The Problem in Cell Block 13

A famous scientist (Prof. S.F.X. Van Dusen, a.k.a. The Thinking Machine, the creation of early 20th century writer Jacques Futrelle) & savant wagers with acquaintances that he can escape from any jail cell within a week. He is locked in with only the clothes on his back (after a few seemingly benign & readily acceded-to requests) & immediately proceeds to contact a local reporter & to drive the prison warden to the brink of madness.