Ellery Queen and his father are driving through a mountainous area of the United States on vacation when they are forced by a forest fire to seek shelter in a private home on the top of a mountain. The home soon becomes impossible to escape due to the fire. Dr. Xavier's aerie is host to an unusual assortment of characters, including his family and guests, a pair of teenage boys who are "Siamese" or conjoined xiphopagous twins, the doctor's assistant "Bones", who keeps burying mysterious parcels in the grounds, and another refugee who insists that his name is "Mr. Smith".
As the fire creeps towards the top of the mountain, first the doctor and then his brother are murdered. Each victim is found clutching half a playing card, and half of a jack of diamonds seems to indicate that one - but only one - of the Siamese twins is the murderer. The limited circle of suspects includes a kleptomaniac who steals only rings, and a blackmailer.
Ellery and his father investigate the murders and battle the fire at the same time. He performs an extended feat of deduction about the handedness of the murderer based upon the torn playing cards. The solution to the crimes is revealed in a dramatic finish when the flames reach the top of the mountain.