Problem

Source: All-Russian MO 2009 Regional 11. 2

Tags: combinatorics



In some cells of the table $10\times 10$ arranged several $X$'s and a few $O$'s. It is known that there is no line (row or column) completely filled with identical symbols (crosses or zeros). However, if in any empty If you place any icon in a cell, this condition will be violated. What is the minimum number of icons that can appear in a table?