I've been thinking about the games I play, and what kinds of games I tend to enjoy playing the most. I've written about soundtracks, atmosphere and mechanics previously, and those apply equally to tabletop (yes, even music and video games. Another thing that often attracts me to a game is the desire to solve a puzzle.
In real life, I like being the guy who solves a problem. I think most people do, because it feels good to be the person who helps everyone else get past something that's been in their way. Pretty early in my life as an adult though, people started acting like I was the guy to go to when they were having issues with tech. I didn't know it at the time, but I was the tech guy, and to my great surprise my skills were in high demand. I'd been collecting a set of tools during my primary school years of being bullied as a "nerd", and those tools (the ability to troubleshoot, the vocabulary of computing, experience with computers and networking and so on) were the keys to solving a whole variety of puzzles that nobody else around me knew how to solve. Maybe it's a chicken-or-the-egg question, but I either had an innate love for solving puzzles, or I was conditioned to love solving puzzles through positive reinforcement after helping people. One way or the other, one thing I've learned about myself is that a good puzzle captures my attention, sometimes whether I like it or not.
As with many motives for playing games, the definition of a fun puzzle, or even a "puzzle" in itself, is subjective. There's a whole genre of tabletop games and video games dedicated to puzzle-solving. Some I like, others I don't. There are even literal [jigsaw] puzzles, and I don't enjoy those at all. Maybe what I actually enjoy are riddles, although I don't actually enjoy verbal riddles.
Whatever the correct definition, I tend to enjoy a game that identifies a goal, and then places interconnected obstacles between me and that goal. Solving one obstacle affects another obstacle, or else it grants me some ability required to get past another obstacle.
Sometimes, solving an obstacle can be as linear as progressing along a skill tree. You can't get past the monster until you get the magical spell. In other cases, solving an obstacle might require collating and correlating a bunch of clues from early in the game. Depending on just how much of a mental load I'm prepared to take on, I can find enjoyment in the simulation of a puzzle just as well as an actual puzzle.
A common problem with puzzles in a game, I think, is that game sessions are often relatively brief, and sometimes all too rare. Maybe you're playing a tabletop roleplaying game with a group that meets for just 3 hours each week, or maybe only fortnightly. Or maybe you're playing a video game on Friday and Saturday nights.
Or maybe you've got lots of spare time and play daily.
If there's a puzzle in a game that takes more than a single game session, then the game needs a way for you to keep track of what you've learned so far and a way to refresh your memory on how the clues relate to one another. Without that, the experience is, at best, lost. At worst, the game is unbeatable unless you start over, because you've forgotten what you're trying to solve, how the clues you've found help you do that, and why.
I sense that there's a trick to puzzle game design, whereby a big puzzle is composed of lots of small solutions. The solutions get pieced together in the end, either as a puzzle or as a free reward, but the solutions only exist because you "unlocked" it by solving a minor puzzle. It relieves the player of the burden of retaining disconnected clues and possible clues in memory until the next time game session, but still provides a puzzle to obtain each milestone, and the multi-step puzzle sequence of obtaining each milestone. It's the same concept as waypoints representing physical progress, but it's for mental progress instead.
Some puzzles in games are actually just an algorithm or, less charitably, a laundry list. To get to point C, you must first get to point A and then B, in that order. If you've been a Game Master or a hobbyist game designer long enough, then you've designed something like this, either intentionally or accidentally. Sometimes this trick does work. I've played games that have sent me on a sequence of fetch quests that actually have ended up feeling like a satisfying puzzle. I honestly think the only difference between those that do work and those that don't is information denial.
When a game tells me that I have to go to the wizard Mirabella to get a key, and then Mirabella tells me I have to take care of her giant spider problem to persuade her to give me the key, then it doesn't feel like a puzzle. When a game shows me a locked door with no commentary, and 12 hours later I'm rewarded with a key after helping a wizard clear out the giant spiders from her store room, it feels like I've solved a little puzzle. It's a basic example, and there are cleverer ways to accomplish this sleight of hand, but the concept often holds true. Don't tell the player there's a problem and, after it's been solved, it retrospectively feels like a puzzle
There's a whole variety of problems that feel like puzzles, from mini-game puzzles to big convoluted mysteries, and everything in between. The important thing is that a good game's puzzle sticks with you in some way. Maybe it consumes every bit of your attention just while you're playing it, or maybe it bleeds over into your time away from the game. Either way, a good puzzle is sometimes the reason players stick with a game. The urge to find a solution to a problem is what makes a gamer, at least of a certain character type, a gamer. That's not so puzzling, is it?