For example, 610 people go to the bookstore to buy books, it is known that
(1) each person bought three books;
(2) any two people have at least one book in common.

How many people at most bought the book that was purchased by the fewest people?
Solution: Let the number of people who bought the most popular book be $x$. Among the 10 people, person A bought three books. Since the other 9 people each have at least one book in common with A, and $9 \div 3=3$, it follows that among A's three books, the most popular one must have been bought by at least 4 people, so $x \geqslant 4$.

If $x=4$, then each of A's three books was bought by 4 people. Similarly, each book bought by the other 9 people was also bought by 4 people. Therefore, the total number of books bought by the 10 people should be a multiple of 4, i.e., $4 \mid 30$, which is a contradiction. Thus, $x \geqslant 5$.

When $x=5$, let $A_{i}$ represent different books. The scenario where the most popular book is bought by exactly 5 people is as follows:
$$
\begin{array}{l}
\left\{A_{1} A_{2} A_{3}\right\} 、\left\{A_{1} A_{2} A_{6}\right\} 、\left\{A_{2} A_{3} A_{4}\right\} 、 \\
\left\{A_{1} A_{4} A_{6}\right\} 、\left\{A_{1} A_{4} A_{5}\right\} 、\left\{A_{2} A_{4} A_{5}\right\} 、 \\
\left\{A_{1} A_{3} A_{5}\right\} 、\left\{A_{2} A_{5} A_{6}\right\} 、\left\{A_{3} A_{5} A_{6}\right\} 、 \\
\left\{A_{3} A_{4} A_{6}\right\} .
\end{array}
$$

In conclusion, the most popular book was bought by at least 5 people.