59
$\begingroup$

This is an image of a Rubik's Cube I found in the Men's Toilets during the first day of a big Scrabble tournament.

This position is impossible for the standard Rubik's Cube (White/Red/Blue opposite Yellow/Orange/Green respectively) for any number of reasons.

Is this position legal for at least one non-standard Rubik's Cube? (i.e. with different permutation of White/Red/Blue/Yellow/Orange/Green)?

enter image description here

$\endgroup$
7
  • 3
    $\begingroup$ Don't be too serious in toilets ... (BTW I think it's totally possible, with Green/White, Red/Blue, Yellow/Orange as opposites.) $\endgroup$
    – WhatsUp
    Mar 6 at 11:15
  • 4
    $\begingroup$ Oh, I didn't know there is a standard of the ordering of the colors. Learn something new everyday! $\endgroup$
    – justhalf
    Mar 6 at 11:26
  • $\begingroup$ @StigHemmer No, that is not the case. Most (if not all) cubes by any manufacturer have the same color scheme. Or at least the companies don't care what Rubik's brand thinks. $\endgroup$ Mar 9 at 4:47
  • $\begingroup$ Remember when you could buy a set of stickers to cover up the ones on your unsolved cube? $\endgroup$ Mar 9 at 16:51
  • $\begingroup$ @StigHemmer I have an original genuine Rubik Cube from back in 1980 or so (I used to be quite good at it) and it has blue opposite white. $\endgroup$
    – SiHa
    Mar 9 at 18:17
75
$\begingroup$

Oo, this is a good one. Let's do some analysis:

We can see the centres of three sides, and the relative positions of the centres cannot be changed, so we know that when/if this cube is solved, the blue side will be adjacent to green and orange.

We can also see a blue-white edge piece, and a blue-yellow edge piece as well. This means that as long as the cube has a solved state,

the red side must be the side opposite blue.

Then, we can take note of the following facts about solved Rubik's cubes in general:

  1. There are always exactly two corner pieces between any two adjacent colours
  2. Out of these pieces, one has the two colours next to each other in a clockwise order, the other piece has them in anticlockwise order

It follows from these two facts that if we

  1. see two sides of a corner piece, and
  2. we know where those two colours are on the cube,

then we can uniquely place that corner piece on the solved cube.

Doing so, and remembering what we learned about red above, we notice that

both of the marked pieces belong in the same place, the top right corner of the orange side.
enter image description here

Because of this,

this cube cannot possibly have a solved state.

$\endgroup$
2
  • 8
    $\begingroup$ Graffiti and a cheater! $\endgroup$
    – jmoreno
    Mar 6 at 23:56
  • 1
    $\begingroup$ How annoying. :-( $\endgroup$
    – Strawberry
    Mar 8 at 14:29
0
$\begingroup$

I'm new here, and I might be wrong, but...

We can see the centers of three adjacent sides, and we can see a corner where three other adjacent sides meet, which happen to be the three we can't see directly. If we turned the cube around, we'd see red, white, and yellow in the same configuration.

So we can identify all the sides: White is opposite to blue, red is opposite to green, and yellow is opposite to orange.

Anything that contradicts this is proof that the cube is impossible—like the edge piece where white borders blue.

Can it really be that easy?

$\endgroup$
2
  • 7
    $\begingroup$ The white-yellow-red corner can be rotated, though. So in theory, blue could be opposite to white, yellow or red. You've just proved that white cannot be opposite to blue, but it's not enough to prove the impossibility to solve. $\endgroup$ Mar 7 at 8:02
  • 2
    $\begingroup$ Ah, I knew there had to be a catch. Don't mind me, then. $\endgroup$ Mar 7 at 8:03

Not the answer you're looking for? Browse other questions tagged or ask your own question.