Problem #75 MEDIUM
The Locked Library
Meta Apple Combinatorics Permutations
Problem Statement
A library has 7 identical-looking books in a row on a shelf. A librarian scrambles them into a random order. You are given the task of sorting them back into the correct order (book 1 on the left through book 7 on the right) using only a sequence of swaps — each swap exchanges the positions of any two books. What is the minimum number of swaps needed in the worst case? What is the average number of swaps needed over all possible random arrangements?
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