Corners remain corners, but that may have been lost the cartoonist. As a joke it is pretty “meh.”
Granted, a corner may stay a corner, but his particular corner has moved from where he last had it.
Since “corner offices” are corners two-dimensionally, not three, in a cube such as this they might also be called “edge” offices. The edge spots remain edge spots, but might not still be where they used to be, and might go from being the exterior to interior if the Rubik structure is part of a larger structure.
James has the definition of “corner office” correct, and the condition that the Rubik structure could be part of a larger structure is not necessary for the joke to work.
The edge piece that connects the front and right faces is a “corner office.” If it becomes, e.g., the edge piece that connects the front and bottom facts, it would no longer be a “corner office.”
Wouldn’t some of these offices be upside down or hanging off of the wall in a shuffle like this, regardless of how corner offices are defined?
(Yes, yes, unless it was just a horizontal twist, but then he wouldn’t be complaining about his corner office being gone…as if he could anyway…which is the point of all this…I’m getting a headache…man, comic physics!)
His center left/right edge office had 2 windows, it was moved to top/bottom center edge where one of his windows became either a floor or a ceiling….or maybe a skylight???
“Don’t corners always remain corners?”
In a Rubik’s Cube, yes, corners always remain corners. But not everybody knows that. (So the artist here either doesn’t know that, or is deliberately ignoring that fact to make a joke.)
I remember reading a webpage which talked about the Rubik’s Cube and gave out certain facts like: “Corners are always corners, centers are always centers, and edges (pieces that are neither corners nor centers) are always edges. No amount of twisting the cube will change that.”
I thought that was obvious, and wondered why the webpage creator took the time to type that out. As it turns out, I later discovered that there are people out there who didn’t realize that fact.
(Then again, until I read it on a web page, I never realized that the position of the center pieces of a Rubik’s Cube never change: if the yellow center is opposite the white center, it will always be opposite the white center — no amount of twisting the cube can change that. (The same goes with the other center pieces.) And with me not previously knowing that, I shouldn’t be so quick to judge others.)
The center pieces rotate, which on a solidly colored cube doesn’t matter, but if the face has a picture on it, or even some kind of pattern that clearly has an up/down, this does matter, and you have to take the rotation of the center piece into account. Back in the day, I was first exposed to this fact by the special Charles and Di commemorative cube that I saw on the news, and they mentioned it was harder to solve; I got that, and figured it was merely marginally harder, that at worst you would have to align the center pieces right at the beginning and make sure they stayed in those orientations, but since I wasn’t going to get the commemorative cube, I never actually got to try it out and see. Thirty-five years later, I’m idly playing with a give-away cube on someone’s desk that had computer logos on each square, so orientation matters. I discovered it was not a simple thing, I was unable to figure out a quick method of moves to rotate the centers without disturbing anything else, and the fallback I was so confident of all those years ago, of aligning them at the start and solving around it, doesn’t work! Apparently at least some of the intervening moves to solve the cube do not conserve center orientation, since that normally isn’t a problem. I wasted a bunch of time on it at work, but I guess the intervening years have bestowed upon me some measure of maturity, because I was able to discard the problem, do the work I was hired to do, and actually I never solved it. Hmm… I should probably get one of those cubes again and play with it some more…
@ larK – One of my relatives gave me one of those patterned cubes as a present. It was tricky, but I found a method that worked, although it’s difficult to describe without diagrams. On a “finished” cube (all pieces in the correct position, but centers not necessarily correctly oriented), there is a simple combination that rotates the central tree within the cube. To do this, you simply push the central “slice” a quarter turn “up”, then rotate the entire cube around the vertical axis by a quarter turn. Repeat those two moves three more times, and you will see that all of the edges are once again “correct”, but the centers have been moved about.
The trick to “rotating” a center is to apply a rotation to one of the sides, then reverse the combination described above, returning all the centers to their correct locations, then “unrotate” the side that you rotated in between.
P.S. Several months ago, I bought an extremely cheap cube (because it was defective) at a flea market, expressly for the purpose of letting my son dismantle it, so that he could see the structure of the central tree.
J-L: I think the fact that corners remain corners and edges remain edges is only “obvious” when your conceptual model for the cube is a bunch of three-dimensional pieces that move around a fixed mechanism. If your model is 6*9=54 flat colored stickers, it’s not so obvious.
