We place the numbers from $1$ to $81$ in a $9\times $ board. Prove that exist $k \in \{1,2,...,9\}$ so that the product of the numbers in the $k$-th column is diferent to the product of the numbers in the $k$-th row.
Source: 2008 Cuba MO 1.1
Tags: combinatorics
We place the numbers from $1$ to $81$ in a $9\times $ board. Prove that exist $k \in \{1,2,...,9\}$ so that the product of the numbers in the $k$-th column is diferent to the product of the numbers in the $k$-th row.