The eponymous dilemma of the play is that of the newly honoured doctor Sir Colenso Ridgeon, who has developed a revolutionary new cure for tuberculosis. However, his private medical practice, with limited staff and resources, can only treat ten patients at a time. From a selection of fifty patients he has selected ten he believes he can cure and who, he believes, are most worthy of being saved. However, when he is approached by a young woman, Jennifer Dubedat, with a deadly ill husband, Louis Dubedat, he admits he can, at a stretch, save one more patient, but that the individual in question must be shown to be most worthy of being saved.
