Questions tagged [recreational-mathematics]

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

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29 views

Expected number of calls for a Bingo win

I have read a few similar questions (see this question and this one), but cannot figure out how to adapt the solutions to fit my question. Unfortunately, my understanding of math is extremely limited, ...
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1answer
51 views

Simplest Turing Machine for a particular binary string

At the Bank of England is a proposed £50 note. Alan Turing was born on the 23rd June 1912. 23061912 in decimal is 1010111111110010110011000. Starting from a blank tape, what is the simplest Turing ...
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1answer
26 views

What can be a function that take integers as input values,and give output as odd Numbers?

I want a function that can get input as integers and give result as odd numbers. for example if x=1,y=1 then (2,3) (3,5) (4,7) (5,9) (6,11) expressing y in terms of x.
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1answer
57 views

Is the coin fair

So, I told my friend a story ... Probability professor assigned a homework to his students. The assignment was to record a 200 tosses of the fair coin. After the assignments were handed, the ...
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0answers
69 views

Minimize sum of guesses to win lottery

Ten boxes are given with $a_1,a_2,a_3,a_4,a_5 ......a_{10}$ number of balls in them respectively .These boxes are randomly ordered but $a_1,a_2 .....a_{10}$ is told.We can arbitrary select a box and ...
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1answer
86 views

Tough problems that, upon solving, made you realize how jubilating and pleasurable mathematics can be? [on hold]

For me, an example would be this pretty well known question: Simplify the following: (x-a)(x-b)(x-c)...(x-z) If you haven't seen this question, I highly encourage you to struggle with it by ...
3
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2answers
41 views

An idealized $\infty$-body problem: is an infinite and regular configuration of massive objects stable?

Suppose I have an infinite amount of massive point shaped objects, and I arrange the objects by putting one object on each point of $\mathbb{Z}^2$ within $\mathbb{R}^2$. By symmetry, the gravity ...
1
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1answer
30 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) => (...
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4answers
4k views

Shortest distance around a pyramid

Transcript: The diagram shows a square based pyramid with base PQRS and vertex O. All the edges are length 20 meters. Find the shortest distance, in meters, along the outer surface of the pyramid ...
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0answers
40 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 ...
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0answers
43 views

How to study for university level math olympiads and competitions? [closed]

I participated in some high school level math competitions but I've never invested much of my time for it at that time, thing that I regret immensely, now being a engineering grad student I what to ...
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0answers
107 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 ...
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434 views
+50

Can we remove any prime number from this strange process?

This is a little algorithm I made today, which may appear to be quite complex, so I will start with an example. Questions are at the end of the post. The process goes as follows: Start with the ...
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1answer
42 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.
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2answers
51 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\...
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1answer
186 views

Circle-separable colorings of finite set of points in the plane

This is problem 12093 of the American Math Monthly, published a few months back: Let $S$ be a finite set of points in the plane no three of which are collinear and no four of which are concyclic. A ...
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3answers
137 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 ...
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2answers
83 views
+50

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 ...
5
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1answer
74 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,...
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0answers
54 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
18 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-\...
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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?
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3answers
188 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 $7$ ...
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4answers
134 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 ...
3
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0answers
62 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 ...
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1answer
52 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. ...
7
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1answer
102 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, ...
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0answers
21 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 ...
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0answers
47 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
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2answers
66 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 ...
2
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0answers
65 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 ...
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2answers
44 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
67 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 ...
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0answers
21 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 $\langle 2,1\rangle$ ...
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1answer
24 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 ...
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1answer
34 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 ...
43
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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
185 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 ...
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1answer
33 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
126 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 ...
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2answers
44 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
16 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 ...
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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, ...
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3answers
293 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 ...
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1answer
23 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 ...
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2answers
47 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
172 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 ...
3
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1answer
294 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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2answers
72 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. ...
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2answers
62 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 ...