2021 IMO Shortlist C8

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 $|T(r, c)-T(s, c)| \geq 2$. Here $T(r, c)$ means the number at the intersection of the row $r$ and the column $c$.

确定最大的 $N$，其中存在一个具有 $N$ 行和 100 列的整数表 $T$，该表具有以下属性： (i) 每行都按某种顺序包含数字 $1,2, \ldots, 100$。 (ii) 对于任何两个不同的行 $r$ 和 $s$，有一个列 $c$ 使得 $|T(r, c)-T(s, c)| \geq 2$。这里$T(r, c)$表示行$r$和列$c$相交处的数字。