# Strategies for Circuit Board Puzzle from NYT

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
• etc.

I am looking for strategies that will help determine exactly where to put the connections.

• Is there an online link to these puzzles somewhere? Searching “circuit board” doesn’t come up with anything Nov 21, 2021 at 2:19
• You can try this link but I think you will need a crossword subscription. The circuit board puzzles are part of the "A Little Variety" ones that come out each week. The first one appeared on Sep. 12, 2021. There is generally a new type of puzzle every 3 months or so, and I have enjoyed most of them. Nov 21, 2021 at 17:56

In general, with logic puzzles it's important to mark not only the parts of the solution, but also things you know can't be part of the solution. Here, that means you should mark segments that you aren't allowed to draw, because there would be no way of completing the puzzle if you did.

For example, there can't be a connection between F1 and F2, because F1 is in a corner and already has one connection. So you could draw an X between them.

And once you've done that, now F2 is in a corner and has one connection! So there can't be one between F2 and F3 either. Then F3 and F4, then F4 and E4...

And now the top-right section is nearly isolated. How does the dot in F4 connect to the rest of the puzzle? It can't go through F6, because corners are always dead ends. So there must be a segment between F5 and E5.

X-markings could be useful in other places, too: Once you've drawn E1-D1, you know that D1 can't be a 3-connection dot, because that would make a tiny loop. So you can then mark off the other two D1 connections:

Continuing like this, marking both connections and Xs, should let you solve the puzzle much more easily.

• In addition to the X-es, I would write a little 1 or 3 next to a dot if I know the number of connections it should have, but don't yet have enough information on which connections those will be. Sep 20, 2021 at 19:47

Certain connectivity rules must always apply. Every corner piece must be 1-connected (not 3-connected), since it could at most be 2-connected (which is illegal). Also, every 1-connected dot connects to a 3-connected dot because if it paired with a 1-connected dot, the two would form a disconnected/unreachable "island."

Next: Fill in lines you know are good with heavy pencil or ink. When you have a choice to make (e.g. a 2-connected dot with two possible ways of making it 3-connected), try one lightly in pencil. Using light pencil, follow the implications of the decision and see if they result in a problem (e.g. a close-in area). If so, erase the light pencil and know that the alternative (if it there were only two possibilities) must be so.

• Logic puzzles should be solved without trial and error. Nov 21, 2021 at 2:21
• @DanielMathias They can be solved with trial and error as long as there's watertight logic: e.g. make a guess, get a contradiction, you know that guess was wrong. Nov 21, 2021 at 5:43
• @Randal'Thor And if you get no contradiction, you know that guess was right. Where's the logic in that? Nov 21, 2021 at 5:57
• @DanielMathias Hence why you make a guess that you believe to be wrong - and if you make a guess and don't find a contradiction, go back and make the opposite guess instead, just to make sure that you do get a contradiction there. Nov 21, 2021 at 6:10