First episode: July 14, 1952
Last episode: September 15, 1952
Seen Monday nights 9:30-10:00 on CBS
Bill was a regular panelist (though he left before the series ended) on this series in which the panel identified famous personalities from props that provided clues to their identities.    Arlene Francis was the host of the show, a rare female emcee. The picture here almost certainly isn't from this particular show.  Bill and Arlene did a lot of RADIO shows together, and this is probably a publicity shot for one of those.
This one's really obscure.  Do the math, there were no more than nine episodes produced, and Bill wasn't even in all of them.  In Bill's listing on the Internet Movie Database, we're pretty sure this series is listed in error under the title That Reminds Me.
Yeah, right.