The previous discussion reminds me of a radio show that the Head of School at Natural Friends did last summer. As an example of the kind of deep problem that kids at Natural Friends might work on, he offered, "there are three people at a party. How many handshakes?"
I was completely baffled by this the first time I heard it. How the heck would I know how many handshakes? There are too many possibilities for a divergent thinker like myself.
There might be zero handshakes, because everyone in the room is germ-phobic.
There might be hundreds of handshakes, because it's a meeting of the Obsessive-Compulsive Handshakers Support Group.
If two of the three people are married to each other, they wouldn't need to shake hands, so there would be two handshakes (the husband and wife each shaking the third person's hand.)
If two of the three people are Orthodox Jewish men (not allowed to touch a woman other than their own wife), and the third is an unrelated woman, the only legal handshake would be between the two men.
Or it could be that each person shakes every other person's hand exactly once, in which case you have three handshakes.
That last possibility is actually the preferred one; the handshake question turns out to be a classic problem. For the problem to work as intended, it must be assumed (or better yet, stated) that each person shakes every other person's hand exactly once.
The problem is fairly sophisticated; as you add people to the party, you wind up taking the sum of an arithmetic series. I think it would go right over the head of a kid brought up on the thin gruel of Trailblazers Math.