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I have a cube that I got as conference swag which they made unintentionally harder to solve. There are two sides where the three middle pieces (number 4, 5 and

by grkvlt 10y ago

I have a cube that I got as conference swag which they made unintentionally harder to solve. There are two sides where the three middle pieces (number 4, 5 and 6 if you think of the arrangement of numbers on a numeric keypad) have a logo printed across them - 'Samsung' in fact. The middle of the three pieces is therefore constrained to be in a certain orientation (normally rotations of that square would not matter) and therefore symmetry is broken. So, there are four extra positions for each of the rotations of the logo centre piece, and two of these pieces. Intuitively, it seems obvious this makes it harder, but I'm not sure by how much. Any ideas?

deleted 10y ago
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jimminy 10y ago
That wouldn't make it any harder. Sides only have a single orientation, with the opposite side suited to the center piece of one of the neighboring sides. Placing the piece with the correct neighboring side addresses the issue automatically. Corner pieces can be rotationally incorrect, through the solving process, and is one of the harder areas to sove on the puzzle.
- grkvlt 10y ago
  No, the center piece on a particular side has a preferred orientation with regards to the pieces on its left and right assuming the cube is like this, with S M G standing for the Samsung logo and o being a standard plain coloured square: o o o S M G o o o The M piece must be correctly positioned to align with the S and G pieces, if it is rotated the logo will look wrong. Obviously if they were plain coloured squares the rotation would not matter.
jeffwass 10y ago
It's almost a "supercube" : https://www.speedsolving.com/wiki/index.php/Supercube https://www.speedsolving.com/wiki/index.php/Supercube There's some math in the regular wikipedia entry, not exactly your case but one for all sides requiring the right rotation relative to neighbors, which increases the state space by a factor of 4^6/2, or 2048x. (Edit - I originally naively thought your configuration would increase the space by 16x, but the calculation is more complicated, as some configurations aren't attainable from a given starting arrangement without disassembly. So it would depend on how the two labelled faces were positioned relative to each other (ie, are they in adjacent or opposite faces), and if your definition of a solution only requires the logos to be restored per face but not the same orientation relative to the initial configuration.)
- grkvlt 10y ago
  You're right, it's a partial 'supercube'. I hadn't known the correct term before, thanks!

by grkvlt 10y ago

deleted 10y ago

[deleted]

jimminy 10y ago

That wouldn't make it any harder. Sides only have a single orientation, with the opposite side suited to the center piece of one of the neighboring sides. Placing the piece with the correct neighboring side addresses the issue automatically. Corner pieces can be rotationally incorrect, through the solving process, and is one of the harder areas to sove on the puzzle.

grkvlt 10y ago
No, the center piece on a particular side has a preferred orientation with regards to the pieces on its left and right assuming the cube is like this, with S M G standing for the Samsung logo and o being a standard plain coloured square: o o o S M G o o o The M piece must be correctly positioned to align with the S and G pieces, if it is rotated the logo will look wrong. Obviously if they were plain coloured squares the rotation would not matter.

jeffwass 10y ago

It's almost a "supercube" : https://www.speedsolving.com/wiki/index.php/Supercube https://www.speedsolving.com/wiki/index.php/Supercube There's some math in the regular wikipedia entry, not exactly your case but one for all sides requiring the right rotation relative to neighbors, which increases the state space by a factor of 4^6/2, or 2048x. (Edit - I originally naively thought your configuration would increase the space by 16x, but the calculation is more complicated, as some configurations aren't attainable from a given starting arrangement without disassembly. So it would depend on how the two labelled faces were positioned relative to each other (ie, are they in adjacent or opposite faces), and if your definition of a solution only requires the logos to be restored per face but not the same orientation relative to the initial configuration.)

grkvlt 10y ago
You're right, it's a partial 'supercube'. I hadn't known the correct term before, thanks!