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Recently, I saw this motivational picture (Clicky to embiggen):

enter image description here (source)

Since I found the message somewhat confusing, I searched Google for more similar images.

Can you tell what do all these pictures have in common with the picture above?

(All images are © their respective owners (credited by source links and image watermarks.). The images are posted here for critique purposes, which falls under fair use under most jurisdictions.)

enter image description here (source)

enter image description here (source)

enter image description here (source)

enter image description here (source)

enter image description here (source)

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They all

depict cubes that cannot be solved.
0. (the original "motivational" picture) The color white is adjacent to every other color. It shares visible pieces with green and yellow (a corner piece), blue (another corner piece), red (a side piece), and orange (the center pieces are on adjacent sides).
1. There are three green center pieces, but also pieces with two reds and two blues, adding up to more than six.
2. The two corner pieces with green and white are oriented the same, and so cannot coexist on a single cube.
3. There are three corner cubes with green and orange.
4. The two corner pieces with orange and yellow are oriented the same, and so cannot coexist on a single cube.
5. The two corner pieces with blue and yellow are oriented the same, and so cannot coexist on a single cube. Furthermore, five corner cubes have blue on them.

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    $\begingroup$ Sheldon Cooper has No. 4. on a T-shirt. It always disturbed me that he if anyone would notice and refuse to wear it, even destroy it. $\endgroup$ – Florian F May 18 at 13:19
  • $\begingroup$ Yup, that's it, exactly! $\endgroup$ – Bass May 18 at 13:29
  • $\begingroup$ What exactly do you mean by "oriented the same way" and why can't that exist on a cube? $\endgroup$ – Chipster May 18 at 21:04
  • $\begingroup$ @Chipster between any two adjacent colours, there are exactly 2 corner pieces: in one corner piece, the two colours are in clockwise order, in the other, counterclockwise. $\endgroup$ – Bass May 18 at 21:12
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    $\begingroup$ @FlorianF wouldn't that constitute an excellent reason to melt the actual cube and wear a commemorative shirt, though? $\endgroup$ – Bass May 18 at 21:36

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