Poirot reveals the outcome of the case to Franklin Clarke, Thora Grey, Megan Barnard, Donald Fraser, and, of course, Hastings. We are not told where this takes place, but Poirot is well prepared.
Before that meeting happens, however, he tantalizes Hastings's, and also the reader's, appetite with his mysterious doings:
During the next few days Poirot was very busy. He made mysterious absences, talked very little, frowned to himself, and consistently refused to satisfy my natural curiosity...
Once Poirot gets all the suspects together—having counted out Mr. Cust as a possible suspect—he takes them through his thinking in a step-by-step way. He tells them that the murderer hid the one murder that really mattered to him by making it part of a series of killings. Poirot says:
When do you notice a pin least? When it is in a pincushion! When do you notice an individual murder least? When it is one of a series of related murders.
Then he explains that he focused on understanding the killer. He realized that such a person must be daring, move around frequently, be attractive to women, and have the kind of methodical mind that would perform murders in alphabetical order. As he went over the suspects, he realized that Franklin Clarke fit his profile perfectly:
The man I had known a long time in my secret mind was the same as the man whom I had known as a person. A.B.C. and Franklin Clarke were one and the same! The daring adventurous character, the roving life... The attractive free and easy manner — nothing easier for him than to pick up a girl in a cafe. The methodical tabular mind...
He explains that Clarke feared that his elderly brother would marry Thora Grey after his sick wife died. Since Clarke was determined to inherit his brother's vast wealth, he arranged to murder him before a second wife could inherit. He set up Cust as the fall guy, arranging for him to be near each crime scene at the time of the murders, but nobody noticed him.
Poirot shows his brilliance when thinks ahead to have the bullets removed from Clarke's gun so he can't commit suicide. He has Scotland Yard officers waiting in the next room to arrest Clarke too.
This is a classic climatic conclusion to a murder mystery novel: all the suspects are gathered while the detective explains what happened and reveals the killer.