He paused to gaze thoughtfully through the window. A traffic-officer was waving his arms at the juncture of 42nd Street and Broadway. “We have established therefore,” he continued lightly, “the factual basis of a point which has been running us ragged for three days: to wit, did the hat for which we are looking leave the Roman Theatre.... To be dialectic—yes, it did. It left the Roman Theatre the night of the murder. Now we approach a greater problem—_how_ did it leave and _when_.” He puffed at his cigarette and regarded the glowing tip. “We know that no person left the Roman Monday night with two hats or no hat at all. In no case was there anything incongruous in the attire of any person leaving the theatre. That is, a man wearing a full-dress costume did not go out with a fedora. In a similar way, no one wearing a silk-topper was dressed in ordinary street-clothes. Remember, we noticed nothing wrong from this angle in _anyone_.... This leads us inevitably, to my staggering mind, to the third fundamental conclusion: that Monte Field’s hat left the theatre in the most natural manner in the world: _id est_, by way of some man’s head, its owner being garbed in appropriate evening-clothes!” The Inspector was keenly interested. He thought over Ellery’s statement for a moment. Then he said seriously, “That’s getting us somewhere, son. But you say a man left the theatre wearing Monte Field’s hat—an important and enlightening statement. But please answer this question: What did he do with his own hat, since no one left with two?” Ellery smiled. “You now have your hand on the heart of our little mystery, dad. But let it hold for the moment. We have a number of other points to mull over. For example, the man who departed wearing Monte Field’s hat could have been only one of two things: either he was the actual murderer, or he was an accomplice of the murderer.” “I see what you’re driving at,” muttered the Inspector. “Go on.” “If he was the murderer, we have definitely established the sex and also the fact that our man was wearing evening-clothes that night—perhaps not a very illuminating point, since there were scores of such men in the theatre. If he was only an accomplice, we must conclude that the murderer was one of two possibilities: either a man dressed in ordinary clothes, whose possession of a tophat as he left would be patently suspicious; or else a woman, who of course could not sport a tophat at all!” The Inspector sank back into the leather cushions. “Talk about your logic!” he chortled. “My son, I’m almost proud of you—that is, I would be if you weren’t so disgustingly conceited.... Things standing where they do, therefore, the reason you pulled your little drama in Panzer’s office....” His voice lowered as Ellery leaned forward. They continued to converse in inaudible tones until the taxicab drew up before the headquarters building.