"Among those people, there’s either a group of three who all know each other, or a group of three who have never met." If your wife's friend knows no one, then

"Among those people, there’s either a group of three who all know each other, or a group of three who have never met." If your wife's friend knows no one, then you can make a group of three in which no one knows each other. Just pick yourself, and not the person you know from from work or your hobbies. or pick the person from work and not their +1 or yourself. In this manner, in a group of 6. You inescapably have one or the other.