Of the Oscar winning films, how many Best Pictures have won the top award without getting a nomination for Best Screenplay (Original or Adapted)?
Only 7:
Most of these in the first decade of the Oscars.
Wings (1927-8)
Broadway Melody (1928-1929)
Grand Hotel (1932)
Cavalcade (1933)
Hamlet (1948)
The Sound of Music (1965)
Titanic (1997)