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The complete conditions for this scrambled cube can be described alternatively as the following:

  • 1. Each face has less than 3 squares of the same color, which leads to

  • 1a. Each face has 5 or 6 different colors.

  • (2. It's a huge bonus if the same-color squares are not adjacent to each other. In other words, they don't share an edge.

  • 2a. It's even better if they don't share a vertex!)

Please provide pictures or sequence algorithms.

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2 Answers 2

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Yes it is possible!

Do you know how to get it into a checkered state? Looking at any face you then do as follows....

Keep the same face towards you the entire time.

  1. Turn left side clock-wise
  2. Turn right side clock-wise
  3. Turn top side clock-wise
  4. Turn bottom side clock-wise
  5. Turn left side clock-wise

enter image description here enter image description here

There are a couple colors that are sharing edges but there are no more then 2 of the same color per side

I had some more time to mess around with it and have the answer for Q2 but not Q2a. There is only one difference

The last step.. Instead of doing Left side clock-wise do left side counter clock-wise

enter image description here enter image description here

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  • $\begingroup$ Checkered meaning this i.ytimg.com/vi/yzEv4aQBb7I/hqdefault.jpg $\endgroup$
    – Saloaty
    Jun 29, 2017 at 20:33
  • $\begingroup$ Thank you! For now conditions 1 & 1a are fulfilled. Can you or anyone solve condition 2? My uneducated guess is that condition 2a is even several times tougher than 2! $\endgroup$
    – 12tn2
    Jun 30, 2017 at 8:02
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    $\begingroup$ Yes! I've found the steps from a solved cube as: D R' L' U D R2 L2 F2 B2. Now we only have the obstacle of 2a left ;) $\endgroup$
    – 12tn2
    Jul 1, 2017 at 3:00
  • $\begingroup$ Oh nice! That one will for sure will be more difficult. $\endgroup$
    – Saloaty
    Jul 1, 2017 at 3:08
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Here is my perfect scramble. This has:

  1. Every color on every face.
  2. No more than two of any color on a face.
  3. No two squares of the same color touching side-by-side on any face.
  4. No two squares of the same color touching on a corner on any face.
  5. No two squares of the same color touching on a corner where two faces meet.
  6. A different pattern on every face.

enter image description here

To create it: D2 F2 R2 D2 L2 U F2 U' F' U F2 U' R2 B' F R' D2 F' D' L

To solve it: L' D F D2 R F' B R2 U F2 U' F U F2 U' L2 D2 R2 F2 D2

Since you can start with the cube in any one of 24 different orientations and since you can do the moves or the mirror image of the moves, there are 48 unique arrangements produced by this pattern.

This is the only solution that meets all of the above criteria.

The program that I wrote to find this solution is available here: https://github.com/telemath/PerfectScramble.

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  • $\begingroup$ 7. All combinations of 4 colors meet at a junction of 4 corners. All but one are present on a face. The last one, green-blue-orange-white, is present only on the edge of the cube. $\endgroup$
    – Florian F
    Mar 3 at 11:32
  • $\begingroup$ Florian F, I started with your criteria from another post but then completely forgot about the four-colors-meeting-at-a-junction feature, so I didn't include that in my program, Since this is the only solution for requirements 1-6, the fact that it also meets part of 7 is a pleasant coincidence. $\endgroup$
    – Bryan Wolf
    Mar 4 at 20:30

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