"Lie back and think – use (as I have heard you say so often) the little grey cells of the mind – and you will <em>know!</em>" (1.5.141)
Poirot's mental prowess aids his investigation. Here M. Bouc repeats Poirot's famous phrase: "the little grey cells."
She was not even looking at him. Her gaze went past him, out of the window to where the snow lay in heavy masses.
"You are a strong character, Mademoiselle," said Poirot gently. You are, I think, the strongest character amongst us."
"Oh, no. No, indeed. I know one far, far stronger than I am."
"And that is – ?"
She seemed to suddenly come to herself, to realize that she was talking to a stranger and a foreigner with whom, until this morning, she had only exchanged half a dozen sentences. (1.5.63-67)
Mary's calm and collected manner convinces Poirot that she is a "strong character." However, he also sees flaws. What are they?
"Come, my friend," said M. Bouc. "You comprehend what I am about to ask of you. I know your powers. Take command of this investigation!" (1.5.139)
Why does M. Bouc have such faith in Poirot?
Her small toad-like face looked even yellower than the day before. She was certainly ugly, and yet, like the toad, she had eyes like jewels, dark and imperious, revealing latent energy and an intellectual force that could be felt at once. (2.6.47)
"I think, Madame, that your strength is in your will – not in your arm."
She glanced down at her thin, black-clad arms ending in those claw-like yellow hands with the rings on the fingers.
"It is true," she said. "I have no strength in these – none. I do not know if I am sorry or glad." (2.15.70-72)
Though she is a feeble, elderly woman, the Princess displays strength of will.
"It might be a question of the influence of mind over body," said Poirot. "Princess Dragomiroff has great personality and immense will power. But let us pass from that for the moment." (3.2.40)
Again, Poirot is able to judge the Princess's role in the plot.
And then, suddenly, after a quarter of an hour's complete immobility, his eyebrows began to move slowly up his forehead. A little sigh escaped him. He murmured beneath his breath:
"But, after all, why not? And if so – why, if so that would explain everything."
His eyes opened. They were green like a cat's. He said softly:
"<em>Eh bien.</em> I have thought. And you?"
Lost in their reflections, both men started violently. (3.3.11-15)
That Poirot is the only one who figures out the solution highlights his strength of mind and powers of detection.
Her voice rang out passionately. She was a true daughter of that mother, the emotional force of whose acting had moved huge audiences to tears. (3.4.35)
The Countess, like her mother, possesses great acting skills.
"To play the part she played – the perfectly natural, slight ridiculous American fond mother – an artist was needed. But there <em>was </em>an artist connected with the Armstrong family – Mrs. Armstrong's mother – Linda Arden, the actress…" (3.9.71)
Linda Arden's talents are obvious as she plays the obnoxious American, Mrs. Hubbard.
"I would have stabbed that man twelve times willingly." (3.9.84)
Here we see that Arden's powers are not limited to acting.