Question 119
A rectangular array has $n$ rows and six columns, where $n \gt 2$. In each cell there is written either $0$ or $1$. All rows in the array are different from each other. For each pair of rows $(x_{1}, x_{2}, \ldots, x_{6})$ and $(y_{1}, y_{2}, \ldots, y_{6})$, the row $(x_{1} y_{1}, x_{2} y_{2}, \ldots, x_{6} y_{6})$ can also be found in the array. Prove that there is a column in which at least half of the entries are zeroes.