Comments on organizing a library
Post
organizing a library
+3
−0
Suppose you have $n>1$ books lined up on a shelf, numbered $1$ to $n$, not in the correct order, and you wish to put them in order. Here's your method: Choose a misplaced book[1] at random, and put it in its correct spot. For example, if $n=5$ and you pick book number $2$ out of spot number $4$, there are now four books left, and you put the book back between the first two, since it's book number $2$.
What's the maximum number of times you might have to do the pick-and-replace before the books are in order?
[1] meaning, a book numbered $k$ which is not in position $k$
2 comment threads