I’m not saying viewing the cube as a a bunch of flat stickers that move around is a great model, but I would bet that’s the model for most people who casually try the cube. Certainly, it seems that most people who casually try the cube are happy to get 9 colored stickers on the same side.
@Kilby: the move sequence you describe, if I’m understanding it right, is the one you do when you want to get pretty patterns, ie: the center square is a different color to the rest of the face. That was the move combo I played with initially when trying to solve this, and I never got it to do what I needed. I just tried it now (with a cube I had that I put some stickers on to show the orientation), and while it works to correctly orient the “side” centers, it does not correctly orient the “top” and “bottom” centers. (And if I rotate the cube so the top and bottom become sides, the new top and bottom don’t get aligned right.) It could very well be that I have to pay more attention, and apply it in a certain way/direction depending on what I want to align, but I never cracked that part.
I also just discovered that the move that does not conserve center orientation is the ultimate move to align the center bottom edges (assuming you use the same method to solve the cube, layer by layer, and in the bottom layer, first align the corners, then align the center edges). I’m playing with applying that move a couple times more to see if I can control which centers get screwed up with it.
So I’ve been able to solve it using the final two move combos used to align bottom center edges. I don’t quite have the mastery to describe it algorithmically, but for me at least, it’s the final piece so I can solve the damn thing. Compared to the trials I was doing the first time around back in the office using the center switching move that I think Kilby is describing, this new tack let me make noticeable progress very quickly, whereas with the other move combo it just seemed random, and I couldn’t control everything. I’m not saying it can’t be done the other way, just for me I failed to get the sense of it the other way, and this new approach let me find a solution rather quickly.
@ larK – I must admit that I described the process from memory, because I don’t have a patterned cube to test it on right at hand. I believe that the method I used applied complementary twists to two of the center pieces simultaneously, the trick was to repeat the process so that they all ended up correct at the same time.
IIRC, I was able to find a sequence that rotates two opposite center cubes, while leaving everything else unchanged. So I could solve the oriented cube like a normal cube, and then just rotate the center cubes at the end. It always seemed a bit inefficient, though.
For the 4x4x4 and 5x5x5 cubes, there was a final parity flip I was never able to figure out, so I only had a 50% chance of success. So my “solving strategy” was to try solving it, and if the parity flip was wrong, completely rescramble it, and then start again. Very frustrating.
I got to within ~96% of the solution to the 4^3 one (two centermost edges on the bottom, side-by-side, were oriented wrong), and then it broke (the smaller pieces were more fragile); I think I got a second one, and similarly, just as I was trying to figure out the last remaining bit, it too broke on me. So I gave up (economic necessity, really).
Never tried the 5^3 one, but I figure it must be even more prone to breakage…
My suspicion was that we were all a bunch of nerds. This thread has convinced me beyond all doubt.
What Stan said. On the other hand, there are so many smart people posting here, which makes CIDU head and shoulders above 99.99% of the other websites which allow comments.
@ WW & larK – The parity problem on the 4x4x4 cube is that it is possible to swap two side-by-side edge pieces. This actually makes it possible to simulate an arrangement that cannot be done on the 3x3x3 cube (swapping just two edges). I know that I solved it (because I have a 4x4x4 cube that is currently solved*), but I don’t remember how I did it. My initial method was the same as WW’s (mess it up and try again).
P.S. (*) The pranksters who gave it to me as a birthday present mixed it up before wrapping it in the package.
@Kilby and @larK:
Kilby’s technique to rotate the center tree works well. I myself discovered the same technique a number of years ago (though described a bit differently). A co-worker called the result “the rose garden” due to the semblance of flowers on each side.
I realized that this “rose garden” pattern was useful for rotating centers 90 degrees at a time, but it always rotates one center by rotating another center 90 degrees the opposite way. Often this is what you want, but occasionally there are times when only one center piece needs to be rotated, and by 180 degrees.
In such a case, you might think you could rotate it 90 degrees at the expense of rotating another center piece 90 degrees, and then finally get them both back by rotating them each 90 degrees back. But that doesn’t work — it’ll simply rotate the original center back to its off-by-180-degrees position.
To fix an off-by-180-degrees-center, orient the cube so that that center is on top. Then swap each of the eight non-center pieces on the top face with its exact opposite (using algorithms that don’t reorient any center piece). If you do that successfully, the center should still be off by 180 degrees, and all the pieces on top should be 180 degrees away from their correct positions. So all that remains is to twist the top face 180 degrees, and then everything will be correct!
