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# Questions tagged [recreational-mathematics]

Puzzles, curiosities, brain teasers and other mathematics done "just for fun".

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69 views

### What are the fractal patterns produced by coloring according to digit sums of coordinates?

I recently encountered something odd and I was wondering if anyone have seen something like it before, and could possibly explain what is going on. Given a coordinate system, for each xy coordinate ...
49 views

### Challenging Mathematical Teasers; Pecking Order

I was going through the book "Challenging Mathematical Teasers" by J.A.H. Hunter, and, of course, I got stumped. Naturally, I went to the solutions part of the book, but here's the kicker, the ...
69 views

### Find large $n$ and calculate $r \equiv L \pmod{n}$ where $L = 999\,998\,997\dots003\,002\,001.$

Update: I provided an answer but I tried something out with Python and I am kind of surprised. Computer technology today is more advanced than I can wrap my head around. Instead of taking any ...
22 views

### A drunk knight's tour [duplicate]

Consider an infinite chess board. A knight moves 2 squares forward on one direction, then turn left or right, move 1 square further on. Let's denote this a normal knight, or $\langle 2,1\rangle$ ...
25 views

### Hamiltonian circuits on rectangular graphs

Let $G=(V,E)$ be a rectangular graph on $n \times m$ vertices. It is easy to show that no Hamiltonian circuit exists for $n,m$ odd, and pretty easy to build a circuit for graph with at least one even ...
38 views

### number of ways to tile a $n\times n$ grid with $k<n^2$ $1\times 1$ tiles?

So, there are alot of questions about tiling in this forum but I could not find this exact question. I am trying to find out the number of possible "tile configurations" in an $n\times n$ grid where ...
3k views

### Extending prime numbers digit by digit while retaining primality

I looked at a table of primes and observed the following: If we choose $7$ can we concatenate one digit to the left so as to form a new prime number? Yes, concatenate $1$ to obtain $17$. Can we do ...
188 views

### Does there exist a non-trivial group that is both perfect and complete?

A group $G$ is called perfect iff $G’ = G$. A group $G$ is called complete iff $Z(G) = \{e\}$ and $Aut(G) \cong G$. Does there exist a non-trivial group $G$, that is both perfect and complete at the ...
36 views

The average rainfall over a given place during the three years period of $2017 - 2019$ was $65$ cm. During the three year period $2016 -2018$ the average rainfall was $63$ cm .The ...
130 views

### Minimal Rook Difference Grids

In the below grid all 18 orthogonal differences are distinct, with a difference of 18 missing. Could the highest number be 18? The resulting graph would have valence 4, making it an Eulerian ...
47 views

### Geometry transformation problem

The question is :- A figure consist of five equal squares in the form of a cross .show how to divide it by two straight cuts into four equal figures which will fit together to form a square. ...
17 views

### Topological genus of 3-d flat space minus a solid ball

Our recreational math geek lunch group got stuck on a question we need help to understand. I apologize in advance, if my explanation is not perfectly rigorous, as we are not professional ...
32 views

### The Mean of the Range, IQR and SD? Will it give an interesting result?

What if we take the Mean of the three chief measures of spread, i.e Range, Interquartile range, and the Standard deviation? Will it give us an "all-purpose" measure of spread that is very reliable, ...
353 views

### Independence problem: one rook and maximum number of knights on the chessboard $8 \times 8$

On the chessboard $8 \times 8$ we can to place one rook and several knights. Find the maximum number of knights, which can be placed on a chessboard along with one rook so that none of the pieces ...
27 views

### How do I compare relative importance of observations when number of observations is different in different datasets

Let me first describe what I mean by dataset and relative importance: Dataset is discrete observations, where identical observations may be recorded. Assume we have dataset A with values ...
52 views

### Mathematics and Predictions [closed]

I was wondering whether there are any theories or formulae in mathematics(other than the general concept of probability) which can be used to make very accurate predictions such as predicting outcomes ...
176 views

### Minimize this real function on $\mathbb{R}^{2}$ without calculus?

When it comes to minimizing a differentiable real function, calculus comes into play immediately. If $f: (x,y) \mapsto (x+y-1)^{2} + (x+2y-3)^{2} + (x+3y-6)^{2}$ on $\mathbb{R}^{2}$, and if one is ...
317 views

