A propos "lateral thinking". Do you know these situation riddles where e.g. a naked man with a match lies in the desert? Someone describes a bizarre situation and the others try to figure out what happened. They may ask questions which may be answered by "Yes" or "No" (or "of no importance").
I know a few of these stories, and if you're interested we could do some. Maybe you know some, too? We should open a new thread for it, though.