#### blade740

##### Mack Daddy

USING SINGLE LAYER TURNS:

**3c3**

average mods per corner (t/2)

average mods per edge (t/3)

**4c3**

average mods per corner (t/4)

average mods per edge (t/4)

average mods per center (t/4)

**5c3**

avg mods per corner (t/4)

avg mods per outer edge (t/4)

avg mods per center edge (t/6)

avg mods per T center (t/6)

avg mods per X center (t/4)

Assuming the standard scramble lengths, these scrambles allow for an average piece complexity of 10 modifications.

USING THICK TURNS:

**4c3**

average mods per corner (t/2)

average mods per edge (5t/12)

average mods per center (t/3)

**5c3**

avg mods per corner (t/2)

avg mods per outer edge (5t/12)

avg mods per center edge (t/3)

avg mods per T center (t/4)

avg mods per X center (t/3)

With thick layer scrambles, we can reduce the MINIMUM, not even the average, complexity per piece, while putting scramble lengths for the 4c3 and 5c3 at 30 and 40 turns, respectively.

Anyway, I started to work out the scramble length required for the same complexity on the 6c3.

I labeled the pieces like so:

[1][2][3][3][2][1]

[2][4][5][5][4][2]

[3][5][6][6][5][3]

[3][5][6][6][5][3]

[2][4][5][5][4][2]

[1][2][3][3][2][1]

Now, we found another problem. Should the ratio of face turns to slice turns be even (2:1:1), or should the ratio of face turns:second slice turns:third slice turns be even(1:1:1)?

Here are the average complexities with a 1:1:1 ratio:

[1]: (t/6)

[2]: (t/6)

[3]: (t/6)

[4]: (t/6)

[5]: (t/12)

[6]: (t/6)

And here are the complexities with a 2:1:1 ratio:

[1]: (t/4)

[2]: (5t/24)

[3]: (5t/24)

[4]: (t/6)

[5]: (t/6)

[6]: (t/6)

This means that we'd need a minimum of 60 single layer turns to scramble a 6c3 either way (if you allow for less complexity on the 5 pieces). The difference is, you get more complexity on the edges and corners and on the [5] pieces.

Here's what you get with multiple layer turns. This time, it will take 35 turns to scramble all pieces except [5] to a complexity of 10.

[1]: (t/2)

[2]: (7t/18)

[3]: (7t/96)

[4]: (4t/9)

[5]: (5t/36)

[6]: (5t/16)

Sorry if I bored you with that. Anyway, that's how we spend our nights in IRC. Mock an I also came up with a scalable notation for bigger cubes than 5c3 (as well as the term 5c3, meaning a cube of order five and dimension three)

We're very bored.