“Here, what are you driving at, Ellery?” asked his father, frowning. Ellery briskly crushed his cigarette in an ash-tray. “Just this,” he said. “Pure reasoning has it that when you have exhausted every possibility but one in a given equation that one, no matter how improbable, no matter how ridiculous it may seem in the postulation—_must be the correct one_.... A theorem analogous to the one by which I concluded that the papers were in this apartment.” “But, Mr. Queen, for the love of Pete—ceilings!” exploded Cronin, while the Inspector looked guiltily at the living-room ceiling. Ellery caught the look and laughed, shaking his head. [Illustration: Bedroom with items indicated by capital letters] A—Ceiling B—Door to Living Room C—Mirror D—Dressing Table E—Damask curtains around bed, from ceiling to floor, concealing shaded portion which represents panel containing hats. “I’m not suggesting that we call in a plasterer to maul these lovely middle-class ceilings,” he said. “Because I have the answer already. What is it in these rooms somewhere that is on the ceiling?” “The chandeliers,” muttered Cronin doubtfully, gazing upward at the heavily bronzed fixture above their heads. “By jinks—the canopy over the bed!” shouted the Inspector. He jumped to his feet and ran into the bedroom. Cronin pounded hard after him, Ellery sauntering interestedly behind. They stopped at the foot of the bed and stared up at the canopy. Unlike the conventional canopies of American style, this florid ornament was not merely a large square of cloth erected on four posts, an integral part of the bed only. The bed was so constructed that the four posts, beginning at the four corners, stretched from floor to ceiling. The heavy maroon-colored damask of the canopy also reached from floor to ceiling, connected at the top by a ringed rod from which the folds of the damask hung gracefully. “Well, if it’s anywhere,” grunted the Inspector, dragging one of the damask-covered bedroom chairs to the bed, “it’s up there. Here, boys, lend a hand.” He stood on the chair with a fine disregard for the havoc his shoes were wreaking on the silken material. Finding upon stretching his arms above his head that he was still many feet short of touching the ceiling, he stepped down. “Doesn’t look as if you could make it either, Ellery,” he muttered. “And Field was no taller than you. There must be a ladder handy somewhere by which Field himself got up here!” Cronin dashed into the kitchenette at Ellery’s nod in that direction. He was back in a moment with a six-foot stepladder. The Inspector, mounting to the highest rung, found that his fingers were still short of touching the rod. Ellery solved the difficulty by ordering his father down and climbing to the top himself. Standing on the ladder he was in a position to explore the top of the canopy.