Determine the largest integer $N$, for which there exists a $6\times N$ table $T$ that has the following properties: $*$ Every column contains the numbers $1,2,\ldots,6$ in some ordering. $*$ For any two columns $i\ne j$, there exists a row $r$ such that $T(r,i)= T(r,j)$. $*$ For any two columns $i\ne j$, there exists a row $s$ such that $T(s,i)\ne T(s,j)$. (Proposed by Gerhard Woeginger, Austria)
Problem
Source: Mediterranean 2018 P4 MMC
Tags: combinatorics, numbers in a table, maximum, Mediterranean