God's Number for the Flat Cube Is at Least 27
Solving the Flat Cube
Mathematician James Propp introduces the Flat Cube, a puzzle that looks like a flattened Rubik's Cube but is made of rhombus-shaped pieces. He proves that solving the worst-case scramble requires at least 27 moves, using two elegant visual arguments: one that adds a dimension by viewing the tilings as stacks of cubes, and another that subtracts a dimension by focusing on the horizontal lozenges as beads on wires. The puzzle was brought to life by puzzle designers Oskar van Deventer and Dmitry Andreev, and Propp discusses its connection to the mathematics of tilings.
Asking questions like these is really a way of asking about the cartography of the land of tilings, where each tiling is a town and each move is a road.
- amelius
Where can you buy them?
- NAR8789
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?
- boothby
> 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.