Anyone who has ever played with a rubik's cube knows that it is possible to only complete 1 of the 6 sides.
Anyone who has ever played with a rubik's cube knows that it is NOT possible to only complete x of the 6 sides.
find x
(I am proud of this one I made it up last night!)
I personnally have spent a lot of wasted time on my Rubik's Cube. And through the many minutes/hours spent on it I had discovered that two adjacent sides control all the other ones. If two adjacent sides are correct, than the whole cube is correct.Originally Posted by MathGuru
Therefore, it is possible to get two opposite sides completed without completing the cube, but a third completed side would automatically be adjacent to both opposite sides, so that side could not be completed unless the cube is.
So,
on a side note, I think there are 1.69267*10^13 different combinations of a Rubik's Cube.
I can solve a Rubik in less approximately 5 minutes.
I believe the solution algorithm was obtained thought group theory. Because it is a puzzle my intuition tells me it has something to do with premutational groups. I was always interested to see how mathematicians derived an algorithm.
I have solved my cube for 3 sides, so this is possible.I personnally have spent a lot of wasted time on my Rubik's Cube. And through the many minutes/hours spent on it I had discovered that two adjacent sides control all the other ones. If two adjacent sides are correct, than the whole cube is correct.
Therefore, it is possible to get two opposite sides completed without completing the cube, but a third completed side would automatically be adjacent to both opposite sides, so that side could not be completed unless the cube is.
So,
on a side note, I think there are 1.69267*10^13 different combinations of a Rubik's Cube.
Note: The Rubik's Revenge (4 squares to a side) CAN be solved for 4 sides.
And though I loath to suggest that I compete with ThePerfectHacker in anything, I can solve the original Rubik's cube in less than 2 and a half minutes.
BTW: If you can solve a Rubik's cube and a Revenge, you can also solve the Professor's cube (5 squares) and any other that they might make with a higher number of cubes. (The guy who sold me the Professor's cube would be mortified to know that I've had it out of the box.)
-Dan
I know of two ways to argue a solution to the Rubik's cube. The first is cheating: figure out how to undo what the person did to mix it up. Obviously if you do it backward, it will be solved. (This is not as trivial as it sounds...there are many physical systems that you can't do this with.) Another one is to do what the person did to mix it up over and over and over and over... I forget what theorem of group theory this refers to, but if you perform a series of moves on the cube and repeat this series long enough, the cube will eventually (several life-times of the Universe, no doubt!) come back to a solved state. I have verified this for a few simple patterns.
Obviously, since we have to know what the person did to mess up the cube in the first place, neither of these methods of proof for the existence of a solution are very satisfying!
-Dan
This is not correct. you can see a jave applet with a rubik's cube that has 3 sides completed here.
Therefore, it is possible to get two opposite sides completed without completing the cube, but a third completed side would automatically be adjacent to both opposite sides, so that side could not be completed unless the cube is.
So,
No one has recognized the obvious answer yet. . .
well you obviously can't only complete five sides, as then the only piece that would have a chance of being incorrect on the 6th side would be the center square, and these don't even move. if one square is in the wrong place another must also be. hence if 5 sides are complete then the 6th must also be.
i don't think four sides are possible either, though.. since if you rotate one corner, you cause 3 sides to be incorrect, and you then must rotate another corner to do this. also if you switch one edge piece with another edge piece you effect three sides. but not sure on this one.
Picture attached, this is two views of the same cube. It has to be possible because you can play the video that will solve this cube from this configuration.
Aradesh is right about 5 not being possible because 5 means all 6 are correct. I am not sure about 4 . . .
The only time I have ever solved the cube for 4 sides is when one of the pieces popped out and I put it back in the wrong way. I don't have a proof, but 4 sides are impossible. (That is to say I couldn't solve the cube from the starting position of when it was in a state of 4 sides solved, so the initial state is "unnatural" in some sense.)
-Dan
As far as the riddle is concerned . . .
with allowing popping out pcs and rearranging them only 4 sides is possible. so 5 sides is the answer to the riddle.
Is it possible to only complete 4 sides of a natural rubik's cube? I do not know.
Is it a good riddle? It is the first one I ever came up with.
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