Hercule Poirot's Christmas #4

The name of my book is "Hercule Poirot's Christmas" by Agathe Christie. I have Finished the book by reading 319/319 pages. During the book; "Hercule Poirot's Christmas" there were two main obstacles. The first obstacle for Hercule Poirot to figure out is "How could the murderer have escaped". Hercule Poirot had to figure this out because, the only window had a burglar pin in it, and the entire time, there was a lady standing in the recess in front of the door. Therefore, the murderer could not have left the room. A quote from page 295 was "I will tell you where I think you were, mademoiselle. you were in the recess with the statues quite close to your grandfather's door". The other main obstacle that Mr. Hercule Poirot faced was that almost everybody's alibi left an amount of time in which their movements were undefined. For example,  there was a man that left dinner at a certain point to make a phone call. Then when the phone records were checked he had only made a phone call for 5 minutes, leaving 10 minutes where his  movements were unknown. These were Hercule Poirot's two main obstacles in the book "Hercule Poirot's Christmas".