They tried to be too clever ”and that was their undoing." Poirot puffed at his tiny cigarette, his eyes fixed on the ceiling. 
Poirot stared fixedly at the floor whilst smoking a cigarette. 
mnli hypothesis: Poirot stared fixedly at the floor whilst smoking a cigarette.  premise: They tried to be too clever ”and that was their undoing." Poirot puffed at his tiny cigarette, his eyes fixed on the ceiling. 