Design and make a catapult to hurl a flaming 'rock' further than the other teams can manage.
Canes - long and short.
Pebble wrapped in a rag (secured with wire seems to work best).
'Launch-pad' for 'rock'. Spoons tied on not very successful. Baked-bean tins cut in half, and slotted (all edges filed smooth & not sharp) much better.
Lighter / matches.
Metal Bucket filled with water (in case of fire).
Each patrols / team gets equal amount of resources, and equal time to build their catapult. Line up completed catapults, and give safety briefing re. fire. Dowse the 'rock' and ignite. All scouts apart from the one 'firing' to stand well back. Using tongs, place the rock on the launch pads, and fire each catapult in turn. Must be launched via a string, so the scout launching it is out of harm's way. Pace out to see which wins. Best done in the dark, for dramatic effect (outdoors, obviously). Paraffin soaked rag/stone messy to dispose of. Leave it somewhere safe to burn out.