But to get this right, the difficulty level and learning curve have to be properly calibrated. If the puzzles are too hard, or the learning curve too steep, people won't be able to progress, and will get frustrated and quit. If the puzzles are too easy, there's no feeling of progress or accomplishment, so it just feels like mindless repetition, and people get bored and quit.
So you need something that in fact anyone who keeps playing can accomplish, but that feels like something that takes skill to accomplish.
My new idea for how to make this work is to cheat. If each level appears to be something that you play over and over again, being confronted with the same challenge each time, but it actually gets easier each time you try it, then it will seem as though you get better with practice and eventually solve it, but in fact anyone can solve it, because you don't need to get better; the puzzle gets easier.
The reason for the question mark in the title is that I have a suspicion that Angry Birds does exactly this. Just as I'm giving up on a puzzle, I seem to make progress that I can't explain. Maybe I've learned to hit the exact right angle to destroy the building. But maybe the laws of Angry-Bird-Physics change depending on the number of times I've played that particular level, and it's not that I've learned to hit "just the right angle", it's that as I play, a wider and wider range of angles are good enough to count as "just right".
This could be tested by switching between two copies of the game that are at the same level, one of which has been played more at that level than the other. If anyone is near the end of the first third of Angry Birds on a droid, and wants to test my theory that it cheats in this way, let me know.
If Angry Birds doesn't 'cheat' in this way, does anyone know of any other games that do? Or is this a new idea in game design? Hard to know for certain, since anyone using this technique would not publicize it; it depends for its effectiveness on the illusion that the player is getting better, when actually the game is getting easier, and the illusion would be ruined if people knew what was really happening.