Here is a problem published by Henry Ernest Dudeney in his book “Amusements in Mathematics” published in 1917. He does not claim authorship of this problem. He notes that Houdini used to use this problem, but he does not know who the author is.
Dudeney states: “The puzzle is to draw with three strokes of the pencil the diagram that the little girl is exhibiting in the illustration. Of course, you must not remove your pencil from the paper during a stroke or go over the same line a second time.”
“You will find that you can get in a good deal of the figure with one continuous stroke, but it always appear as if four strokes are necessary.”
I was not familiar with this problem until I read Dudeney’s book. I have seen this diagram before, but the problem was stated differently. As I recall, it is a diagram show the floor plan of a house with 5 rooms. Each room has a doorway to enter any adjacent room, and a doorway to the outside of the house in every wall that borders the outside of the house. The goal is to find a route to visit each room in the house just one. You do not have to pass through every doorway, but the doorways you do pass through can only be used one. My question is “Is there a solution to this problem?”