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Results for rubik cube
Search options not deleted
92
votes
11
answers
14k
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What are possible applications of deep learning to research mathematics?
A neural network can, given a scrambled cube, suggest the next action toward solving it. … Their neural network-guided tree search, once trained, can perfectly solve a scrambled cube. …
78
votes
What's a groupoid? What's a good example of a groupoid?
I'm surprised this example hasn't been mentioned already:
The 3x3x3 Rubik's cube forms a group.
The 15-puzzle forms a groupoid. … The reason is that any move that can be applied to a Rubik's cube can be applied at any time, regardless of the current state of the cube.
This is not true of the 15-puzzle. …
45
votes
Real-world applications of mathematics, by arxiv subject area?
math.GR Group Theory
Group theory provides methods for understanding the Rubik's cube, and for generating algorithms for solving the cube remarkably quickly from any state the cube may be in. …
41
votes
2
answers
5k
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Projective Plane of Order 12
The Cube was solved by reducing the total problem size to "only" 2,217,093,120 distinct tests, which could be run in parallel. … search the rest, if the problem size is on the order of the Cube search? (Maybe too much to hope for that someone knows this....)
Any partial information in this vein? …
- 881
37
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Which popular games are the most mathematical?
There's also the famous Rubik's Cube, which is popular and heavily maths-related. …
32
votes
20
answers
6k
views
What are your favorite puzzles/toys for introducing new mathematical concepts to students?
We all know that the Rubik's Cube provides a nice concrete introduction to group theory. …
32
votes
Cool problems to impress students with group theory
We discussed the game of 15, SET, wallpaper patterns, and Rubik's cube. …
29
votes
1
answer
4k
views
A Presentation for Rubik's cube group?
Let $G$ be Rubik's cube group. It is generated by the rotations by 90 degrees $L,R,D,U,F,B$ (left, right, down, up, front, behind), but what relations beyond $L^4=R^4=...=B^4=1$ do they satisfy? … From "The Mathematics of Rubik's cube" by W. D. Joyner I know that $G$ is generated by two elements and presentations are known, but I have not found one. …
- 63.1k
26
votes
4
answers
2k
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What relationship, if any, is there between the diameter of the Cayley graph and the average...
It's known that every position of Rubik's cube can be solved in 20 moves or less. … That page includes a nice table of the number of positions of Rubik's cube which can be solved in k moves, for $k = 0, 1, \ldots, 20$. …
- 14k
24
votes
Categorical foundations without set theory
By contrast, type theoretic methods build up the universe
by means of the actual operations that you actually want to
consider, just as the symmetry group of the Rubik cube is built
up from individual …
- 8,481
22
votes
Noteworthy achievements in and around 2010?
Tomas Rokicki, Herbert Kociemba, Morley Davidson, and John Dethridge proved that diameter of the Rubik's cube group is 20. …
22
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4
answers
2k
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Open problems which might benefit from computational experiments
The groups include N-dimensional Rubik's cube and other puzzle motivated groups like "Globe". … For example even the diameters of the N-dimensional Rubik's cube are still unknown, so computational experiments may shed light on these questions. …
21
votes
1
answer
817
views
Who wins the Rubik's cube game?
The cube is forbidden from ever repeating a position (besides the start position). This guarantees the game is finite. … An example game would be F,F;F,F (using basic rubik's cube notation). Solver wins this game. …
- 6,353
21
votes
What are possible applications of deep learning to research mathematics?
Such a
network could be in some sense a (rather large) cousin of the neural network
dealing with Rubik's cube mentioned by the OP. …
20
votes
Which popular games have been studied mathematically?
Rubik's Cube puzzle https://www.youcandothecube.com/blog/puzzling-science-using-the-rubiks-cube-to-teach-problem-solving gives an excellent possibility for some musings in mathematics and physics. … I'd like to add also this book https://jhupbooks.press.jhu.edu/content/adventures-group-theory (Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys, by David Joyner) …