When Joan and Ellery determined upon their course of action, Ellery’s immediate part was to make a thorough investigation of Carter Woodman’s movements. Apparently he had a perfect _alibi_—as good as Ellery’s own—absolving him of all part in the events of the fatal Tuesday night. Indeed, in the eyes of the law he had scarcely needed an _alibi_, for nothing had occurred to throw any real suspicion upon him. Ellery suspected him nevertheless almost to certainty; but he admitted to himself that even now his suspicion was based on what others would regard as no more than a guess. Tuesday, therefore, seemed the best starting-point; for if Woodman’s _alibi_ for that occasion held good, that would finish the matter, and prove that the whole edifice of suppositions which Ellery had built up was founded on nothing. It was easy enough for Ellery to walk into the Cunningham Hotel, where he was already known, under pretext of a visit to Marian Brooklyn. But, having made his entry, he did not proceed to the suite of rooms which she shared with the Woodmans. His object was to explore the hotel in order to discover whether there was in fact, as the porter and the manager had stated to Inspector Blaikie, only one possible exit. The porter, who had been at the door from ten o’clock onwards through the night had been quite certain that Woodman had not gone out that way. He had come in with his wife and Mrs. Brooklyn at about a quarter past ten, and he had not returned to the entrance hall until about a quarter to twelve, when he had given the porter his late letters for the post, and had gone straight upstairs again. That seemed clear enough; for the porter was very positive that Woodman had not gone out at any time during the evening. There was, the manager had told the police, another exit, of course, for the hotel servants. But the only way to this from the club quarters lay through the great kitchen, and it would be quite impossible for a guest to leave by this way without being observed. Ellery had chosen eleven o’clock at night for his visit to the hotel, and meeting the manager, whom he knew, he asked to be shown into the kitchens. The management was excessively proud of these, and made a regular show of them to its guests. The manager readily agreed to take him round, and even a cursory inspection was enough to show Ellery that, even at that hour in the evening, no guest could possibly have left by the servant’s exit without being seen by at least half a dozen persons. The preparation of theatre suppers was in full swing, and the kitchens were alive with chefs and waiters at least until midnight.