A flexagon is an interesting paper construction that allows you to fold or "flex" to different positions which rearrange the various faces. Given this property, it's interesting to try putting a maze on a flexagon. On this page you'll find instructions on how to make a flexagon maze and some hints on how to get started solving it. Even a seemingly simple maze turns out to be much harder to solve than you'd expect.
Click on the following image to get a larger version. Print it, then cut it out and pre-crease all the edges. Many of the triangles have a small number of dots or an X in the corner. Copy these onto the back side of the triangles.
Four of the triangles have portions of the maze on them. Two of these are only connected by a single edge. Fold these two triangles back and tape or paste them in place, giving you the following:
Next you should see two pairs of adjacent triangles with four markers on them, one pair on each side of the strip of paper. Fold the adjacent 4ís against each other, giving you the following arrangement:
Now you should see two pairs of adjacent triangles with three markers on them, both on one side of the strip. Fold these together. Now you should have something that looks like this:
Do likewise with the two pairs of adjacent 2ís. At this point you should have only five triangles left. One side has four maze triangles and an X. The other side has four 1ís and an X. Tape or paste the two Xís together, creating a pyramid with 1ís on the inside and the maze on the outside.
Now the flexagon maze is ready. To get familiar with how this flexagon operates and how to explore a maze, start with the dashed green maze. You should see the beginning of the maze on one of the triangles. This path continues onto a second triangle and then onto a third before the path disappears. You now need to perform a flex in order to continue following the path.
There are two ways to fold the flexagon flat. One of the two ways allows you to open the flattened pyramid back up from a different corner. Once you perform this flex, the inside will contain all 2ís and the outside maze faces will be slightly rearranged. The start of the green path will now be cut off, but the second two segments will still be together. You can follow these segments to a fourth segment thatís now connected to them.
From here, you can again fold the flexagon flat in two different ways. One way can be opened back up to the original configuration, with all 1ís on the inside. But the other way can be opened up to reveal 3ís on the inside. Looking at the rearranged maze triangles, you should be able to travel one more section of the puzzle.
As before, you can either flex back to the previous arrangement, with all 2ís on the inside, or forward where the inside will have all 4ís. The position with all 4ís allows you to complete the maze, ending at the final arrow head.
Now that youíve gotten a feel for how a maze on this flexagon works, you can try the much trickier red maze with the solid lines. Look for the start of the red maze, and notice how it travels to a second triangle, splitting into two paths. One leads to a bottom edge, where you canít continue following the path without one or more flexes. The other path leads onto a third triangle which splits the trail again. One of these paths seems to dead end, turning right back to the second triangle where thereís no continuation. But this isnít necessarily a dead end, since multiple flexes may align that path with a path on another face.
More information on the pyramid flexagon or "flexacup"
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