One of the many entertaining things you can do with a flexagon is build and solve mazes. Here's a Pyramid Flexagon Maze.
Another kind of puzzle is the "path puzzle" where you keep flexing until you see an entire looped path. On a 3-sided dodecaflexagon, this can be suprisingly difficult.
Here's a path puzzle on a 4-sided decaflexagon.
Picture puzzles can also work well. Here you can try an Egyptian picture puzzle on a bronze hexaflexagon.
A path puzzle on the silver octaflexagon allows you to explore this interesting flexagon.
The enneaflexagon is an intriguing flexagon, with 9 triangles per face. Here's a hexagonal enneaflexagon with several mazes on it.
At first glance, the pentaflexagon, with only 5-fold symmetry would seem to be pretty limited. But both the slot flex and pyramid shuffle can sometimes be used. It turns out to be an interesting challenge to completely swap out all the sides on the 8-sided pentaflexagon.
The following is an interesting illusion where flexing swaps the king in and out of prison.
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