"No, indeed. It's a hard nut to crack."

"Oh, as far as that goes, I am very good at cracking the nuts! A veritable squirrel! It is not that which embarrasses me. I know well enough who killed Mr Harrington Pace."

"You know? How did you find out?"

"Your illuminating answers to my wires supplied me with the truth. See here, Hastings, let us examine the facts methodically and in order. Mr Harrington Pace is a man with a considerable fortune which at his death will doubtless pass to his nephew. Point No. 1. His nephew is known to be desperately hard up. Point No. 2. His nephew is also known to be - shall we say a man of rather loose moral fiber? Point No. 3."

"But Roger Havering is proved to have journeyed straight up to London."

"Précisément - and therefore, as Mr Havering left Elmer's Dale at 6:15, and since Mr Pace cannot have been killed before he left, or the doctor would have spotted the time of the crime as being given wrongly when he examined the body, we conclude quite rightly, that Mr Havering did not shoot his uncle. But there is a Mrs Havering, Hastings."

"Impossible! The housekeeper was with her when the shot was fired."

"Ah, yes, the housekeeper. But she has disappeared."

"She will be found."

"I think not. There is something peculiarly elusive about that housekeeper, don't you think so, Hastings? It struck me at once."

"She played her part, I suppose, and then got out in the nick of time."

"And what was her part?"

"Well, presumably to admit her confederate, the black-bearded man."

"Oh, no, that was not her part! Her part was what you have just mentioned, to provide an alibi for Mrs Havering at the moment the shot was fired. And no one will ever find her, mon ami, because she does not exist! 'There's no sech person,' as your so great Shakespeare says."

"It was Dickens," I murmured, unable to suppress a smile. "But what do you mean, Poirot?"

"I mean that Zoe Havering was an actress before her marriage, that you and Japp only saw the housekeeper in a dark hall, a dim middle-aged figure in black with a faint subdued voice, and finally that neither you nor Japp, nor the local police whom the housekeeper fetched, ever saw Mrs Middleton and her mistress at one and the same time. It was child's play for that clever and daring woman. On the pretext of summoning her mistress, she runs upstairs, slips on a bright jumper and a hat with black curls attached which she jams down over the gray transformation. A few deft touches and the makeup is removed, a slight dusting of rouge, and the brilliant Zoe Havering comes down with her clear ringing voice. Nobody looks particularly at the housekeeper. Why should they? There is nothing to connect her with the crime. She, too, has an alibi."

"But the revolver that was found at Eating? Mrs, Havering could not have placed it there?"