Rules: Have everyone break off into small, equal-sized groups. (patrols) Give each group a different jigsaw puzzle with the same difficulty level. The goal is to see which group can complete their jigsaw puzzle the fastest. However! Some pieces will be mixed around in other group's jigsaw puzzles. It's up to the team to come up with a way to get those pieces back — either through negotiating, trading, exchanging team members, etc. Whatever they decide to do, they must decide as a group.
Or, dump all the bits in the middle of the room...
Enough puzzles, of a similar size and piece size, so that there is at least one for each group... or more!
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