ths are occurring exactly as the poem states. After one of them is killed, according to the first verse of the poem, they figure out that the murderer is one of them. As more people are killed off, one by one, the group narrows the suspect list down, until only one is left alive. The woman that was left alive figured that she would never get off the island anyway, and she hung herself from the ceiling by putting a noose around her neck and kicking the chair away on which she was standing, but she was not the killer.
             One of the mysteries to this book was, of course, who killed all of the innocent
             people. Another mystery was that every time another person was killed a little Indian
             figure would disappear from the edges of a serving plate. One more mystery was that
             every murder followed, in order, the famous poem "Ten Little Indians", which reads:
             Ten little Indian boys went out to dine;
             One choked his self and then there were nine.
             One overslept himself then there were eight.
             ...