Question 14
A $(2k+1) \times (2k+1)$ table, where $k$ is a positive integer, contains one real number in each entry, where these numbers are pairwise different. After each row, one writes the median of the row, i.e., the number occurring in this row such that the row contains the same amount of numbers less than it and greater than it. Let $m$ be the median of the column of medians. Prove that more than a quarter of the numbers initially in the table are less than $m$.