The Battle of the Books

     Andrew the Assured, Brian the Big, Casey the Careful, Dootles the Dreamy and Edwina the Eager are all members of a reading club, 'The Burping Bookworms'. They have a bizarre rule in the club: for each 5-person group, they must read 5 books in week, but in a special way--after they finish reading each book they must exchange them within the group, so that after several switches, each of them could finish reading the same 5 books at the same time. (Suppose they could all read at the same speed and swap books at the same time.)

     After a pleasurable week of switching-and-reading, Casey the Careful was chatting with her friend, '3M', Mazy the Mathematics Maniac.

     Suddenly, Casey piped up, 'You're a math frenzy, Mazy, and you know about our 'Burping Bookworms' reading club, so I'll give you a puzzle to solve.'

     Casey took out a sheet of paper on which she jotted down facts:

1. The last book Andrew read was the second book Brian read;
2. The last book Casey read was the fourth book Brian read;
3. The second book Casey read was handed to her by Andrew;
4. The last book Dootles read was the third book Casey read;
5. The fourth book Brian read was the third book Edwina read;
6. The third book Dootles read was the book Casey had borrowed from the library (and read) in the first place.

     'Could you figure out the sequence in which we read these 5 books?'

     Well, as a matter fact, Mazy was a real math maniac, and in a short time she was proudly handing her work over to Casey. Can you?

This problem was sent to WTM by Wanting Zhong, our friend from China.