Second, suppose that you are playing a visual problem-solving game, such as Rush Hour, or completing a jigsaw puzzle.Here is, perhaps, a simpler way to get to my point. Suppose that problem solving is a behavior. Then, one might have extended behavior without extended cognition. Cognitive processes are one thing; behavior another. Cognitive processes contribute to cognitive behavior is the idea. That's what I take to be the standard cognitivist line. (Somewhere Chomsky says something like "linguistic behavior is the product of linguistic competence, along with poorly understood factors such as attention, set, etc." I'm thinking this appeared in Chomsky's Language and Mind, or earlier.) What muddies the water, perhaps, is the idea that problem solving is properly described as cognitive behavior. But, why is it cognitive behavior? Because it includes a cognitive process in the brain of course.
Moreover, I think that essentially the same story can be told about Gary Williams example of decision making in sortilege.