“We could have tried. But tell me: how much of our conversation does this gentleman overhear? And whereabouts in your room could you have hidden with any safety? Honestly, I don’t believe he would have come out except while he knew that you and Gordon were busy watching the wrong side of the door.”

“You’re assuming, of course, that he can’t have got in at the door by a duplicate key after Reeves and I went to bed?”

“I am not assuming that, I know it. I took the liberty of putting a bit of that useful chewing-gum across the lock of the door, and it was still undisturbed in the morning. Whereas the chewing-gum which stretched between the chairs had been ploughed up in every direction.”

“As it is, though, we’ve still got to find the entrance to the passage.”

“As you say. I thought we might spend a happy morning looking for it. Let’s see, there is a piano in your rooms; do you play it?”

“Very badly.”

“That’s exactly what we want.”

“How do you mean?”

“Why, if you sit in your rooms playing the piano, the gentleman on the other side of the partition will probably assume that nothing much is happening. If you play it loudly, you will drown any little thumping noises we may happen to make. And if you play it very badly, the gentleman on the other side, if he is at all musical, will probably retreat to the utmost limits of his hiding-place.”

“But look here,” said Gordon, “we’re not certain this man is the murderer. Is it quite humane——”