Questions tagged [recreational-mathematics]

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

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1answer
34 views

Grid translation

I have a 6x6 grid, and in its first cell (row 1, column 1), its value is (-3, 2) and on its last cell (row 6, cell 6), its value is (2, -3). Another values inside this grid are: $(x_0, y_0) => (...
6
votes
2answers
115 views

How to call complementary sides in tiling shapes

How mathematically can we describe the relation between two shapes which fit to each other? Is there a word in geometry for expressing that two sides of a tiling are complementary? How to describe two ...
4
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0answers
114 views

Is there a finite number of binary-prime loops?

All natural numbers have a unique factorization into primes. I'm interested in a set $Q$ for which all natural numbers have a unique factorization into distinct elements of $Q$. This leads inductively ...
1
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0answers
57 views

Packing of consecutive cubes

Using the Ponting Square Packing, squares of size 1-49 can be packed in a 7x7 array so that the 25 interior squares are completely surrounded. Another way to look at the above squares is with the ...
0
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4answers
774 views

Is there a list of the number of sets of consecutive integers that sum to n?

I'm trying to solve this problem on POJ and I thought that I had it. Since I can't figure out what's wrong with my code, I'd like to test it against a huge list of correct answers. This will make my ...
6
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3answers
2k views

Does there exist a tool to construct a perfect sine wave?

For example, a perfect circle can be constructed using a compass and a perfect ellipse can be constructed using two pins and a piece of string, because a circle can be defined as the locus of points ...
308
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8answers
32k views

Calculating the length of the paper on a toilet paper roll

Fun with Math time. My mom gave me a roll of toilet paper to put it in the bathroom, and looking at it I immediately wondered about this: is it possible, through very simple math, to calculate (with ...
3
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2answers
7k views

How to construct magic squares of even order

Could someone kindly point me to references on constructing magic squares of even order? Does a compact formula/algorithm exist?
0
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1answer
48 views

two cards are drawn without replacement from an ordinary​ deck

Two cards are drawn without replacement from an ordinary​ deck, find the probability that the second is not a queen​, given that the first is a queen.
0
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2answers
57 views

What does the notation $^{10} C_3$ mean? Or: I am confused by a birthday card…

I've just seen a gift card on the internet that is supposedly for a mathematician's 21st birthday. It says $$ \text{Happy } ^{10} C_3 - 11\ln(e)-\frac{289}{3}+\left(\int_{\pi/6}^{\pi/3}\sec^2(x)dx\...
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 ...
8
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5answers
17k views

What does “twice as likely” mean?

Once in a while I hear people say something like X is twice as likely as Y. What they usually mean is: $$p(X) = 2 \cdot p(Y)$$ and - in the context they refer to - they usually have $p(Y) < \...
8
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3answers
167 views

Is there more to this relationship with the Fibonacci numbers?

So I recently thought of a cool way to represent the Fibonacci sequence, which provides many identities really interestingly. The key is to define $$x^2=x+1$$ And consider the integer sequences ...
5
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1answer
134 views

Knights and knaves gathering

The 16 inhabitants of Knightsland are either knights or knaves (always tell the truth or always lie). Some, or all of them, meet every Sunday at the local restaurant and sit around a circular table,...
19
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2answers
378 views

Making numbers from 2, 0, 1, 7. Also: are the the iterative factorials and square roots, starting from any $s>2$, dense in $[1,\infty)$?

My daughter (10 years old) was given the task by her math teacher to form as many numbers as she could using the numbers: 2, 0, 1, 7, exactly once each, and the operations of addition, subtraction, ...
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1answer
54 views

Find absolute position of objects when only distances are known.

I have a set of objects u1, u2,..., un and an algorithm which gives a R(1000) [1000 dimensional] vector for each object. ...
0
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0answers
59 views

One knight and one queen on an infinite chess-board (a simple game)

On an infinite chessboard player A places the queen wherever he wants. Then player B places the knight wherever he wants. Then the game starts. One rule is that the square where player A places his ...
2
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0answers
21 views

How often is $N/(2N-\sigma(N))$ a palindrome (in base-$10$) if $N$ is deficient-perfect?

