Digital logic game
I've been thinking about a puzzle game idea that could be pretty fun. Basically, you're given an input signal and you have to turn it into the right output signal by adding components. So you get a square wave in, you want an inverted square wave out, and you need to put a NOT gate in the middle. As the levels get more sophisticated, you need more and more components.
But what could be really interesting about it is that, unlike a lot of puzzle games where you try a solution and then it works or it doesn't, this would have live feedback. So you see your square wave input moving in real time, and as soon as you connect the NOT gate to it you see the inverted square wave on the other side. The expected output is live too, so you don't have to click a "try my solution" button. As soon as your solution works you'll know.
In a sense, the "input" and "output" ideas are arbitrary too, because they really just represent fixed nodes. You could say you need to make the input match the output, but it would be equivalent to say the output has to match the input. In fact, you could really have any number of fixed nodes that you have to connect in a way that works.
At first the levels could be simple things to introduce basic digital logic concepts, but before long you could do more sophisticated stuff, build complex gates out of simple gates, make half-adders, full adders, flip-flops, that kind of thing. You could even break out of digital logic land entirely and go analogue, have resistors and capacitors and so on, though that would really be a different (but similar) game where you have to think about current as well as voltage.
I think there's something very interesting in the space of these games that are educational in the sense that they are based on rules from real life, but not specifically designed to teach. Rather, they assume the topic is inherently interesting, and just let that interestingness express itself through the rules of the game.