Four.

Since the introduction of the supporting awards in 1936,
the six major awards have been evenly distributed in 1952, 1956, 2005, and 2012:

 
1952
1956
Best Picture The Greatest Show on Earth Around the World in 80 Days
Best Director John Ford (The Quiet Man) George Stevens (Giant)
Best Actor Gary Cooper (High Noon) Yul Brynner (The King and I)
Best Actress Shirley Booth (Come Back Little Sheba) Ingrid Bergman (Anastasia)
Best Supporting Actor Anthony Quinn (Viva Zapata!) Anthony Quinn (Lust For Life)
Best Supporting Actress Gloria Grahame (The Bad and the Beautiful) Dorothy Malone (Written on the Wind)
 
2005
2012
Best Picture Crash Argo
Best Director Ang Lee (Brokeback Mountain) Ang Lee (The Life of Pi)
Best Actor Phillip Seymour Hoffman (Capote) Daniel Day-Lewis (Lincoln)
Best Actress Reese Witherspoon (Walk the Line) Jennifer Lawrence (Silver Linings Playbook)
Best Supporting Actor George Clooney (Syriana) Christoph Waltz (Django Unchained)
Best Supporting Actress Rachel Weisz (The Constant Gardener) Anne Hathaway (Les MisÚrables)

 

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