Question 53
In a school there are $2013$ boys and $2013$ girls. For each pair of a boy and a girl, together they have to choose one (and only one) of $25$ different clubs to join. Determine the maximum possible value of the integer $k$, such that no matter what the choices of the students are, there is a club with $k$ or more members. (A boy and a girl in a club together are counted as two members.)