The Inspector shrugged. “But it would have made a considerable difference,” he said. “If only we had reasoned it out—Well! When finally we did get round to dissecting the problem of the hat, we asked ourselves first of all: Why was the hat taken? Only two answers seemed to make sense: one, that the hat was incriminating in itself; two, that it contained something which the murderer wanted and for which the crime was committed. As it turned out, both were true. The hat was incriminating in itself because on the underside of the leather sweat-band was Stephen Barry’s name, printed in indelible ink; and the hat contained something which the murderer very emphatically wanted—the blackmail papers. He thought at the time, of course, that they were the originals. “This did not get us very far, but it was a starting-point. By the time we left Monday night with the command to shut down the theatre, we had not yet found the missing hat despite a sweeping search. However, we had no way of knowing whether the hat had managed in some mysterious manner to leave the theatre, or whether it was still there though unrevealed by our search. When we returned to the theatre on Thursday morning we settled once and for all the question of the location of Monte Field’s pesky topper—that is, negatively. It was _not_ in the theatre—that much was certain. And since the theatre had been sealed since Monday night, it follows that the hat must have left that same evening. “Now everybody who left Monday night left with only one hat. In the light of our second search, therefore, we were compelled to conclude that somebody had walked out that night with Monte Field’s hat in his hand or on his head, necessarily leaving his own in the theatre. “He could not have disposed of the hat outside the theatre except when he left at the time the audience was allowed to leave; for up to that time all exits were guarded or locked, and the left-hand alley was blocked first by Jess Lynch and Elinor Libby, next by John Chase, the usher, and after that by one of my policemen. The right-hand alley, having no exit other than the orchestra doors, which were guarded all night, offered no avenue of disposal.