It's from one of the Gaki no Tsukai Batsu Game shows:
I think I have a general idea of what it does. I think it's similar to "のか" in:
These particles seem to be separating the sentences into 2 distinct parts, or defining one part so you can then make a comment on it.
In any case, I'm not sure what this aspect of grammar is called, and don't know the difference between の, か, のか, こと, and とか when they are used in this way. Any help would be much appreciated, thanks.