Problem

Source: Baltic Way 2007

Tags: combinatorics proposed, combinatorics



We are given an $18\times 18$ table, all of whose cells may be black or white. Initially all the cells are coloured white. We may perform the following operation: choose one column or one row and change the colour of all cells in this column or row. Is it possible by repeating the operation to obtain a table with exactly $16$ black cells?