Comics I Don't Understand 
Corners remain corners, but that may have been lost the cartoonist. As a joke it is pretty “meh.”
Granted, a corner may stay a corner, but his particular corner has moved from where he last had it.
Since “corner offices” are corners two-dimensionally, not three, in a cube such as this they might also be called “edge” offices. The edge spots remain edge spots, but might not still be where they used to be, and might go from being the exterior to interior if the Rubik structure is part of a larger structure.
James has the definition of “corner office” correct, and the condition that the Rubik structure could be part of a larger structure is not necessary for the joke to work.
The edge piece that connects the front and right faces is a “corner office.” If it becomes, e.g., the edge piece that connects the front and bottom facts, it would no longer be a “corner office.”
Wouldn’t some of these offices be upside down or hanging off of the wall in a shuffle like this, regardless of how corner offices are defined?
(Yes, yes, unless it was just a horizontal twist, but then he wouldn’t be complaining about his corner office being gone…as if he could anyway…which is the point of all this…I’m getting a headache…man, comic physics!)
His center left/right edge office had 2 windows, it was moved to top/bottom center edge where one of his windows became either a floor or a ceiling….or maybe a skylight???
“Don’t corners always remain corners?”
In a Rubik’s Cube, yes, corners always remain corners. But not everybody knows that. (So the artist here either doesn’t know that, or is deliberately ignoring that fact to make a joke.)
I remember reading a webpage which talked about the Rubik’s Cube and gave out certain facts like: “Corners are always corners, centers are always centers, and edges (pieces that are neither corners nor centers) are always edges. No amount of twisting the cube will change that.”
I thought that was obvious, and wondered why the webpage creator took the time to type that out. As it turns out, I later discovered that there are people out there who didn’t realize that fact.
(Then again, until I read it on a web page, I never realized that the position of the center pieces of a Rubik’s Cube never change: if the yellow center is opposite the white center, it will always be opposite the white center — no amount of twisting the cube can change that. (The same goes with the other center pieces.) And with me not previously knowing that, I shouldn’t be so quick to judge others.)
The center pieces rotate, which on a solidly colored cube doesn’t matter, but if the face has a picture on it, or even some kind of pattern that clearly has an up/down, this does matter, and you have to take the rotation of the center piece into account. Back in the day, I was first exposed to this fact by the special Charles and Di commemorative cube that I saw on the news, and they mentioned it was harder to solve; I got that, and figured it was merely marginally harder, that at worst you would have to align the center pieces right at the beginning and make sure they stayed in those orientations, but since I wasn’t going to get the commemorative cube, I never actually got to try it out and see. Thirty-five years later, I’m idly playing with a give-away cube on someone’s desk that had computer logos on each square, so orientation matters. I discovered it was not a simple thing, I was unable to figure out a quick method of moves to rotate the centers without disturbing anything else, and the fallback I was so confident of all those years ago, of aligning them at the start and solving around it, doesn’t work! Apparently at least some of the intervening moves to solve the cube do not conserve center orientation, since that normally isn’t a problem. I wasted a bunch of time on it at work, but I guess the intervening years have bestowed upon me some measure of maturity, because I was able to discard the problem, do the work I was hired to do, and actually I never solved it. Hmm… I should probably get one of those cubes again and play with it some more…
@ larK – One of my relatives gave me one of those patterned cubes as a present. It was tricky, but I found a method that worked, although it’s difficult to describe without diagrams. On a “finished” cube (all pieces in the correct position, but centers not necessarily correctly oriented), there is a simple combination that rotates the central tree within the cube. To do this, you simply push the central “slice” a quarter turn “up”, then rotate the entire cube around the vertical axis by a quarter turn. Repeat those two moves three more times, and you will see that all of the edges are once again “correct”, but the centers have been moved about.
The trick to “rotating” a center is to apply a rotation to one of the sides, then reverse the combination described above, returning all the centers to their correct locations, then “unrotate” the side that you rotated in between.
P.S. Several months ago, I bought an extremely cheap cube (because it was defective) at a flea market, expressly for the purpose of letting my son dismantle it, so that he could see the structure of the central tree.
J-L: I think the fact that corners remain corners and edges remain edges is only “obvious” when your conceptual model for the cube is a bunch of three-dimensional pieces that move around a fixed mechanism. If your model is 6*9=54 flat colored stickers, it’s not so obvious.
