Question 97
Find the largest positive integer $n$ for which there exist $n$ finite sets $X_{1}, X_{2}, \ldots, X_{n}$ with the property that for every $1 \leq a \lt b \lt c \leq n$, the equation
$$
\left|X_{a} \cup X_{b} \cup X_{c}\right| = \lceil \sqrt{a b c} \rceil
$$
holds.
$$
\left|X_{a} \cup X_{b} \cup X_{c}\right| = \lceil \sqrt{a b c} \rceil
$$
holds.