AMC 8 Daily Practice Round 11
Complete problem set with solutions and individual problem pages
There are students, and no two students own the same set of books. However, each pair of students shares exactly one common book, and each book is owned by exactly two students. How many different books are there in total?
- A.
- B.
- C.
- D.
- E.
Represent the students as points , and use a line connecting two points to indicate that the corresponding pair of students shares exactly one common book. Since each book is owned by exactly two students, there is exactly one line between any two points.
To find the total number of books, we count the total number of lines in a complete graph with points. The number of lines (or edges) in a complete graph with points is given by:
For , the total number of lines is:
Thus, the students share a total of different books. The answer is .
