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Questions tagged [recreational-mathematics]

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

1
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1answer
161 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
votes
1answer
27 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 ...
9
votes
2answers
203 views
+50

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 ...
5
votes
1answer
72 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
39 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
13 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 ...
2
votes
3answers
249 views

Right Triangle: Hypotenuse and Side differ by 1

So I have search to the best of my abilities but cannot find mathematically why this is true and if it is called something specific, the closest thing would be Pythagorean Triples but this is not the ...
3
votes
1answer
248 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 ...
1
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0answers
30 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, ...
0
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1answer
22 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
votes
2answers
41 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
votes
2answers
109 views

Number of different fault-free $2 \times 1$ domino tilings on a $5 \times 6$ rectangle

Fifteen $2 \times 1$ dominoes can be used to tile a $5 \times 6$ rectangle. In tiling the rectangle we might generate what are known as fault-lines. A fault-line is any horizontal or vertical line ...
2
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9answers
169 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 ...
9
votes
0answers
196 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 $e$. $K_3$ is the minimal valence 2 graph with $e=3$. $K_4$ is ...
1
vote
1answer
62 views

Two numbers that multiply to a product that contains the original digits

Recently I found an interesting combination of factors that forms a product that contains the original digits from those factors, as presented below: $$86 * 8 = 688.$$ Is there a name for these ...
3
votes
2answers
63 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
vote
2answers
55 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 ...
1
vote
1answer
890 views

Base 12 Versus Base 16

I'm not good when it comes to math, so forgive me. I'm doing a personal study of is there a better base number for our culture to use? I have to consider factors like: the number of digits to write, ...
0
votes
2answers
80 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 ...
0
votes
1answer
36 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 ...
-1
votes
0answers
41 views

Calculating amount left at the end of a repetitive cutting down cycle

Let's say I have a group of X's characters that I want to cut down. I use a method similar to 'find-and-replace-all' tool, which takes an amount of X's each time, deletes them, and replaces them with ...
2
votes
2answers
84 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, ...
28
votes
0answers
757 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 ...
15
votes
3answers
10k views

The Best Strategy and Highest Possible Score for the “Threes!” Game.

[There's still the strategy to go. A suitably robust argument that establishes what is statistically the best strategy will be accepted.] Here's my description of the game: There's a $4\times 4$ ...
2
votes
1answer
41 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
votes
2answers
87 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)^{...
2
votes
2answers
974 views

Pig Wheel question

A friend of mine was playing the bar game Pig Wheel recently and posed some interesting questions to me. He was playing with others as a group of four and, acting collectively, they came out about ...
0
votes
0answers
35 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 ...
5
votes
1answer
699 views

How to find Misiurewicz Points without solving huge polynomials? (Mandelbrot Set)

Here is a plot of 17,723 Misiurewicz Points. The code below generates a set of polynomials u[m,n], the roots of which have periodicity (m-n) starting at iteration n. I stopped at 17,723 points ...
1
vote
3answers
88 views

Find the smallest $n$ such that the $n$-th prime $p_n \equiv 330 \mod n $.

Find the smallest $n > 1$ such that the $n$-th prime $p_n \equiv 330 \mod n $. I was investigating the remainders when the $n$-th prime is divided by $n$. For every positive integer $a < 330$, ...
0
votes
1answer
49 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
votes
1answer
91 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
41 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
51 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?
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0answers
30 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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0answers
35 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
39 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?...
39
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3answers
1k views

A new interesting pattern to $i\uparrow\uparrow n$ that looks cool (and $z\uparrow\uparrow x$ for $z\in\mathbb C,x\in\mathbb R$)

Many of you may recall "An obvious pattern to $i\uparrow\uparrow n$ that is eluding us all?", an old question of mine, and just recently, I saw this new question that poses a simple extension to ...
1
vote
1answer
25 views

Density of appearances of word in a shifted grid

Let $w = w_1 \dots w_n$ for $n \geq 1$ be your favorite word, chosen from some alphabet $\Sigma$. Say you like the word ALPHA. Now consider the following infinite table: ...
-1
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1answer
107 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 ...
25
votes
1answer
951 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 ...
7
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0answers
411 views

Oblongs into minimal squares

Consider $a(n)$, the minimal number of squares into which the oblong of size $(n+1)\times(n)$ can be divided. What is the behavior of $a(n)$? The first 379 terms of the oblong square packing sequence ...
46
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0answers
2k views

Mondrian Art Problem Upper Bound for defect

Divide a square of side $n$ into any number of non-congruent rectangles. If all the sides are integers, what is the smallest possible difference in area between the largest and smallest rectangles? ...
17
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1answer
441 views

New Year Maths 2016: $\sum_{r=3}^{\; 3^2}r^3=2016$

Decode the following summation to welcome the new year! Find integer $n$ such that $$\large\color{darkblue}{\sum_{\qquad \qquad r={\sum_{m=0}^\infty\left(\frac{n-1}n\right)^m }}^{\qquad \qquad \...
1
vote
1answer
1k views

Make y the subject of x = y/(y-z)

I'm struggling with this GCSE question, but I think I'm just being silly. I've removed the fraction, making it: x(y-z) = y And then tried removing the brackets, making it: xy-xz = y But I'm not ...
10
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3answers
670 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 ...
1
vote
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
24 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 ...
5
votes
5answers
216 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/...