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# A total of 8 different books are to be distributed among 4 students so that each student receives at least one book. At most 2 of the students are to receive the same number of books, and no two of the remaining students are to receive an equal number of books. What is the least possible number of books needed for distribution?

Sunday 31 March 2024,

A total of 8 different books are to be distributed among 4 students so that each student receives at least one book. At most 2 of the students are to receive the same number of books, and no two of the remaining students are to receive an equal number of books. What is the least possible number of books needed for distribution?

A. 8
B. 10
C. 12
D. 14
E. 16

To find the least possible number of books needed, we need to distribute the books in a way that minimizes the total number of books while satisfying the given constraints.

We can distribute the books as follows:

2 books each for 2 students
3 books for the third student
1 book for the fourth student
This distribution ensures that no two students have the same number of books, except for the case where two students have 2 books each.

So, the least possible number of books needed is 2 + 2 + 3 + 1 = 8.

The best answer is therefore A.

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