7. (10 points) Four people went to a bookstore to buy books. Each person bought 4 different books, and every two people have exactly 2 books in common. Therefore, these 4 people bought at least $\qquad$ kinds of books.
【Analysis】From simple properties: If there are only two people, to meet the requirements of the problem, there must be 6 different books. Number these 6 books: $1, 2, 3, 4, 5, 6$. Suppose A buys $1, 2, 3, 4$, and B buys $1, 2, 5, 6$. At this point, C arrives. To meet the requirements, C can choose not to buy any other books, and he buys the books numbered $3, 4, 5, 6$, which also meets the requirements. Note that when three people only buy 6 books, after A and B's book choices are determined, C's book choices are unique. C cannot buy the books that both A and B have bought, so he must buy one book that is "unique" to him. To make the problem easier to understand, use a table (see the solution section).

【Solution】If there are only two people, to meet the requirements, there must be 6 different books, numbered $1, 2, 3, 4, 5, 6$. Suppose A buys $1, 2, 3, 4$, and B buys $1, 2, 5, 6$. At this point, C arrives. To meet the requirements, C can choose not to buy any other books, and he buys the books numbered $3, 4, 5, 6$, which also meets the requirements. Note that when three people only buy 6 books, after A and B's book choices are determined, C's book choices are unique. C cannot buy the books that both A and B have bought, so he must buy one book that is "unique" to him. Use a table:
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline A & $\checkmark$ & $\checkmark$ & $\checkmark$ & $\checkmark$ & & \\
\hline B & $\checkmark$ & $\checkmark$ & & & $\checkmark$ & $\checkmark$ \\
\hline C & & & $\checkmark$ & $\checkmark$ & $\checkmark$ & $\checkmark$ \\
\hline
\end{tabular}

At this point, D arrives. From C's perspective, he must have at least one "unique" book, so when there are 4 people, there must be at least 7 books.

That is, A buys the books numbered $(1, 2, 3, 4)$, B buys the books numbered $(1, 2, 5, 6)$, C buys the books numbered $(3, 4, 5, 6)$, and D can buy $(1, 3, 5, 7)$. Therefore, when there are 4 people, they must buy at least $(1, 2, 3, 4, 5, 6, 7)$, which is 7 different books.

Thus, the answer is: 7.