Jigsaw puzzles are often found spread out in various stages of completion or disarray at our house. We clean around them, try not to knock pieces onto the floor, try to keep the grandkids from walking off with bits or disassembling what has been assembled. They sometimes serve as coasters for a cup of tea or coffee, and I wouldn't be surprised to see a piece in the dishwasher as a result of this somewhat unorthodox treatment.
Most of our friends pitch in when they visit. One family actually couldn't stand to leave the puzzle unfinished, so they took it home with them as it was midnight and we wanted to go to bed. I can't remember what elaborate system we worked out so that it would travel without falling apart, but I guess it worked well enough. I think it involved a cookie sheet and some cling film.
We always have one in process during the winter holidays, but they have lately been showing up at any old time of the year. Right now there is one taking up most of the dining room table, and it is right on the heels of one that was just completed two days ago.
There is a meditative experience that grows as we chat and work to put the pieces together. And everyone has a different method. I'm pretty straightforward (well, as I see it anyhow), I like to put the edges together first, then sort the pieces by color. I see that as the most organized approach, of course. My husband, however, will find a few pieces that fit, and then start building out from there. I find his approach curious, but it seems to work pretty well. Our daughter has an uncanny eye for what fits where and can grab a piece out of the middle of a group and place it immediately. Our son, the engineer, has a method that is more methodical and very efficient, although I could not tell you what it is.
We have figured out, or pieced together, lots of things over our puzzles. Of course we still have questions about each other's methods. Problem-solving is not a one size fits all. Of course we find each other's approach curious, or too complicated, or not organized enough. But we do know, that in the end, everyone will have contributed to the process, and the finished product will be satisfying and just as perfect as if we had all used the same approach. We shared the goal, and that is what matters, in the end.