Question 16
Determine the largest $N$ for which there exists a table $T$ of integers with $N$ rows and 100 columns that has the following properties:
(i) Every row contains the numbers $1,2, \ldots, 100$ in some order.
(ii) For any two distinct rows $r$ and $s$, there is a column $c$ such that $|T(r, c)-T(s, c)| \geqslant 2$.
Here $T(r, c)$ means the number at the intersection of the row $r$ and the column $c$.
(i) Every row contains the numbers $1,2, \ldots, 100$ in some order.
(ii) For any two distinct rows $r$ and $s$, there is a column $c$ such that $|T(r, c)-T(s, c)| \geqslant 2$.
Here $T(r, c)$ means the number at the intersection of the row $r$ and the column $c$.