With my informal Coding for Teens group, I like to start each session with a puzzle that we do as a group. My reasoning is that programming is not primarily about semicolons and syntax, but about logical thinking. And logical thinking can be demonstrated and honed with puzzles.
So far I've used grid puzzles (Alice, Betty, Carol, and Dawn have dates with Roger, Steve, Tim, and Ulmer...), and I'm thinking about using the Towers of Hanoi (obviously that's a one-session puzzle), but I'm wondering if there are other formats that are good for this type of group activity.
To be clear, I'm not asking for a list of specific puzzles / links. I'm asking for puzzle types. For instance, if I were asking for puzzle types that hone language and / or lateral thinking, "crossword puzzle" might be a good answer.