In the United States, Puzzle Swap panels appear to be distributed by State. That is, each state gets a particular puzzle, and to find other puzzles, you need to Streetpass with people in other states. It tied to your initial region selection, so unless you reformat the 3DS's system memory, you will always get the same initial panel.
Does anyone know how the puzzles are distributed in Europe? Is it broken down by country, or is (hopefully) more granular than that? My wife and I both live in Berlin, and we've now both completed the Mario, Luigi, and Bowser panel.