“To a certain extent. I don’t spend much time at it, however. The game is not purely mathematical; and it’s insufficiently speculative to appeal to a wholly scientific mind.”

“Did you find the Shapiro-Marshall position difficult?”

“Not so difficult as tricky.” Drukker was watching Vance shrewdly. “As soon as I discovered that an apparently useless pawn move was the key to the impasse, the solution was simple.”

“How long did it take you?”

“Half an hour or so.”

“Until about half past ten, shall we say?”

“That would be about right.” Drukker settled deeper into his chair, but his covert alertness did not relax.

“Then you must have been in the archery-room when Mr. Robin and Mr. Sperling came there.”

The man did not answer at once, and Vance, pretending not to notice his hesitancy, added: “Professor Dillard said they called at the house about ten and, and after waiting a while in the drawing-room here, went down to the basement.”

“Where’s Sperling now, by the way?” Drukker’s eyes darted suspiciously from one to the other of us.