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Questions tagged [recreational-mathematics]

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

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2
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0answers
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 ...
1
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2answers
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 ...
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2answers
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 ...
1
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0answers
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 $\langle 2,1\rangle$ ...
0
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1answer
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 ...
0
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1answer
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 ...
44
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3answers
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 ...
3
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1answer
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 ...
-5
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1answer
36 views

problem about rainfall

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 ...
6
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2answers
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 ...
0
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2answers
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. ...
0
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0answers
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 ...
1
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0answers
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, ...
10
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3answers
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 ...
0
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1answer
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 ...
-2
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2answers
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 ...
2
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9answers
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 ...
4
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1answer
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 ...
4
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2answers
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. ...
1
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2answers
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 ...
0
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2answers
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 ...
20
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2answers
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 ...
0
votes
1answer
39 views

Keep the relationship between two values

I have two variables. $x$ represent the number of months that a human will live, and $y$ is the quality of his life for those months. I want to use these two values to get a new one. If I do that $x ...
13
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2answers
213 views

Greatest perimeter polygon on a geoboard

A physical geoboard is an organized set pegs that are distributed in a grid pattern which sits on (or is a part of) a thin rectangular base. Different sized Rubber bands can wrap around the pegs of ...
2
votes
2answers
93 views

How many tuples of {$a, b, c, …$} satisfy $abc… \leq n$?

Let $n$ and $k$ be positive integers. Let $a, b, c, ...$ be $k$ positive integers such that $abc... \leq n$. How many tuples of {$a, b, c, ...$} satisfy the inequality? Note that the tuples {$a=1, ...
2
votes
1answer
43 views

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 ...
2
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2answers
100 views

Even stronger than Sophomore's dream [duplicate]

Sophomore's dream states that: $$ \int_0^1x^{-x}dx=\sum_{n=1}^\infty n^{-n} $$ and $$ \int_0^1x^{x}dx=-\sum_{n=1}^\infty(-n)^{-n} $$ A friend of mine noticed that numerically: $$ \int_0^1\int_0^1(xy)^{...
32
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0answers
921 views

Mathematics for the afterlife

Paul Erdős said this about the $3n + 1$ conjecture: Mathematics may not be ready for such problems. Similarly, there are parts of mathematics that I am not yet ready for. Some things, however, I ...
0
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0answers
128 views

“implied multiplication” operator precedence?

I hold a masters in computer science from one of the worlds top universities and until today I thought I more or less know basic math. I'm sure you guys all know these click-bait simple "90% of ...
0
votes
1answer
52 views

Alternation of Rationals and Irrationals?

I'm in a lunch group at work of recreational math geeks and we came up with a question which we need help to resolve. I apologize in advance, if my explanation is not perfectly rigorous. Given these ...
0
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0answers
49 views

Mathematical card tricks

For quite some time I have taken interest in analyzing card tricks that make use of a deep knowledge of advanced mathematics and there's been some progress. However, all the tricks I've tried decoding ...
-2
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1answer
67 views

How many solvable and unsolvable problems exist

I am unable to quantify it as there are many problems which are in polynomial time and certain problems can be reduced to polynomial time.How exactly to quantify them?
0
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0answers
41 views

Calculating the parity of number of heads on a 8x8 chessboard?

Below is an article where I facing a problem! Please refer this completely before answering my question! Impossible Escape : http://datagenetics.com/blog/december12014/index.html I got all the sub-...
0
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1answer
96 views

Discretizing a mathematical equation

This is a 3D map that maps every $(x,y,z)\to (x',y',z')$ uniquely. If i want to implement it's discrete counterpart on matlab platform, i do the following $$\text{if} (i<=\dfrac{n}{2} \wedge ...
0
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0answers
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 ...
0
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0answers
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?...
10
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3answers
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 ...
25
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1answer
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 ...
1
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2answers
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 ...
2
votes
1answer
31 views

Constructing an “Announcement Bingo” card with highest chance of win

There's an event coming up where $FAVORITE_COMPANY is going to announce a bunch of upcoming products. A fan of that company has 25 anticipated/desired announcements, ranked by likelihood, and wants to ...
-1
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1answer
162 views

What's a minimal origami construction realizing a cube root?

The constructible numbers are those that can be achieved as lengths of line segments via compass and straightedge, starting with a segment of length $1$. The origami (constructible) numbers are those ...
0
votes
1answer
58 views

Hard puzzle about people walking in the street. [duplicate]

We have a 1 dimensional street (straight) where people can either walk left or right. They all walk with the same speed. If two people meet they instantly change their direction (without loss of speed)...
3
votes
6answers
101 views

Equation of the line that lies tangent to both circles

Consider the two circles determined by $(x-1)^2 + y^2 = 1$ and $(x-2.5)^2 + y^2 = (1/2)^2$. Find the (explicit) equation of the line that lies tangent to both circles. I have never seen a clean or ...
7
votes
5answers
293 views

Why $(-2)^{2.5}$ isn't equal to $((-2)^{25})^{1/10}$?

I've tried both calculations on Wolfram Alpha and it returns different results, but I can't get a grasp of why it is like that. From my point of view, both calculations should be the same, as $2.5=25/...
0
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0answers
20 views

General formula for the $(i,j)$ term in number spiral? [duplicate]

Several times I have to do with this configuration: \begin{pmatrix} & & & & & & & & & & \\ & & & & & & & & &...
1
vote
1answer
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 ...
1
vote
2answers
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 ...
7
votes
1answer
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 $b$ , ...
1
vote
2answers
126 views

The Connect Infinity game

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 ...
-3
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1answer
69 views

Equation of Tango dancing [closed]

Good evening! I have been encouraged to ask my question on this forum, even though it might be perceived as a pure subjective and open-ended question, but I am 100% sure there is a perfectly ...