Tagged Questions
1
vote
2answers
182 views
Burnside's Lemma application
I am trying to understand the Burnside's lemma in order to use it in an example but all my efforts are in vain.
The example is as follows:
Cards are to be constructed from equilateral triangles, ...
22
votes
1answer
433 views
Six Frogs - Puzzle
I had come across a puzzle:
The six educated frogs in the illustration are trained to reverse their order, so that their numbers shall read 6, 5, 4, 3, 2, 1, with the blank square in its ...
8
votes
3answers
170 views
Group of sphere transformations, impressing friends
Ok, so here's the story: I am reading a book on algebra and, via some exercises, discovered that in any group $G$, the order of $x \cdot y$, written $o(x \cdot y)$, equals $o(y \cdot x)$. Now, this is ...
7
votes
1answer
118 views
“Multi-facets” rope puzzle
I've done the following, can you tell me if it's correct?
If $n$ is the number of sides of the rope and $k$ is the number of rotation, e.g. $k=0$ for glue each side to itself then I think the ...
5
votes
3answers
141 views
What are good ways of understandng a permutation group from a set of generators?
I'm trying to understand the structure of a Rubik's Cube-style puzzle I'm playing with; I have an expression of the solutions as the permutation group generated by four elements of $S_{16}$, each a ...
11
votes
3answers
462 views
Two seemingly unrelated puzzles have very similar solutions; what's the connection?
I think it's an interesting coincidence that the locker puzzle and this puzzle about duplicate array entries (see problem 6b) have such similar solutions. Spoiler alert! Don't read on if you want to ...
2
votes
1answer
170 views
When does an orthomorphism of the cyclic group exist?
I thought I would post (as a puzzle) one of my favourite results in combinatorics. I actually use variants of this result in research quite often. It's not impossible that someone will post an ...
