Thirteen problems

The book I am reading now is a collection of short stories and I already finished the first one. There were six characters, including the main one - Miss Marple, who decided to create the "Tuesday night club". They would meet every Tuesday to discuss a murder or a story that only one of them had read about. He would state the facts and the others would have as a challenge to figure out what happened and who did it. The purpose of that game is to prove who is the most intelligent of them all. I liked the story, because the murder itself was very original, but it was a little bit hard to believe that Miss Marple managed to figure out what happened, which was something COMPLETELY unexpected, without being at the crime scene. So in the end, I think that it might have been a better idea to have just made it like a typical detective story rather than "The Tuesday night club".