When the economist arrives home, he turns on the garden hose in his front yard and sprays a huge blast of water on the fire. This completely puts out the fire, but now a section of the house is covered in water.
The next day, the arsonist lights a chemist’s house on fire.
When the chemist arrives home, he carefully studies the fire, then meticulously studies the water in his hose. Then he sprays just enough water on the fire that the fire is put out, and the house remains completely dry.
The next day, the arsonist lights a mathematician’s house on fire.
When the mathematician arrives home, he looks at the fire, looks at his garden hose, says, “A solution exists,” and goes inside.