of the players can't make his turn. What maximal number of the cells can remain unpainted when the game stops?