This activity could be just a simple opportunity to help build community or it could also be used as a creative way to lead into a discussion topic. First, you will need a puzzle. It could be either a regular jigsaw puzzle or you could get blank puzzles from a craft store and write or draw something on the puzzle related to a specific discussion topic or Bible study focus. Divide the puzzle pieces evenly to correspond to the number of teams appropriate for the size of your group. For example, if you have 36 pieces and 6 teams, you'll have six even piles of puzzle pieces.
Next, select scavenger hunt locations around your church -- the same number of locations as you will have groups. At each location, place one of the piles of puzzle pieces and a list of trivia questions (possibly related to a specific discussion topic) for each group to try to answer. Provide an answer key at the location as well so teams can check their answers. Once groups finish with the trivia, they take one puzzle piece and move on to their next location. When a group has cycled through all the stops, answering trivia questions and taking one puzzle piece each time, they should return to a central location where youth work together to complete the puzzle. Obviously, the puzzle cannot be completed until all group contribute their pieces.
This activity can be particularly fun if the final puzzle shares a special message or clue to the evening's study or topic which is slowly revealed as the students work together to complete the image.