### Is Paley-13 a graceful graph?

The 13-node Paley graph has vertices 1 to 13 that are connected by an edge when their difference is one of the values $(1,3,4,9,10,12)$. Is Paley-13 a graceful graph? Can the 13 vertices be labeled ...
83 views

### Can an $(a,b)$-knight reach every point on a chessboard?

An $(a,b)$-knight moves $a$ units horizontally and $b$ units vertically (or $b$ horizontally and $a$ vertically) for each move. For example, the traditional knight is a $(1,2)$- or $(2,1)$-knight. ...
68 views

### How many tuples of {$a, b, c, \ldots$} satisfy $a+b+c+\ldots \leq n$?

Let $n$ be a non-negative integer and $k$ be a positive integer. Let $a, b, c, \ldots$ be $k$ non-negative integers such that $a+b+c+\ldots \leq n$. How many tuples of {$a, b, c, \ldots$} satisfy ...
98 views

### Searching for a special book in the Library of Babel

In The Library of Babel, there are all the possible 410-page books of a certain format and character set. There is a legendary book, called a total book, which is supposed to be the catalogue of the ...
600 views

### Graceful graphs with Valence $k$

For a graceful graph ( code ), vertices are labeled with values from 0 to $e$ so that the $e$ edge differences are all values from 1 to $e$. The below is now OEIS sequence A308722. $K_3$ is the ...
39 views

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### Algorithm generating subset of primes, can we classify which of them or estimate how large percent of primes are generated?

Assume I have following algorithm: Two lists of numbers, first starting at 2, second starting empty. We now follow rule: Add a number to first list which makes difference with latest number the ...
100 views

39 views

### A D20 (dice) has sides where $N-1,N,N+1$ are always neighbours on surface of solid. For which DN is this possible?

A regular gon D20 dice used for example in various forms of gambling and trading card games is shown below As can be seen each number $N$ residing on some face has two of it's neighbouring faces with ...
51 views

### Puzzles and exercises to improve mathematical intelligence and spatial thinking

In your childhood or adolescence, or maybe as an adult, have there been types of exercises or puzzles that you think have improved your mathematical intelligence and in particular the spatial thinking?...
752 views

### How to minimise the cost of guessing a number in a high/low guess game?

In a high/low guess game, the "true" number is one of $\{1,\cdots,1000\}$. You'll be told if your guess is $<,>$ or $=$ the true number for each guess you make, and the game terminates when you ...
1k views

### Strange acknowledgment in Serge Lang's Linear Algebra

Recently I open this book to look up a certain theorem and saw something peculiar about the acknowledgments I've never notice before: Acknowledgments I thank Ron Infante and Peter Pappas for ...
35 views

### Solving a statement question based on reasoning and logic.

The question is as follows, In the Land of Liars there are exactly three Clans. Black clansmen always tell lies. White clansmen always speak the truth. Red clansmen are sometimes truthful. A,B and C ...
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### General formula for the $(i,j)$ term in number spiral? [duplicate]

Several times I have to do with this configuration: \begin{pmatrix} & & & & & & & & & & \\ & & & & & & & & &...
70 views

### best cut for microwave oven

Suppose, that there is a Pizza which is round and has radius $1$. Now one would like to find the best way, under $n$ cuts, to cut the Pizza so as to obtain the minimum 'Microwave Oven Distance'- For ...
110 views

### How to find the total number of auras possible for a tile of a given tier?

PLEASE NOTE! A different problem that uses the same ruleset (technically a subset of this one since i ask multiple questions here) that can be solved with brute force and pen-and-paper has been posted ...
180 views

### Is there a palindrome prime $p>3$ that is also palindrome in base $\ 5\$?

A prime $\ p\$ is called palindrome, if the digits in reverse order give the same prime. For bases $\ b=2,3,4\$ , there are large examples of palindrome primes that are also palindrome in base $b$ , ...
Recently Joel David Hamkins posted an entry on the Connect Infinity game. Connect-$\omega$ is Connect Four but played on an $\omega\times n$ grid ($n$ finite)! The above shows $n=6$. The difference ...