This is a scavenger hunt where you send out each team with a coat hanger (or another small item if you wish) and you instruct each team to go door to door in the neighborhood asking people if they will trade for something bigger (strictly the size) or better (quality, value, etc.). The team that brings back the biggest or best item back is the winner. Teams must trade the items, not come back with a stockpile of items. Each team will come back with one item and judges will determine the winner. 

You must trade each item you receive for the next item
No money or anything else can be offered on the side
Your team must stay together

Another option: 

The Edible Bigger and Better Hunt:  

The Edible Bigger and Better Hunt: You can start each team with a small food (carrot, celery stick, tomato, anything small). Have the teams then go out into the neighborhood and knock on doors asking for something edible that is bigger or better then what they have already. The team who ever comes back with the best object wins. Rules: the object must be human food, which means no dog or cat food. Prize: For the team that wins let them pick something that another team has gotten for a prize. Or- pizza in never a bad idea!