## Monday, March 11, 2013

### Lanlan Gear Dodecahedron

My great puzzle accomplishment of late? I have finally figured out the Gear Dodecahedron. This has got to be one of the simplest puzzles ever. After thoroughly and thoughtfully scrambling it, if you just keep making random twists and turns and watch, eventually you'll notice that the 8 corners are all solved relative to one another. If you want to actually solve the corners with a little effort, you can do so in no more than 4 moves from any given scramble.

What I call the edges are the pieces that correspond to the edges of the Gear Cube. They can be positioned in ways similar to the Gear Cube, so a refresher of my old Gear Cube notes was in order.

But with the Gear Dodecahedron, the "edges" can also be flipped in a weird sort of way, but early on in my experimentation I stumbled on a simple algorithm that worked well.

The 6-cog gear pieces can be oriented correctly just like with a Gear Cube.

So what was the big challenge? What I call the centers—because they are the centers of rotation of the outer layers—can be flipped. On the Gear Cube the centers are a single color and square, so orientation does not matter. And for some reason it took me forever—well, a couple weeks or so anyway—to come up with a way, by trying different sequences, that could be used to flip centers. The sequence happens to also tweak all 12 of the 6-cog gears, as well as flipping 4 centers.

I might mention that I had pretty much lost interest in puzzling for several months. I may be back. :)