Questions tagged [recreational-mathematics]
Applications of mathematics for the design and analysis of games and puzzles
297
questions
-6
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0
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Power-2 cascade sequence [closed]
Definition: if a number is odd multiplied by 2 to the power k and add 2 to the power k, if a number is even divide it by two repeat this process it ends on one.
Example: let the number be 5
And k be 2
...
8
votes
0
answers
175
views
Placing triangles around a central triangle: Optimal Strategy?
This question has gone for a while without an answer on MSE (despite a bounty that came and went) so I am now cross-posting it here, on MO, in the hope that someone may have an idea about how to ...
- 7,771
3
votes
1
answer
583
views
Euro2024-inspired scoring problem
Motivation. The Euro 2024 soccer football championship is in full swing, and the male part of my family are avid watchers. Right now the championship is in the group stage where every group member ...
11
votes
1
answer
1k
views
Order of the "children's card shuffle"
Motivation. My eldest son thinks the following procedure is a "perfect shuffle" for a deck of cards: Take the first card, put the second on top of it, put the 3rd below cards 2 and 1, put ...
8
votes
0
answers
72
views
$2$-for-$2$ asymmetric Hex
This is a crosspost from Math stackexchange as I left the question open a while and bountied it but received no answers.
If the game of Hex is played on an asymmetric board (where the hexes are ...
- 181
0
votes
0
answers
124
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Does there exists a $\sigma \in S_{2N}$ such that $\sum_{n=1}^{N} \sigma(2n-1) ^ {\sigma(2n)}$ is a perfect square?
Does there exists a $\sigma \in S_{2N}$ such that $\sum_{n=1}^{N} \sigma(2n-1) ^ {\sigma(2n)}$ is a perfect square? ($S_k$ denotes the group of permutations of $\{1, 2, 3, ..., k\}$)
To me, it seems ...
- 101
7
votes
2
answers
813
views
What are the Nash equilibria of the “aim for the middle” game?
Consider the following three-player game: Alice chooses an integer congruent to $0$ mod $3$, Bob chooses an integer congruent to $1$ mod $3$, and Chris chooses an integer congruent to $2$ mod $3$. (...
- 30.8k
1
vote
1
answer
160
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Permutation graph with insert-and-shift
Motivation. I am working with a database software that allows
you to sort the fields of any given table in the following
peculiar way. Suppose your fields are numbered $1,\ldots, 18$.
Next to every ...
1
vote
3
answers
179
views
Graph on $\mathbb{N}$ where almost every vertex is shy
The following question is loosely based on the friendship paradox.
Let $G=(V,E)$ be a simple, undirected graph. For $v\in V$, we let the neighborhood of $v$ be $N(v) = \big\{w\in V:\{v,w\}\in E\big\}$ ...
19
votes
1
answer
1k
views
Does a function from $\mathbb R^2$ to $\mathbb R$ which sums to 0 on the corners of any unit square have to vanish everywhere?
Does a function from $\mathbb{R}^2$ to $\mathbb{R}$ which sums to 0 on the corners of any unit square have to vanish everywhere?
I think the answer is yes but I am not sure how to prove it.
If we ...
- 4,822
3
votes
1
answer
199
views
Proof of an unknown source Fibonacci identity with double modulo
Many years ago, I saw the following Fibonacci identity from somewhere online, without proof:
Let usual $F(n)$ be Fibonacci numbers with $F(0) = 0, F(1) = 1$, then we have
$$F(n) = \left(p ^ {n + 1} \...
- 131
2
votes
0
answers
109
views
Proof that a pandiagonal Latin square of order $n$ exists iff $n$ is not a multiple of $2$ or $3$?
A pandiagonal Latin square of order $n$ is an assignment of the numbers $\{0,\ldots,n-1\}$ to the cells of an $n \times n$ grid such that no row, column, or diagonal of any length contains the same ...
- 21
5
votes
1
answer
198
views
Does every integer appear in the modular sum sequence?
$\newcommand{\N}{\mathbb{N}}$Let $\N$ denote the set of non-negative integers. We inductively define a sequence $a:\N\to\N$ by:
$a(0) = 0, a(1) = 1$ and
$a(n) = \big(\sum_{k=0}^{n-1}a(k)\big)\text{ ...
1
vote
0
answers
104
views
Expected value of maximal cycle length in fixed-point free bijections
$\newcommand{\n}{\{1,\ldots,n\}}$
$\newcommand{\FF}{\text{FF}}$
$\newcommand{\lc}{\text{lc}}$
Motivation. A group of my son's peers decided to have a few days of Secret Santa before last year's ...
4
votes
0
answers
117
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Reorganizational matching
Motivation. My friend works in an organization that is re-organizing itself in the following somewhat laborious way: There are $n$ people currently sitting on $n$ jobs in total (everyone has one job). ...