Assume there are two columns $c_1$ and $c_2$ with $c_1$ having more liars than the other column or equal number of liars but at least one position is different. Then there exists a liar in $c_1$ directly to the left of a knight in $c_2$ (I'm row $r$. So by the proposition we have $c_1\leq r<c_2$, but this is a contradiction because $c_1\geq c_2$. Therefore all columns are equal. If we have a liar the proposition is always satisfaied because $r_i=n\geq c_j$ and if we have a knight the proposition is almost always satisfied because $r_i=0<c_j$ if there is at least one liar in the row. Therefore we can choose freely any row, with the exception of all knights, leading to $2^8-1=255$ possibilities