The Mysterious Affair at Styles by Agatha Christie

Agatha Christie is an author I haven't read much of, though I love the tv series, particularly Poirot with
 David Suchet. So when I saw that Mysteries in Paradise was hosting an Agatha Christie Carnival I thought that I would join in. It's my intention to read her work in order of publication as far as possible, so the first on my list is The Mysterious Affair at Styles.
It is a Poirot story and when we meet the detective he is living in Styles St Mary with other Belgium refugees from the war. It is narrated by Hastings (I don't know his first name, I'm not sure if it's mentioned in the book). Of course Hastings features in many Poirot stories, but in this one he is not yet in the police force. He is home from the army after having being wounded. He is staying with an acquaintance at Styles Court, the big house of the village.
The victim in the novel is his hostess, Mrs Inglethorp. She is poisoned with strychnine. The people with motives include her stepsons, who are in want of money, her second husband Alfred Inglethorp who the rest of the family believe to be a gold digger. The people with the means include the mysterious Dr Baurstein, a world expert in toxicology, and Mrs Inglethorp's ward Cynthia, who is a pharmacist.
It is a troubling case for Poirot and he seems puzzled by it. The timings don't make sense, and the strongest suspects have the tightest alibis. Usually when I read a detective novel I am happy to let the author tell me who the culprit was at the end, I don't usually try to work it out. But I know that Christie is  well respected for her plotting, so with this book I tried to follow the clues carefully and guess the murderer. I was pretty certain I had it right - but I didn't. Hopefully I will get better as I read more of her work.