# Joke with my own added punchline

An engineer, a physicist and a mathematician take part in a study. The three of them are each sent into three separate rooms with white walls, given a bucket of green paint, and asked to paint all the walls green. However, there is not enough paint in each bucket to accomplish this task.

After an hour, the experimenters come to observe each room. They find the engineer’s room painted on two walls, but hardly painted on the third wall. When asked about his solution, the engineer replies, “This was the most thorough job I could do with this amount of paint.” The experimenters nod, and move on.

Next they visit the physicist. They find the walls completely white. They ask the physicist to explain why that is the case. “I can prove that the total surface area of these walls exceeds the maximum area that anyone can cover with paint,” the physicist replies. Again, the experimenters nod, and move on.

Finally they enter the mathematician’s room. To their amazement, the entire room is painted green! “How did you manage to do that?!” they exclaim in shock. The mathematician says:

“Simple. I proved to the physicist that the total surface area of these walls exceeds the maximum area that anyone can cover with paint. Then I took his paint.”

The canonical punchline is “SImple. I painted just the rational points green.”