This is a good game to play right after Invisible Maze
and reuse the sheets of paper.
Have a patrol on each side of the center line - you might mark this with tape if needed.
Distribute the paper balls across both sides of the play area.
Have an unbiased timekeeper stand at the center line with his back to the play area so he does not see how the game is going.
On 'GO' signal, teams throw all the paper from their side to the other side.
When the timekeeper yells, 'STOP!' the round ends and balls on each side are counted.
The timekeeper should give about a minute for each round.
Either have the winning team face the next team or record scores and have two new teams play.
You could have a tournament with a double-elimination or round-robin structure.