Let $\sigma(N)$ denote the sum of divisors of the positive integer $N$. If $(2N-\sigma(N)) \mid N$, then $N$ is said to be deficient-perfect. Note that, if $N$ is deficient-perfect, then $N/(2N-\...
4
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3answers
201 views

How to get $6$ from the numbers $\{6, 7, 8, 9\}$ using only addition, subtraction, division, and multiplication.

Is there a way you can get the number $6$ from the numbers $6, 7, 8$, and $9$ using only addition, subtraction, multiplication, and division, without combining two numbers e.g. using the $6$ and $7$ ...
0
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4answers
143 views

How to get 5 from the numbers {6, 7, 8, 9} using only addition, subtraction, division, and multiplication.

Is there a way you can get the number 5 from the numbers 6, 7, 8, and 9 using only addition, subtraction, multiplacation, and division, without combining two numbers e.g. using the 6 and 7 to create ...
0
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1answer
38 views

Calculating my improvement via daily compounding [closed]

If I improve at something 1% daily what will be my overall improvement after 1 year? What is the formula to calculate this?
10
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3answers
344 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 ...
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 ...
4
votes
1answer
316 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 ...
3
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0answers
76 views

Deceptively difficult coin weighing puzzles

A coin weighing problem is a problem that looks something like this: You have twelve coins. Eleven of them weigh the same; one of them is either heavier or lighter than the other eleven. You want ...
1
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0answers
24 views

Generalization of Specialized Card Sort

Problem: Given $n$ unique cards in a series from 1 to $n$ inclusive, arrange the cards such that drawing the first card, then placing the next card at the back of the deck, then drawing the next card ...
7
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1answer
120 views

A “proof” for $0=1$ by integrating $\int \frac{dx}{x\ln x}$ by parts [duplicate]

Let's consider the indefinite integral $$\int \frac{dx}{x\ln x}.$$ We will compute it by integrating by parts: $$\int \frac{dx}{x\ln x}=\int (\ln x)'\frac{dx}{\ln x}=1+\int \frac{dx}{x\ln x}.$$ Hence, ...
44
votes
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 ...
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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0answers
52 views

The 8 Queens Puzzle [closed]

The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, ...
2
votes
2answers
80 views

$ 4x -5y + 24z = 4A $, $ 2x - 2y + 2z = 10$. What is the largest possible value of $A$?

If $x,y,z$ integers that satisfy $$ 4x -5y + 24z = 4A $$ $$ 2x - 2y + 2z = 10$$ with $y < 2x$ and $y-20z< 0$, what is the largest possible value of $A$? Attempt: We can rewrite the equations ...
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 ...
1
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2answers
68 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 ...
3
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2answers
1k 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 ...
1
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2answers
81 views

What would be the best way to memorize the 10 by 10 multiplication table?

Hear me out before you start downvoting please. I have a learning disability so no matter how hard I try I can’t memorize the table. Please give some tips/hints on how to memorize the table. Thanks in ...
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 $\langle 2,1\rangle$ ...
13
votes
3answers
536 views

A problem with 26 distinct positive integers

I am trying to solve the following problem. Assume that we are given 26 distinct positive integers. Show that either there exist 6 of them $x_1<x_2<x_3<x_4<x_5<x_6$, with $x_1$ ...
0
votes
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 ...
3
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2answers
83 views

Probability of winning a 7-game series if you win game no. $j$

This question is inspired by the ongoing baseball playoffs, but pertains to any tournament where 2 teams play a 7-game series, where the first to win 4 games is the overall (series) winner. In times ...
0
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1answer
37 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 ...
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 ...
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 ...
2
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3answers
267 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 ...
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, ...
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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2answers
143 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
votes
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 ...