Rubik's Cubes!

Everyone here should know about Rubik's Cubes. If not, you might not be prepared for this problem.

So the cube above is 1 of the 43 quintillion possible combinations for the cube. Look closely. You can see there are 2 stickers of the same color next to each other. In fact, in the picture, there are 4 of those blocks.

The question is "How many combinations are there that don't contain any of those blocks in any of the 6 faces of the cube? If there are none, what is the minimum number of blocks available?"

Looking forward to great solutions!

#Combinatorics

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

There does exist this kind,but I'm not sure about how many.

X X - 3 years, 1 month ago

Yes, there are many such possible cases.

Ram Mohith - 3 years ago

You should ask the staff and moderators

Mohammad Farhat - 2 years, 10 months ago

How? Do I mention them?

Long Plays - 2 years, 10 months ago

Calvin Lin's messageboard - 4

Ram Mohith - 2 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$