"The door is locked, the window is inaccessible.

Was it through the chimney ?" "The grate is much too small," he answered.

"I had already considered that possibility." "How then ?" I persisted.
"You will not apply my precept," he said, shaking his head.

"How often have I said to you that when you have eliminated the impossible whatever remains, HOWEVER IMPROBABLE, must be the truth?
We know that he did not come through the door, the window, or the chimney.

We also know that he could not have been concealed in the room, as there is no concealment possible.