You're solution is not correct, as you are not using the fact that after a book is read, it goes on the top of the stack. For example, if a book is read 10 times in a row, then that's in no way different than being read just once. So you see, the amount of times is not always connected with the position of the book.

Now let's say the books are read in order {1,3,5,4,2} for example. Then, no matter how the initial stack looked, after {1,3,5,4} are read, 2 will be below all of them. So, regardless of how you order them, you will have to lift those four to read book 2. Well, then it is logical to put 2 on the bottom.

Continuing with that logic then when picking up 4, regardless of the order, 1,3 and 5 will be lifted, so again, 4 should be directly above 2 and so on.

Then if you think about it, it's easy to come up with the author's solution, which is ordering the books as their relative order of first occurrences in the reading requirements.

I didn't quite figure out the significance of placing the book on top after reading initially. Thanks for the answer!