# Rubik's cube with no squares of same color nearby

It's easy to 'scramble' a Rubik's cube so no squares of the same color are touching each other. The moves U2 D2 R2 L2 F2 B2 accomplish that.

A side with no squares of the same color nearby requires that the colors are not touching horizontally, vertically or diagonally. Like this:

The question is: Can you 'scramble' a cube so there are no squares with the same color nearby in all sides?

Here is one possibility

U D' R2 L2 F B'

• Six is indeed optimal - Brute force Try it online. (Sorry it is a tinyurl, the original is unfortunately too long for a comment. Alternatively adjust the code from this codegolf.se answer to have this as its is_harlequin function.) Nov 24, 2023 at 20:43

The simplest way must be

S E2 M

which looks like this:

Now that I look at Bennett Bernardoni's answer, it seems to be doing exactly the same thing, except using face turns only.

I found a super-scramble that has the following properties:

• No squares of the same color touch orthogonally or diagonally
• Each color is present on all sides 1 or 2 times
• All combinations of 4 colors are present at an intersection of 4 squares. Possibly over the edge.

I am still missing

• No squares of the same color touch diagonally over an edge.

Here it is: F2 L2 B2 F2 D B2 F2 D L2 U2 B F' L' F2 D U' R2 F' D U'

Note that these properties don't make the cube hard to solve.

• THIS. IS. SATISFYING. Jan 12, 2020 at 14:17
• Beautiful scramble!
– Mark
Feb 5, 2022 at 21:41

We can categorize them as slice moves , and the list can be:

S E2 M

S2 E M

S E M2

S2 M E

S M2 E

S M E2,

after that all positions are just symmetry, in fact these 6 configurutions are related in symmetry too to one another, but just to show the possibilities , I have illustrated them.