One of the things I say that I love about the show is that they'll have Mystery Guests who -- especially in today's day and age -- you would never see on a game show. And this episode fits in with that perfectly. It's Sir Edmund Hillary.
What's most fascinating about this is that, actually, he's not officially a Mystery Guest. The panelists don't have their eyes covered -- and he even signs in with his own name! (Albeit with his initials, but still, that "Hillary" name at the time had to have been renown. No, he didn't just become the first man to reach the top of Mt. Everest, that was nine years earlier, in 1953. But that's not all that long before. And he looks like Sir Edmund Hillary (for good reason). And the panelists on What's My Line? are pretty erudite. But still, he has a good time with it all. (Hurting the panelists is that they go way off the track, and host John Daly lets them...)
At one point afterwards, during the discussing, they mention Tensing Norgay, who was Hillary's Sherpa guide. It was fun to hear, and I mention that because years ago, 30 years or so, my dad took an organized hiking trip in the area, and the leader of is group was...Tensing Norgay!
Hillary is the first guest, or you can just jump to the 3:30 mark.