All Questions
9
questions
2
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1
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275
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Number of essentially different Rubik's cube permutations, or rather arrangements
I can find everywhere (e.g. wikipedia, ruwix.com and MIT) the information that the standard $3\times3$ Rubik's cube can be scrambled in $4.3 \times 10^{19}$ different configurations. These are ...
- 2,405
4
votes
1
answer
709
views
Necklace combinations with three group of beads
I have a hard question about a way how many different necklaces can be made.
Suppose that we have the following restrictions:
We have 3 groups of beads:
4 triangle beads
6 square beads
8 circle ...
- 204
6
votes
2
answers
3k
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How many triangles are there in the 'picture' of $K_5$? Different ways to count it
So, my cousin asked me to count the number of triangles in a picture. The picture was the complete graph on $5$ vertices, known as $K_5$ in graph theory. Here's a "picture" of $K_5$:
A partial answer ...
- 8,220
0
votes
1
answer
78
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finite group theory - combinatorial approach to determine number of subgroups rank 3 from $A_4$
How many different subgroups of order $3$ are in alternating group $A_{4}$?
Using direct listing is doable, but primitive. I wonder how to apply combinatorial approach (intuitively it would be much ...
user410985
3
votes
0
answers
407
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When solving a big Rubik cube (100x100x100), do you reduce the solution to like 50x50x50, and then 25x25x25, and then like 10x10x10 and then 3x3x3?
My question is about Rubiks cube.
Say you're solving a 100x100x100 cube (you can see examples in youtube by computer program - https://www.youtube.com/watch?v=0cedyW6JdsQ)
When solving a big Rubik ...
- 3,942
3
votes
0
answers
2k
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Given a number of items, how many sets of three are there where no two sets are two thirds similar?
Sorry if the title isn't proper math-talk. Hopefully I can explain it better here.
So let's say we have a set. 1, 2, 3, 4, 5, 6, 7, 8, 9. I want to know how many groups of three can be made where no ...
2
votes
0
answers
158
views
Describing the sequence A224239.
I've been trying to describe mathematically the $n$th term $a_n$ of the sequence A224239. We get $a_n$ by counting the distinct ways to fill an $n\times n$ grid with squares of smaller integer size, ...
- 45.7k
12
votes
2
answers
1k
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 $3 \times 3$ Rubik's Cube and shuffle it so that, for every face, ...
- 123
16
votes
2
answers
2k
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 ...
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