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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.
Futrelle's story was tailor made for live TV broadcast, but as far as I know, Cell 13 was the only one that made it to prime time, on the fine anthology series, Kraft Mystery Theater. Futrelle himself, a native of Georgia, perished in 1912 aboard the Titanic.