Here are Rodgers and Hammerstein as the mystery guests. They appear at 17:37. And I meant to include Rodgers's EGOT details the other day - - I've put them at the bottom of this post. Courtesy of our friends at Wikipedia.
Richard Rodgers (1902–1979), a composer, received his fourth distinct award in 1962. Between 1945 and 1979, Rodgers received a total of 13 awards. He was the first person to win all four, and primarily a composer.
Academy Awards:
1945: Best Song – "It Might as Well Be Spring" from State Fair
Primetime Emmy Awards:
1962: Outstanding Achievement in Original Music Composed – Winston Churchill: The Valiant Years
Grammy Awards:
1960: Best Show Album (Original Cast) – The Sound of Music
1962: Best Original Cast Show Album – No Strings
Tony Awards:
1950: Best Musical – South Pacific
1950: Tony Award for Producers, Musical – South Pacific
1950: Best Score – South Pacific
1952: Best Musical – The King and I
1960: Best Musical – The Sound of Music
1962: Best Composer – No Strings
Special Awards:
1962: Special Tony Award "for all he has done for young people in the theatre and for taking the men of the orchestra out of the pit and putting them onstage in No Strings"
1972: Special Tony Award
1979: Special Tony Award, Lawrence Langner Memorial Award for Distinguished Lifetime Achievement in the American Theatre