The New York Times publishes a collection of variety puzzles each week, and new to the rotation recently is one called "Circuit Board". Here is an example of a puzzle (I added coordinates for sake of discussion):
The puzzle is solved when "every point is connected to either one or three (never two) other points, and so that no areas are enclosed. When you’re done, all the points must be interconnected".
Beyond some basic observations, I am having trouble finding good strategies to be able to finish these puzzles. In the example, I have noted the following:
- E1 needs a third connection and must connect to D1.
- F1 and F2 can't connect, nor can F2 and F3 because either would enclose an area.
- Any corner point will have one connection (because three is impossible).
The problem I'm having is that it is hard to find specific connections that must be made. I can only find lots of instances where one of two connections must be made, for example:
- C6 to either C5 or D6
- D4 to either C4 or E4
- C2 to either C3 or B2
- A1 to either B1 or A2
I am looking for strategies that will help determine exactly where to put the connections.