Apart from having a small group of children complete a jigsaw puzzle, there are many other puzzles that provide enjoyment and a sense of accomplishment when completed as a team. These team activities are suitable for parties or when a small group of children get together.
The first activity or puzzle that I would suggest is to place a well known story in the correct order (sequence). This is best done, with younger children, by giving each of them a picture from a story they all know well (such as little red riding hood), and having them arrange themselves in the correct order for the story to be told. The rules of this game are that the party guests can only speak and show their picture to one other party guest at a time and then decide if they need to stand next to the person they have just spoken to or continue to look for their correct neighbors. For younger children this rule can be relaxed and a free for all can break out as the kids try to line up in the right sequence. Also, if appropriate, the story can be told ahead of time using the actual pictures that are subsequently given out. In this way all of the guests know the story and have seen the order and content of the pictures ahead of time.
Variations of this game, for older children, include having the guests describe (not show) the pictures and lining up based on the verbal descriptions given. Also, again for older children, a lesser known story can be given out including a story that is not known to the group so both the order and story itself needs to be deduced from the pictures.
Pictures of well known stories can be printed from the internet or cut out from an inexpensive story coloring book. If a coloring picture story book is to be used then the kids can color their picture just prior to the game, as an additional party activity.
This party game also lends itself to a themed party, as an appropriate story (to match the theme) can be selected.
The second activity (puzzle) that I would suggest is to give each party guest a piece of a jigsaw puzzle and have them arrange themselves in the correct position around a large room. This is relatively easy for a standard small square jigsaw as the corners and edges are a huge clue. The game can be varied by creating your own jigsaw puzzles, which could be circular, i.e. pizza shaped pieces. The guests can also be restricted to not showing, only describing their pieces, to make the game more challenging. The rules can also be relaxed, as per the first game, in that a free for all can break out.
The second activity is similar to having a group complete a jigsaw but they become the piece and need to place them self in the correct position, relative to the other pieces (guests).
Given the quality of printers, today, it is relatively easy to create a suitable jigsaw puzzle for any number of guests on card stock.