Questions on the mathematics behind the famed toy invented by Ernő Rubik.
Questions tagged [rubiks-cube]
237 questions
11
votes
1 answer
Solving $3\times 3\times 3$ Rubik's cube positions using a $4\times 4\times 4$ cube?
Someone hands you a $4\times 4\times 4$ cube for solving. It is scrambled as if it were a $3\times 3\times 3$, i.e. without ever separating the $4$ central pieces of each face (which implies that edge pairs remain together too).
If this restriction…
7
votes
1 answer
What is "tetrad twist" in relation to Rubik's cubes?
I am trying to write a computer program to solve Rubik's cubes using a version of Thistlethwaite's algorithm. Instead of using lookup tables to perform each phase of the algorithm, I'm using a breadth-first search. However, this requires me to…
Ord
- 407
6
votes
3 answers
Minimum number of random moves needed to uniformly scramble a Rubik's cube?
Follow up from my last question: $3 \times 3$ Rubik's cube scrambling question
I am talking about $3 \times 3$ Rubik's cubes. Start with a solved cube. Then make some amount of random moves (where moves are defined using the half-turn metric: any…
MT_
- 19,603
- 9
- 40
- 81
6
votes
1 answer
How many colors of a Rubik's Cube must be known to locate all?
I wonder if I can apply some kind of formula given a few colors with the location on a Rubik's Cube to calculate the locations of all other colors on it.
Best would be if this formula would be so general that one could apply it for any kind of…
Cold_Class
- 163
5
votes
2 answers
Can you compute the state of a 3x3x3 Rubik's cube if you only see three adjacent faces?
I've learned from How many colors of a Rubik's Cube must be known to locate all? that you need to know a minimum of 17 stickers (spread across all its faces) for a 3x3x3 cube in order to compute its state, but if we just see three full adjacent…
Stefan
- 153
4
votes
1 answer
Rubik's cube with different neighboring color
How many valid configuration of the 3x3x3 Rubik's cube are there so that no two adjacent faces are the same color?
Thanks.
lasagne.victim
- 67
- 3
4
votes
3 answers
$3 \times 3$ Rubik's cube scrambling question
It was proven that a Rubik's cube needs at most $20$ moves to solve. This implies that any configuration of a Rubik's cube can be reached from an unscrambled Cube in at most $20$ moves.
So, say when I scramble, I choose any move to do at random.…
MT_
- 19,603
- 9
- 40
- 81
4
votes
2 answers
Rubik cube number of alternative solutions
If a cube is in a configuration that requires 20 moves to solve, is that sequence unique, or are there multiple sequences that arrive at a solution? That is: are there are two or more sequences that only have the start and finish position in…
user3111005
- 41
2
votes
2 answers
Is there a proof, that for any Rubik's cube, after solving the first 2 layers, there will always be an even amount of oriented edges?
I've always wondered if there was a proof for this, since the beginners method to solving the last layer depends on this (you either have no edges oriented correctly, an L, a line or a cross, and each case has an even amount of oriented/ unoriented…
Julian Jefko
- 507
2
votes
2 answers
Rubik's cube repetitions, weird behaviour (Best if you know cube rotation notation)
In this question, I'll refer to standard cube rotation notation, seen here: J perm website - cube notation.
The move U, can be performed 4 times and return a solved cube (or any cube) to its original state.
This isn't surprising, it's making use of…
Leonhard Euler
- 631
2
votes
0 answers
How to "validate" a Rubik's Cube configuration?
Looking at a picture of a Rubik's cube how can I tell if it's in one of its possible configurations (image is not fake)? By "possible configuration" I mean a configuration that can be achieved by simply rotating the cube (no dismantling). I'm aware…
3k-
- 121
2
votes
2 answers
Proving impossible Rubik's Cube permutations
It turns out that the Rubik's Cube has 12 orbits, because there are a few impossible cases just by turning the edges:
cannot have just one corner twisted (/3)
cannot have just one edge flipped (/2)
cannot have only two pieces swapped (/2)
Every…
Roxy
- 131
2
votes
2 answers
Understanding Rubik's cube
I learnt how to solve a 3x3 Rubik's cube 10 years ago. Every now and then, I picked up a cube, scrambled it, and solved it for fun. I used to work on speed-solving, and memorised lots of formulae for it. However, now I'd like to go a different way:…
Student
- 1,822
2
votes
1 answer
What is the probability of this Rubik's cube configuration?
What percentage of the total number of combinations on a Rubik's Cube have the following property:
On every face, no two adjacent squares have the same color.
By adjacent I mean:
adjacent: sharing a common side.
Truth-seek
- 1,427
2
votes
1 answer
Is it possible to achieve a Rubiks Cube with Complementary colors as center piece?
Info
Achieving a Rubik's Cube with different center pieces (like a dot) is fairly simple when you have a correctly solved Cube. From the top of my head, you can get something like orange edges with a blue dot, blue edges with a white dot, yellow…
D.Kallan
- 129