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Dissection puzzles
Dissection puzzles are puzzles in which you have to transform one shape into another using the smaller shapes within it. They can be very challenging depending on the size of the shapes, and the amount of smaller shapes. However, this is pretty much all there is to this puzzle, but you can add a lot to make it fit in an RPG setting.
This puzzle could obviously be used as challenges given by pesky tricksters, but also as security systems (passcode-esque), forming a map or other image, creating different power sources, create futuristic, shapeshifting buildings or ships, and so on.
Other than that there isn't a huge amount of variety, but this is one of those puzzles that could be replicated in real life. Simply design a puzzle, or copy one to make things far easier, print it out, cut the pieces out, and present it to the group. There's all sorts of creative things you can do with a real life version, but I suppose the effort you want to put into it does depend on how crucial this puzzle will be to the story. At the very least it could make for a fun memento of the game.
