Tagged Questions
0
votes
0answers
46 views
What's the difference between a 2-sided and 2-sided strip polytan
There are 14 2-sided tetratans and 13 2-sided strip tetratans. The sets are identical, except the square is missing in the strip version. My best guess is that for strips, no vertex can have an edge ...
2
votes
1answer
48 views
Does this Graph converge in a finite number of steps? How fast is it?
Suppose you have a finite, planar Graph $G = (V,E)$ and a function $f_0:V \rightarrow \mathbb{Q}$.
Now you define the function $f_{i \in \mathbb{N}}$ like this:
$$f_i(v) := \frac{f_{i-1}(v) + ...
10
votes
2answers
140 views
Integer sequences which quickly become unimaginably large, then shrink down to “normal” size again?
There are a number of integer sequences which are known to have a few "ordinary" size values, and then to suddenly grow at unbelievably fast rates. The TREE sequence is one of these sequences, which ...
9
votes
4answers
310 views
A problem about symmetric relations on finite sets.
We have these assumptions:
$X$ is a finite set.
$\sim$ is an irreflexive symmetric relation on $X$.
for any subset $Y\subseteq X$ we define $$\mathcal{Cl}(Y)=\{A\subseteq Y\mid(\forall a,b\in ...
17
votes
1answer
1k views
The $n$ Immortals problem.
I saw this riddle posted on reddit a long time ago, called the "Seven Immortals."
In the beginning, the world is inhabited by seven immortals, ageless and sexless, who begin to multiply and ...
3
votes
2answers
148 views
A less challenging trivia problem
There are 25 people sitting around a table and each person has two cards. One of the numbers 1,2,..., 25 is written on each card, and each number occurs on exactly two cards. At a signal, each person ...
1
vote
2answers
128 views
100 roads in a city, 1 is closed
In a certain country, 100 roads lead out of each city, and one can travel along those roads
from any city to any other. One road is closed for repairs. Prove that one can still get from
any city to ...
1
vote
1answer
65 views
List number of moves to defeat the opponent
Given the position of chess board of two players, we have to find the minimum number of moves (and output them) so that only one player playing continuously and optimally defeat the other one ...
14
votes
3answers
3k views
Average Scrabble graph structure: diameter?
Tonight a game of Scrabble ended in what I consider a very unusual graph structure,
unlike this generic web image, which seems more typical:
...
2
votes
1answer
236 views
What's behind Conway's Game of Life search algorithms?
I've been looking at a program gfind, that searches for spaceships in Conway's Game of Life. The documentation says a bunch of stuff about searching De-Bruijin graphs. I couldn't find any useful ...
5
votes
1answer
423 views
Handshake problem
I was given the following math puzzle which (I thought) has an interesting solution.
A mathematician and her husband attended a party with $n-1$ other couples. As is normal at parties, handshaking ...
8
votes
1answer
108 views
A game played on graphs by “flipping” the state of a vertex and its neighbors
This is a well-known game: We are given a finite undirected graph $G=(V,E)$ whose vertices are labeled by "0". At each turn, we pick a vertex, and then it and all its neighbors flip their label (0 ...
16
votes
1answer
385 views
How to create mazes on the hyperbolic plane?
I'm interested in building maze-like structures on the [5, 4] tiling of the hyperbolic plane, where by maze-like I mean something akin to a spanning tree of the underlying lattice: a subgraph of the ...
9
votes
1answer
162 views
Cube skeleton bindings
Imagine that you have a cube skeleton, like so:
Further imagine that you have three rubber bands that you can loop through any of the faces. However, only one rubber band may go through any ...
8
votes
1answer
462 views
How many disconnected graphs of the Rubik's cube exist?
Let us say that a Rubik's cube in a particular configuration is in a particular "state". All other configurations of this cube (other "states"), which can be achieved by rotations of the cube can be ...
