Amélia and Beatriz play battleship on a 2n×2n board, using very peculiar rules. Amélia begins by choosing n lines and n columns of the board, placing her n2 submarines on the cells that lie on their intersections. Next, Beatriz chooses a set of cells that will explode. Which is the least number of cells that Beatriz has to choose in order to assure that at least a submarine will explode? combinatorics unsolvedcombinatorics