Choosing another track in August, I wrote:
The genius of Blow-Up is that, though the mystery remains unsolved, you feel that if you watch the film just once more you will crack it. The Draughtsman's Contract has the same quality.And Ode to Billie Joe has the same quality. Listen to it once more and you are sure you will understand what is going on.
Wikipedia claims it know the reason for the mystery:
The original recording, with no other musicians backing Gentry's guitar, had eleven verses lasting seven minutes, telling more of Billie Joe's story. The executives realized that this song was a better option for a single, so they cut the length by almost half and re-recorded it with a string orchestra. The shorter version left more of the story to the listener's imagination, and made the single more suitable for radio airplay.However, I can find no authoritative source for this claim and the lost verses seem never to have emerged. All of which makes the song even more mysterious.
Bobbie Gentry was 23 when this song, which she wrote, reached no. 1 in America and no. 13 in the UK. This video shows her singing it for the BBC the following year.
I remember it from those days and would still like to solve the mystery.