Question 223, Find the largest positive integer $n$, such that there exists a set with $n$ elements, where the set contains exactly 1 element divisible by $n$, exactly 2 elements divisible by $\mathrm{n}-1$, $\cdots$, exactly $\mathrm{n}-1$ elements divisible by 2, and $\mathrm{n}$ elements divisible by 1.
When $\mathrm{n}=5$, the set $(1,2,6,12,60\}$ satisfies the conditions.
Assume $\mathrm{n} \geq 6$, there exists a set that satisfies the conditions. According to the conditions, $n-1$ elements are multiples of 2, which means there is only one element that is odd in the set. Also, exactly $n-2$ elements are multiples of 3, so at least $n-3$ elements are both multiples of 2 and 3. Therefore, at least $\mathrm{n}-3$ elements are multiples of 6. However, the problem states that exactly $n-5$ elements are multiples of 6, which leads to a contradiction.