Shortly before the dénouement, Poirot asks each of his "pigs" a question. For Angela Warren, the "question he did want to ask her could wait", so he improvises a different one:
“At the time of the tragedy, you had lately read, had you not, Somerset Maugham’sThe Moon and Sixpence?”
Angela stared at him. Then she said:
“I believe—why, yes, that is quite true.” She looked at him with frank curiosity. “How did you know?”
“I want to show you, mademoiselle, that even in a small unimportant matter, I am something of a magician. There are things I know without having to be told.”
The connection to The Moon and Sixpence is not obvious, and in fact is never explained in the novel. This blog post attempts to uncover Poirot's reasoning.
Briefly, The Moon and Sixpence is a novel (1919) by Somerset Maugham based on the life of Gaugin. The main character, Strickland, leaves his family to become an artist, eventually dying of leprosy.
Angela's literary tastes are mentioned in her narrative:
Besides, just at that time, I’d suddenly begun to discover theintoxication of words. Things that I read, scraps of poetry—of Shakespeare—would echo in my head. I remember now walking along the kitchen garden path repeating to myself in a kind of ecstatic delirium “under the glassy green translucent wave”…It was just so lovely I had to say it over and over again.
Even though her recollectionof Comus is faulty*, it is clear that the literature she reads is bubbling over into her everyday mental life.
Miss Williams' narrative brought out that:
Angela ... was also a passionate reader and showed excellent taste in what she liked and disliked.
We can assume that in the 1920s (when the events surrounding Amyas Crale's death take place) that the popular Maugham's The Moon and Sixpence would be something a literary young woman of excellent taste might have read. Had Angela done so, she could not fail to have identified Crale with Strickland - in his artistry, his selfishness, his sexual conquests. The clinching connecting clue is in Philip Blake's narrative:
Amyas and Angela had a first-class row, I know, and the rest of us rather welcomed it. It avoided other difficulties. Angela rushed off to bed with a final vituperative outburst. She said A, she’d pay him out. B, she wished he were dead. C, she hoped he’d die of leprosy, it would serve him right. D, she wished a sausage would stick to his nose, like in the fairy story, and never come off. When she’d gone we all laughed, we couldn’t help it, it was such a funny mixture.
Point C, together with Angela's anticipated reading and her reading's tendency to break into her thoughts, seems to have formed the basis for Poirot's guess(although he artfully, and quite rightly, claims to know).
* The phrase has 'cool' for 'green' in Comus but is reproduced as Chrisitie has it in Wet Magic by Edith Nesbit. We may note the children in Wet Magic read The Water Babies at the beginning of the novel and, of course, Amyas is named so from a character in Kingsley's Westward Ho! Perhaps Poirot could deduce what Christie read to her daughter?