Solving the Flat Cube

mathenchant.wordpress.com

47 points·surprisetalk··7 comments

I'm confused... The introduction allows twists of 60 degrees, but the explanation seems to switch to assuming 180 degree twists.

What am I missing?

edit: ah, I missed an "at least" at the beginning. He shows god's number is *at least* 27 (I misread this as meaning exactly 27). And he does this by showing god's number for the uncolored flat cube is 27. The uncolored flat cube happens to be equivalent to the colored cube with 180 degree twists.

Though... given that, the colors like a bit of an unnecessary red herring. Just a literary bridge I suppose? From his amusing introduction about a magic schoolbus running over rubik's cubes?

180 degree was for Rubik’s cube, not this flat cube.

Where can you buy them?

> I’m undecided as to whether every rotation should count as one move or whether rotations by 120 or 180 degrees should count as two or three moves respectively, so there are two versions of “God’s number” here.

Clearly, it should be the sum of (absolute) turn angles. In radians, please.

How is it called a cube if it is flat?

That is a puzzle thing. The word cube is used very loosely. Douglas Hofstadter wrote about it back when Rubiks Cube was still new.

In this case it is a stretch, but the Rubiks Cube inspiration is so clear, that I think it sort of makes sense.

People in the cubing community often call all twisty puzzles "cubes".

In this parlance, the "pyraminx" (regular tetrahedron twisty puzzle) is a cube, the face-turning octohedron is a cube, and the "Megaminx" (dodecahedron) is a cube. I've even heard Rubik's Clock[1] called a cube.

[1] Which isn't even a god-damn platonic solid https://en.wikipedia.org/wiki/Rubik's_Clock

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