MathDB

numbers 1-8 in 9x9 board

Source: 2008 Cuba MO 1.1

August 27, 2024

combinatorics

Problem Statement

We place the numbers from

1

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.