33
votes
3answers
3k views

Can a Rubik's cube be mapped knowing only two sides?

Is it possible to know the entire configuration of a Rubik's cube looking at only two sides and not rotating the cube? In other words: what is the minimum information required to create a ...
10
votes
2answers
388 views

Is it possible to shuffle a 3x3 Rubik's cube so that there's no more than 2 pieces of the same color in every face?

I'm not sure if this question belongs here but I see lots of Rubik Cube's questions around so here it goes: Can I take a standard 3x3 Rubik's Cube and shuffle it so that, for every face, there are no ...
18
votes
3answers
1k views

Why should Rubik's cube get attention from mathematicians?

I've seen a lot of math debate, calculations and other stuff related to Rubik's cube lately, but I don't really understand why is it important, why should anyone spend time asking and answering ...
21
votes
3answers
1k views

Brute force method of solving the cube: How many moves would it take?

Given that Rubik's cube has finitely many positions, one possible "brute force" method to solve it would be to determine once a sequence of moves which eventually reaches every possible position of ...
8
votes
2answers
647 views

Orders of moves in the Rubik's cube

Playing with my Rubik's cube, I was thinking of facts about it that are immediate to mathematicians but novel to others. Here's one: Given a Rubik's cube in the solved state, any sequence of moves, ...
0
votes
1answer
132 views

Rubik's cube notation [closed]

Various Rubik cube guides use the notation F and R to describe the front and right faces of the cube. However, in the illustrations they show the cube in isometric projection. So which side is right, ...
0
votes
1answer
223 views

Are actions in the $3\times 3\times 3$ rubik cube a group?

Are actions in the $3\times 3\times 3$ rubik cube a group? You can see here Rubik's Cube Not a Group? that $4\times 4\times 4$ rubik cubes or higher arent groups. But what about $3\times 3\times ...
21
votes
1answer
1k views

Rubik's Cube Not a Group?

I read online that although the 3x3x3 is a great example of a mathematical group, larger cubes aren't groups at all. How can that be true? There is obviously an identity and it is closed, so ...
3
votes
2answers
490 views

Rubik's cube puzzle

If we cut along the plane orthogonal to the largest diagonal of a Rubik's cube, what is the maximum number of small cubes can we cut? I thought this should be $9$, but apparently this is not the ...
20
votes
2answers
6k views

How to tell if a Rubik's cube is solvable

How can I determine if a certain Rubik's cube, that is in a certain state, is solveable? By "certain state" it could mean that the cube has been dismantled and put together again. And in my experience ...
8
votes
2answers
715 views

All possible permutations on a Rubik cube ($3\times3\times 3$) can be reached from the initial state?

If I were to represent a state in the Rubik cube as a permutation of the colors on the 9 tiles per side on all sides of the cube, could I reach all possible states (i.e. colorings) by the permutations ...
3
votes
1answer
334 views

Does solving a Rubik's cube imply alignment?

Today, I got my hands on a Rubik's cube with text on it. It looks like this: Now, I would love to know whether solving the right cube will also always correctly align the text on the cube or ...
13
votes
2answers
548 views

Mathematics Behind the 4×4 and 5×5 Rubik's Cube

A lot is known about the math behind the 3×3 Rubik's cube (symmetries, generators, group structure etc...). Is the same true for the 4×4 and 5×5 cubes? I haven't had much success finding this ...
6
votes
1answer
534 views

Solving a scrambled $3 \times 3 \times 3$ Rubik's Cube with at most 20 moves!

I read somewhere that any scrambled form of $3 \times 3 \times 3$ Rubik's cube can be solved using at most $20$ moves, and I just said "wow"! I am wondering can we prove this by mathematical ways? Or ...
10
votes
1answer
2k views

What are the 2125922464947725402112000 symmetries of a Rubik's Cube?

In a recent talk, Marcus du Sautoy says there are 2125922464947725402112000 (2.1*10^24) symmetries of a Rubik's cube, but doesn't explicitly identify what qualifies as a symmetry. What counts as a ...
13
votes
1answer
625 views

Rubik's cube interesting questions?

The upper bound for the number of moves required to solve a regular Rubik's cube has been shown to be 20. Two questions come to mind: Does this result have more general significance? What are the ...
5
votes
3answers
591 views

How many ways can I make six moves on a Rubik's cube?

I am writing a program to solve a Rubik's cube, and would like to know the answer to this question. There are 12 ways to make one move on a Rubik's cube. How many ways are there to make a sequence of ...
4
votes
2answers
313 views

How is done the calculation of the minimum number of movement to solve any configuration of Rubik's Cube?

I have read a few weeks ago that some mathematical researchers have discover that the minimum number of movements to solve any initial configuration of a Rubik's cube has been downsized to 20. How do ...
9
votes
1answer
568 views

How many disconnected graphs of the Rubik's cube exist?

Let us say that a Rubik's cube in a particular configuration is in a particular "state". All other configurations of this cube (other "states"), which can be achieved by rotations of the cube can be ...