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.
Best Answer
With Nintendo's revamp of the Streetpass Puzzle system this question is irrelevant as-written, and the new way they're distributed is more transparent.
Different countries, and different regions in larger countries, still get different puzzles. These regions are identified in Streetpass Mii Plaza's map feature. On top of that there are special pieces you can't buy in particular regions at all and must Streetpass someone from another region to get; these are indicated by purple squares.
With the new system, new puzzles can also be distributed by Spotpass.