Problem

Source: V International Festival of Young Mathematicians Sozopol 2014, Theme for 10-12 grade

Tags: combinatorics, table



We will call a rectangular table filled with natural numbers “good”, if for each two rows, there exist a column for which its two cells that are also in these two rows, contain numbers of different parity. Prove that for $\forall$ $n>2$ we can erase a column from a good $n$ x $n$ table so that the remaining $n$ x $(n-1)$ table is also good.