Although Poirot constantly emphasize the importance of his logical approach to solving crime and using hia "little gray cells" he expresses admiration of Caroline's intuition and in fact many of Caroline's pronouncement are proved correct.
How can we reconcile these two seemingly opposite methods of arriving at the truth?
Although many characters in the novel act on impulse and are motivated entirely by emotion, Poirot’s brilliance lies in his ability to distance himself from his emotions and consider every fact objectively. He constantly references the importance of his “method” – the way he systematically considers the facts, taking nothing for granted and no one at his word, until he can painstakingly build the truth from the facts he has collected. Unlike Flora or Colonel Melrose, for example, both of whom are convinced but unable to prove that Ralph is innocent because of their emotional connection to him, Poirot maintains objectivity with regards to Ralph. Poirot is able to prove Ralph's innocence through thorough investigation of the facts. It is only with this “method” that Poirot ultimately triumphs over the seemingly impossible case that manages to baffle every other character in the novel.
