A group of children are playing with water balloons. First, they each select a position on the playground, and then at a signal, everyone throws their balloon at the person closest. If there are multiple people with minimal distance to them, they can freely choose who they aim at.
How many children were playing at most if in the end only 12 got wet, and everyone hit the person they aimed at?
To deter guessing without thinking, we ask that you also solve the following simple arithmetic problem before checking your answer:
What is three plus seven, plus three?