“Undoubtedly it is strange. Indeed, without the theory that I hold, it would be inexplicable.” “Aha!” said M. Hautet. “An accomplice. An accomplice within the house!” “Or outside it,” said Giraud with a peculiar smile. “But some one must have admitted them? We cannot allow that, by an unparalleled piece of good fortune, they found the door ajar for them to walk in?” “_D’accord___, M. le juge. The door was opened for them, but it could just as easily be opened from outside—by some one who possessed a key.” “But who did possess a key?” Giraud shrugged his shoulders. “As for that, no one who possesses one is going to admit the fact if they can help it. But several people _might___ have had one. M. Jack Renauld, the son, for instance. It is true that he is on his way to South America, but he might have lost the key or had it stolen from him. Then there is the gardener—he has been here many years. One of the younger servants may have a lover. It is easy to take an impression of a key and have one cut. There are many possibilities. Then there is another person who, I should judge, is exceedingly likely to have such a thing in her keeping.” “Who is that?” “Madame Daubreuil,” said the detective dryly. “Eh, eh!” said the magistrate, his face falling a little, “so you have heard about that, have you?” “I hear everything,” said Giraud imperturbably. “There is one thing I could swear you have not heard,” said M. Hautet, delighted to be able to show superior knowledge, and without more ado, he retailed the story of the mysterious visitor the night before. He also touched on the cheque made out to “Duveen,” and finally handed Giraud the letter signed “Bella.” Giraud listened in silence, studied the letter attentively, and then handed it back. “All very interesting, M. le juge. But my theory remains unaffected.” “And your theory is?” “For the moment I prefer not to say. Remember, I am only just beginning my investigations.” “Tell me one thing, M. Giraud,” said Poirot suddenly. “Your theory allows for the door being opened. It does not explain why it was _left___ open. When they departed, would it not have been natural for them to close it behind them. If a _sergent de ville___ had chanced to come up to the house, as is sometimes done to see that all is well, they might have been discovered and overtaken almost at once.” “Bah! They forgot it. A mistake, I grant you.” Then, to my surprise, Poirot uttered almost the same words as he had uttered to Bex the previous evening: “_I do not agree with you.___ The door being left open was the result of either design or necessity, and any theory that does not admit that fact is bound to prove vain.” We all regarded the little man with a good deal of astonishment. The confession of ignorance drawn from him over the match end had, I thought, been bound to humiliate him, but here he was self satisfied as ever, laying down the law to the great Giraud without a tremor.