2
votes
0answers
70 views

A mathematical game: moving tiles

There is a mathematical game called moving tiles. There are $8$ different movable tiles on a $3 \times 3$ board, At the beginning the tiles' location is given as following: ...
3
votes
0answers
72 views

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 ...
1
vote
0answers
47 views

Visually apealing holologous transformation of a given contour

There is this problem which roughly says: You want to put a framed picture onto the wall with a cord to the picture frame. The cord is a single one, and both ends are attached to the frame. ...
1
vote
2answers
355 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, ...
27
votes
1answer
1k 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
189 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
147 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
170 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
630 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
207 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 ...