Questions tagged [recreational-mathematics]

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

3,324 questions
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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 ...
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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In writing a number with decimal notation, how to write extra .n numbers in inline form? [closed]

Like 3.141592 and then {.4} and {.3} and so on..
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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 ...
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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, ...
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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 ...
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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 ...
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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 $4\times 4$ ...
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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 ...
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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 ...
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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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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-...
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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 ...
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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?...
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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 ...
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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: ...
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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 ...
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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 ...
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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 ...
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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? ...
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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 \...
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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 ...
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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 ...