What was Kuhn's demarcation criterion to determine whether something is or is not science? I know that he spoke about paradigms, but do those define what is or is not science? Or is it about puzzle solving, and whether a candidate for science-ness is involved with solving puzzles? (That is, trying to create a model to fit all the information gathered from observation in)
For Kuhn the demarcation between science and non-science is institutional. It parallels institutional theories in other areas of philosophy, like aesthetics. In short, science is what is undertaken by the body of workers called scientists—especially professional scientists. The question of whether something is or isn't science is a matter of whether it's part of the human institution of science.
An institution in this sense is collection of things in the world, typically recognizable to insiders and outsiders. Among the examples of institutions in this sense are a country's legal system and higher education. We can recognize the institution of science as collection of people, organizations, activities, and events, inputs, and outputs, including things like researchers, laboratories, journals, books, courses, experiments, techniques, specialized terminology, theories, hypotheses, bodies of data, physical tools, field-stations, articles, and so forth.
Defining science institutionally of course stands in contrast to other preceding philosophers' efforts to define science in terms of its internal characteristics like verifiability (Logical Empiricists) or falsifiability (Popper). Kuhn would not argue this way. At the same time, he would not allow that anything goes as science, because he thinks the institution of science approaches the world with certain values that rule out some activities or claims as unscientific.
One of the characteristics of the institution of science is normal science, and normal science involves puzzle-solving. Puzzle-solving is what you may be remembering as the typical activity of the institution of science. It is the characteristic activity of normal science, on Kuhn's view. Not all science is a matter of puzzle-solving, though, since some scientific activity is revolutionary—reevaluating the basic assumptions about what the major questions and puzzles for the discipline are.