The Dilettantes Club is a gathering of five savants who dine once a fortnight in Soho, and debate any problem besetting mankind. One evening, into this distinguished company, there intrudes a Professor of Logic and Philosophy, an odd little man. The Assistant Commissioner of Scotland Yard is one of the Dilettantes, and a baffling problem of criminal investigation is debated. The little Professor is able to point the finger at those who currently are eluding the police net. A series of intriguing impossible crimes unfold, until . . .