Challenge indeed ...
I called up Billboard.com, looked for archives (near the bottom of page), selected the magazine for the week ending after my birthday (Nov 26, 1952), searched 'singles' (people born after 1955 can simply type in top 100 or hot 100) - result #3 got me "best selling singles", Then I went to You Tube and typed the #1 song from that chart, select embed, copied and pasted it in the YouTube icon and presto - nothing ...
However, now that Chrissi has shown me the errors of my way, here it is.
Joni James - Why Don't You Believe Me?
[youtube=425,350]http://www.youtube.com/watch?v=sHJQ6BGyFXg[/youtube]
BTW, I hate that song. Don't much care for her body of work either; she had nearly two dozen top 40 hits in the 50's, this being her only #1.