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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 carefully.
Water Pistols
Age 16 to 18
Challenge Level 
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 carefully.
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