(If you are not interested in the backstory, you can skip right to the picture.)
At Most Complicated Illegal Partial State of Rubik’s Cube, user @happystar asks a very interesting question about cubers' favourite pastime: instead of finding sloppily created pictures of cubes, and then proving that the depicted cube cannot possibly be solved, what happens if you intentionally colour in a cube in a way that's illegal in the subtlest way possible?
Here's my go at the task:
(Cross-posted as a separate question, because the original question is a "request for puzzles")
Here are the rules:
- This cube might have a non-standard colour pattern. White being next to yellow is not an error in itself.
- Apart from the colour pattern seen in the picture, nothing else is known of the cube
- Yet, this cube cannot possibly be solved so that each side only has one colour
and most importantly,
- It is possible to rigorously prove it.
So now your task, should you choose to accept it, is to find a reason why any cube that looks like this cannot ever be solved.