Questions on the mathematics behind the famed toy invented by Ernő Rubik.
Questions tagged [rubiks-cube]
237 questions
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A central 3-cycle in a 4x4x4 Rubik's cube
I am looking for a way to rotate three central squares in a 4x4x4 Rubik's cube while leaving all the other squares intact. See picture.
Remark. Of course, if the squares have the same color, they are indistinguishable in the original puzzle, so let…
Anvita
- 633
2
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2 answers
Is it possible to make it so that on a $2\times 2 \times 2$ Rubik's cube, no similar colours are on the Same face
On a $2 \times 2 \times 2$ Rubik's cube, is it possible to make it so that each of the similar colours are not on the same face? I've played around with it at the moment, but never had a state where each of the colours on a single face are unique.
Xetrov
- 2,089
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2 answers
No of unit cubes in a n*n*n cube
Imagine a cubic array made up of an $n\times n\times n$ arrangement of unit cubes: the cubic array is n
cubes wide, n cubes high and n cubes deep. A special case is a $3\times3\times3$ Rubik’s cube, which
you may be familiar with. How many unit…
ViX28
- 647
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1 answer
Rubik's Cube Thistlethwaite Four Phase Algorithm
I am trying to understand The Four-Phase-Algorithm ( Thistlethwaite's 52-move algorithm ) for Rubik's Cube but no easy understandable explaination is given. It would be helpful if given with a small example. I am trying forward to write a code on…
Rohan
- 23
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Rubik's Cube Group: Number of Elements With Each Order
In the Rubik's Cube group, for each order, how many elements are there that have that order?
timidpueo
- 2,049
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vote
2 answers
Can you uniquely define a cube knowing the color of the faces but not its orientation?
I'm doing an university project for one of my subjects.
I have the 6 faces of the Rubik's cube but i don't know if they have been rotated or not, i just know their colors. Is that enough information to reconstruct the original cube? If that's not…
elr
- 41
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What is the Shortest Set of Moves Needed to Solve a Rubik's Cube?
The question is asking what is the shortest sequence of moves that will have the cube solved at some point during the sequence. The most obvious such sequence would be one that has every solution to every position followed immediately by its…
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How to calculate the minimum number of moves for resolve the Rubik's cube (3x3) from any position or the level of difficulty?
I want to shuffle the 3x3 cube randomly in quarter turn metric and determine the minimum number of moves of each position with some mathematical solution. I know that the minimum moves from the most shuffled position is 26 in quarter turn metric,…
doulos
- 11
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vote
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Can someone show a configuration of rubik's cube which is exactly 20 optimal moves away from the solved state.
It takes atmost 20 optimal moves to solve a Rubik's cube, was just curious to see the cube on other end of the diameter.
No Name
- 11
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vote
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Observation on Rubik's Cube's tiles
Might be a naive question.
While playing with a Rubik's cube, my cousin noticed that at least 2 tiles of same colour (any one of the six colours) always remain adjacent to each other.
Is this always true ? If yes, can it be proven mathematically ?
user537100
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How many configurations are possible in a Rubik's cube?
A Rubik's cube has 54 visible facelets. There are 6 colours and each colour has 9 facelets. How many configurations are possible? How do you find that?
Sagnik Pal
- 121
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What do I need to learn to solve the math behind a Rubiks cube?
I stopped studying math at precalc. What should I study to be able to understand how to solve a Rubics cube using mathematics? I don't think this is an opinion question, and I really want to learn this on my own, but I don't know where to start. …
Everett
- 151
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1 answer
Rubik's Cube algorithm with Optimal Algorithm
I'm confused about Thistlewaite's, Kociemba's, and Korf's algorithms for optimal Rubik's cube solving. What are the differences and how is each of the groups defined for each algorithm? I understood that with each group, they're trying to get rid of…
xiguner
- 1
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False Rubik Cube and math
imagine you are given an scrambled Rubik cube :D , how would you know that this cube has a solution ?
imagine i am a bad person and put the colors around the cube :d in a certain form that it has no solution how could you guess it ?
Jose Garcia
- 8,506
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Rubik's cube $5 \times 5 \times 5$ numbered arrangement
If you take a $5 \times 5 \times 5$ cube and enumerate each little square with a number, following an ascending order, then scramble it, how many possibilities you have to solve it? With all numbers in order and same rotation as initial.