I’m not saying viewing the cube as a a bunch of flat stickers that move around is a great model, but I would bet that’s the model for most people who casually try the cube. Certainly, it seems that most people who casually try the cube are happy to get 9 colored stickers on the same side.
@Kilby: the move sequence you describe, if I’m understanding it right, is the one you do when you want to get pretty patterns, ie: the center square is a different color to the rest of the face. That was the move combo I played with initially when trying to solve this, and I never got it to do what I needed. I just tried it now (with a cube I had that I put some stickers on to show the orientation), and while it works to correctly orient the “side” centers, it does not correctly orient the “top” and “bottom” centers. (And if I rotate the cube so the top and bottom become sides, the new top and bottom don’t get aligned right.) It could very well be that I have to pay more attention, and apply it in a certain way/direction depending on what I want to align, but I never cracked that part.
I also just discovered that the move that does not conserve center orientation is the ultimate move to align the center bottom edges (assuming you use the same method to solve the cube, layer by layer, and in the bottom layer, first align the corners, then align the center edges). I’m playing with applying that move a couple times more to see if I can control which centers get screwed up with it.
So I’ve been able to solve it using the final two move combos used to align bottom center edges. I don’t quite have the mastery to describe it algorithmically, but for me at least, it’s the final piece so I can solve the damn thing. Compared to the trials I was doing the first time around back in the office using the center switching move that I think Kilby is describing, this new tack let me make noticeable progress very quickly, whereas with the other move combo it just seemed random, and I couldn’t control everything. I’m not saying it can’t be done the other way, just for me I failed to get the sense of it the other way, and this new approach let me find a solution rather quickly.
@ larK – I must admit that I described the process from memory, because I don’t have a patterned cube to test it on right at hand. I believe that the method I used applied complementary twists to two of the center pieces simultaneously, the trick was to repeat the process so that they all ended up correct at the same time.
IIRC, I was able to find a sequence that rotates two opposite center cubes, while leaving everything else unchanged. So I could solve the oriented cube like a normal cube, and then just rotate the center cubes at the end. It always seemed a bit inefficient, though.
For the 4x4x4 and 5x5x5 cubes, there was a final parity flip I was never able to figure out, so I only had a 50% chance of success. So my “solving strategy” was to try solving it, and if the parity flip was wrong, completely rescramble it, and then start again. Very frustrating.
I got to within ~96% of the solution to the 4^3 one (two centermost edges on the bottom, side-by-side, were oriented wrong), and then it broke (the smaller pieces were more fragile); I think I got a second one, and similarly, just as I was trying to figure out the last remaining bit, it too broke on me. So I gave up (economic necessity, really).
Never tried the 5^3 one, but I figure it must be even more prone to breakage…
My suspicion was that we were all a bunch of nerds. This thread has convinced me beyond all doubt.
What Stan said. On the other hand, there are so many smart people posting here, which makes CIDU head and shoulders above 99.99% of the other websites which allow comments.
@ WW & larK – The parity problem on the 4x4x4 cube is that it is possible to swap two side-by-side edge pieces. This actually makes it possible to simulate an arrangement that cannot be done on the 3x3x3 cube (swapping just two edges). I know that I solved it (because I have a 4x4x4 cube that is currently solved*), but I don’t remember how I did it. My initial method was the same as WW’s (mess it up and try again).
P.S. (*) The pranksters who gave it to me as a birthday present mixed it up before wrapping it in the package.
@Kilby and @larK:
Kilby’s technique to rotate the center tree works well. I myself discovered the same technique a number of years ago (though described a bit differently). A co-worker called the result “the rose garden” due to the semblance of flowers on each side.
I realized that this “rose garden” pattern was useful for rotating centers 90 degrees at a time, but it always rotates one center by rotating another center 90 degrees the opposite way. Often this is what you want, but occasionally there are times when only one center piece needs to be rotated, and by 180 degrees.
In such a case, you might think you could rotate it 90 degrees at the expense of rotating another center piece 90 degrees, and then finally get them both back by rotating them each 90 degrees back. But that doesn’t work — it’ll simply rotate the original center back to its off-by-180-degrees position.
To fix an off-by-180-degrees-center, orient the cube so that that center is on top. Then swap each of the eight non-center pieces on the top face with its exact opposite (using algorithms that don’t reorient any center piece). If you do that successfully, the center should still be off by 180 degrees, and all the pieces on top should be 180 degrees away from their correct positions. So all that remains is to twist the top face 180 degrees, and then everything will be correct!