Oscar: Best Picture and Best Screenplay

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)