This post was adapted from an answer to one of my playtesters questions:
What methods do you usually use to design this game’s puzzles, and which of those methods do you think lead to the best (most enjoyable?) result?
There are three main approaches to designing puzzles in this type of game that I’m aware of.

1.Top-Down Method
This approach starts with the solution state and works backwards to constrain the puzzle so that this is the only solution.
This is an approach which I very rarely, if ever, have used in Taiji. There can be some valid reasons to choose it–if one is in a tight spot and needs to solve another design problem perhaps–but generally you don’t have much luck making good puzzles with this approach.
As a caveat, all design approaches include at least some “top down” elements. For example, one has to pick an idea that seems interesting in the first place. Though it should be easy to see the difference between “this point is connected to this other point” as a top down imposition, and “this is the exact path that you take to get there”. So the problems of this approach often come with the extent to which it is applied. Keeping things in balance I think is a theme that will be clear through this discussion.
Also, if I move to include the observational puzzles in the game, you could argue that those are fully top down designs. But since those puzzles are more about observation or abstracting something in the environment than they are about logic within a grid, the design approach is different. This discussion will be long enough just focusing on the logic puzzles, so I’m going to have to leave the topic of environmentally-clued puzzles undiscussed for now.
Moving on to the next approach.

2. Experimental Method
In this approach you basically just plop down some random things and see what happens.
This sometimes produces good puzzles, but it’s difficult to make larger puzzles that have good solution paths through them. Getting good puzzles this way is mostly down to luck, and with smaller puzzles you just tend to have better luck. Regardless, this approach is the only one you can take early on, since when you are still adding new mechanics to the game, you still have a lot to learn about how your own game functions.
Another downside to this approach that perhaps just affects me personally, is that when just plopping things down randomly, I tend to draw symmetrical shapes because they “look nicer.” Unfortunately this also tends to create symmetrical solutions in Taiji. This is still in the game often enough that players can notice the pattern, but I’ve worked hard to make sure that it is not a universally applicable tactic. It’s okay to have symmetry show up sometimes, as it is thematically appropriate, but too many times and the game falls flat.
And the final design method.

3. Forwards Method
This is the trickiest to explain. Here is a link to a long form explanation and example, but the basic gist is that you start with some deducible situation and place that into the puzzle. You can then add more deductive moves into the panel, creating as much specificity as you want.
This method is useful because it gives you the most control over the players path through the puzzle. You are designing the moves that they will make in the order they will make them.
With that said, it is a tool that must be used with care. Just because you can fully specify every tile in the solution doesn’t mean that you must. Sometimes leaving a little play in the puzzle is more interesting. In a pen-and-paper puzzle, you don’t want multiple solutions because the solver needs to check against a canonical solution in the back of the book, but in a video game you can be more flexible and you should.
Use your discretion as a designer and prune alternate solutions if they allow the player to miss the main idea of the puzzle, but there’s more than one way to skin an electric eel and part of the magic of video games is that they are a bit different for every player. Try to embrace that whenever your design goals allow it.
In the best case, the forwards design technique can allow you to focus your puzzle designs around strong core ideas. But in the worst case, it can lead to a flat feeling, where all puzzles become a sort of paint by numbers.
Still, it is the most powerful technique that I have learned over the course of designing Taiji, and even through it is dangerous, I think it is a requirement to have this tool in your toolbox. It’s just important to remember that you are designing puzzles to serve the overall game design and not to serve the tool.
My Approach
So I mostly use a combo of methods 2 and 3; the experimental and forwards methods. But I think the best puzzles tend to come from a mixture of forwards design and some happy accidents. There are also meta aspects that I could get into which can really take puzzles to another level, but I’ve gone on long enough so that will have to wait for another time.
In any case, over time I have leaned more towards judging puzzles by their content instead of by their enjoyability. I think this is a more stable approach once one becomes more sure of themselves as a designer. However, this does sometimes lead to situations like one I had the other day. There is a particular puzzle in the game that I always loved, but which I have come to realize many players find annoying. I was so convinced that the idea for the puzzle was good, that I didn’t worry too much about its enjoyability. Sometimes this is a good approach, however in this case, my disregard for the enjoyability of the puzzle led me to overlook its failure to communicate any appreciation for that core idea. Players found the way in which I was presenting the idea so repulsive that they came away finding the idea itself repulsive.
I knew the idea was good though, so yesterday I went back to the drawing board and designed a new introduction to the idea.
So, as with all game design, be sure to test your design theories against reality and see if you’re getting an acceptable response. Not everyone has to enjoy every puzzle, but if most people hate a puzzle that you’re in love with, then perhaps there is something about the way you presented that idea that could be improved.
As an aside, I want to mention the two biggest mistakes that I see other designers make. The first is not listening enough to others early on in their careers, and the second is listening too much to others once one becomes more established. When you’re starting out, you don’t even know what you don’t know, and it’s more likely than not if someone has a criticism of your game, that you probably should change something. However, as you develop skill and experience as a designer, it is important to learn what your own tastes and values are, and accept that sometimes these will conflict with those of other people who play your game. Accepting feedback and having a guiding vision are both important forces to keep in balance.
Conclusion
In summary, I think the best puzzles are the ones that have a strong idea at the core of them. Something that can be verbalized like “this puzzle shows you that when X and Y are the case that Z occurs” or “this puzzle is about carefully interweaving 4 things while maintaining symmetry” or “this puzzle introduces this new mechanic, but requires the player to deduce its meaning by virtue of it being the only possible explanation”.
I haven’t always lived up to this standard with every single puzzle in the game, but when I haven’t, I have at least made sure that the puzzles serve a pacing reason or form a sequence or meta-structural element that has some unique interest to it.
And well…sequences and meta-structure can add immensely to the enjoyment of a puzzle game, but that’s a whole additional discussion which will have to come at a later time.
Additional Recommended Reading
Elyot Grant’s 30 Puzzle Design Lessons, Extended Director’s Cut – This is a fantastic resource, and although lengthy, is an extremely enjoyable watch as well.