This collaborative mystery is not to be taken seriously. While I got quite a kick out of it, it's a good thing that the members of The Detection Club didn't really make a habit of this - there are a total of three of these collaborative mysteries, each with a different spin.
At the end of the day, this was really an over-complicated mess with a not particularly convincing solution. The Appendix does provide alternative solutions, with each author beyond Chapter 3 providing their own. Christie's made me laugh out loud, it was so perfectly Agatha Christie. The others were entertaining as well, albeit a bit long-winded.
I'm glad I read it, but once was enough. This isn't a book with significant rereading potential.