It's called And Then There Were None.
It's your classic "locked door" mystery, where all the participants are stuck in the same place, unable to leave, the mystery and the bodies popping up chapter by chapter. Of course, in this case the people are on a small island. I do remember reading and thinking, there was simply no WAY I could know whodunnit. A great book indeed, but don't take my word for it:
- 'One of the very best, most genuinely bewildering Christies.' The Observer
- 'The most astonishingly impudent, ingenious and altogether successful mystery story since The Murder of Roger Ackroyd.' Daily Herald
- 'One of the most ingenious thrillers in many a day.' Time Magazine