Age 16 to 18
A group of children are in a field and no two pairs of children are
at the same distance apart. Each child has a water pistol and
shoots the child nearest to them.
For different numbers of children, can you construct configurations
in which $0, 1, 2, 3, \cdots$ children get wet? Can you construct
configurations in which $0, 1, 2, 3, \cdots$ children stay dry? Is
there a largest or smallest number who could get wet in each case?
Do any patterns emerge?
It is a hot day and all of the children want to get wet? Can you
place them so that this is possible. Prove your results