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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
71 views

Second derivative of itself

I know the $ \frac{d^2x}{dx^2}= 0 $, since $dx/dx = 1 ...$ But by playing with some equations it is easy to get that $d^2f/dx^2=f''(x)$, so $d^2f=f''(x)dx^2$ and $df=f'(x)dx$, so $df^2=f'(x)^2dx^2$. ...
2
votes
1answer
59 views

Number of permutations differing in at least $d$ spots in pairwise comparisons

A friend and I were thinking about this problem today but we were unable to come up with a solution. Problem: Consider the the numbers $S=\{1,\ldots,n\}$. Given $2\le d \le n$ what is the ...
1
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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 $a < 330$, ...
-3
votes
1answer
92 views

How many people are there when the word “with” is used? [closed]

How many people are there is the following statement: "Bob with his family of 4..." Is it: a total of 4 (Bob + 3 members) or a total of 5 (Bob + 4 members) ?
2
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3answers
90 views

When to apply negative sign when number is squared

I always had this confusion of when I need to apply the negative sign in the calculation. I understand that $(-1)^2 = 1$ however why isn't $-1^2 = 1$?
2
votes
1answer
69 views

Version of Fitch Cheney's card trick

Fitch Cheney's card trick is well known. Alice picks five cards from a deck. Bob takes them, gives one back to Alice and arranges the other four in some order. Chuck then enters the room, looks at ...
0
votes
1answer
108 views

Why do we not use letters as numbers? [closed]

To me, it seems like such a waste of energy to teach children a new set of symbols $(0,1,2.....)$ after they have learnt the alphabet. Why do we not replace $a=0$ and $b=2$ until $j=9$ and use the ...
0
votes
0answers
27 views

Is there a way to narrow down the choices to the picture below given the price?

So I saw this post somewhere and I’m curious if there’s a way to narrow down the possible things a person did given the total price he/she add up among the things listed in the picture below. https://...
2
votes
0answers
54 views

An order-6 configuration

Here's an example of an order $96_6$ configuration found by L.W. Berman. Every point has six lines, every line has six points. The unique 6,6 cage graph is bipartite and is a Levi graph for the ...
6
votes
1answer
70 views

Long anti-arithmetic permutation

A permutation is a sequence $(a_1, \ldots, a_n)$ in which each number $1, \ldots, n$ appears precisely once. We call a sequence anti-arithmetic if there are no non-trivial arithmetic subsequences in ...
1
vote
1answer
56 views

Generating all possible Domino tilings on a $4 \times 4$ grid

I have a task to write a program which generates all possible combinations of tiling domino on a $4 \times 4$ grid. I have found many articles about tilings, but it is for me quite difficult and I ...
23
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1answer
1k views

How to colour the US map with Yellow, Green, Red and Blue to minimize the number of states with the color of Green

I want to colour the US (only the states) map with Yellow, Green, Red and Blue. I was wondering what would be the lowest number of states with the colour of Green. We can of course use the other ...
9
votes
1answer
335 views

Hopping to infinity along a string of digits

Let $s$ be an infinite string of decimal digits, for example: \begin{array}{cccccccccc} s = 3 & 1 & 4 & 1 & 5 & 9 & 2 & 6 & 5 & 3 & \cdots \end{array} Consider ...
0
votes
2answers
143 views

$\frac{\left(10^4\right)}{x^2}=\frac{\left(x^{\left(8-2\log x\right)}\right)}{10^4}$ Solve for x.

$\frac{\left(10^4\right)}{x^2}=\frac{\left(x^{\left(8-2\log x\right)}\right)}{10^4}$ Solve for x. $\frac{\left(10^4\right)}{x^2}=\frac{\left(x^{\left(8-2\log x\right)}\right)}{10^4}\Rightarrow 10^8=\...
1
vote
1answer
58 views

Green-eye paradox (an information paradox) or the Dragon puzzle

I was trying to solve this puzzle but I believe I have run into a paradox.Found the puzzle in https://io9.gizmodo.com/can-you-solve-the-hardest-logic-puzzle-in-the-world-1642492269 "There are 100 ...
0
votes
0answers
12 views

galactic to ecliptic coordiantes

I want to describe the position of a point with an ecliptic coordinate system. Using this celestial coordinate system to represent the apparent position of 3D points is my goal. The output values ...
1
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0answers
34 views

Linear equations problem from CAT

How do I solve this question. Here is what I've been thinking: lotion A can relieve 75 spasms and lotion B 120 spasms. So going by options buying only lotion B would be cheaper right? Is my reasoning ...
1
vote
0answers
30 views

How limitations affect the number of possible pandigital numbers

First, I understand that the definition of "pandigital" can vary, somewhat, so for the purposes of this question, here's the definition we'll use: "Positive and whole numbers that include each ...
0
votes
2answers
34 views

Linear equation problem for aptitude exam

This is a question that has been asked by my teacher who is helping me prepare for the Common Admission Test conducted in India for admission into postgraduate management programmes of Indian ...
7
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0answers
59 views

Borromean Weaving

Here's a picture by Rashmi Sunder-Raj. Is this topologically equivalent to Borromean Rings?
1
vote
1answer
21 views

Ratio and Proportion quantitative aptitude exam for management entrance in India [closed]

The following is a question from the Common Admission Test which is an aptitude exam conducted in India for admission into postgraduate management programmes of premier management institutes of the ...
1
vote
1answer
66 views

“Human Knot” solvability probability

Somewhat surprisingly, I don't see a question about this. There is a team-building (or just fun mathematical) game where a group of people hold hands with each other, usually trying not to hold hands ...
1
vote
4answers
52 views

Showing that $\arcsin x + \arccos y = \frac{\pi}{2}$ if and only if $x = y$

I was just wondering about this identity: $$\arcsin x + \arccos x = \frac{\pi}{2} .$$ That a thought came to my mind that in general $$\arcsin x + \arccos y = \frac{\pi}{2} \qquad \textrm{if and ...
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1answer
46 views

TI 84 CAN'T SOLVE THIS SIMPLE PROBLEM [closed]

why does my TI 84 answer .06 divided by 365 = 1.643835616E -4?? the answer is .000164383
3
votes
0answers
65 views

How can I generate tilings using a computer? [closed]

I was reading this wikiperdia article on polyminos. The pictures look very nice. Example I want to learn how to generate these figures myself in an interactive way. Basically I want to start with a ...
0
votes
1answer
9 views

Formula to calculate percentage withdrawal that will yield same value as principle decreases.

So I created this retirement calculator here http://www.abrandao.com/retire And the idea is if you save enough you can so when you withdraw say 4% you don't eat too much into your savings. But ...
2
votes
1answer
68 views

When is the matrix $I-P$ nilpotent?

Note: sorry for the long post. My question is in the second quote. A few years ago, I saw the following problem on Facebook. I would like to ask a generalised version of this problem. Here is the ...
1
vote
0answers
99 views

Generalizing the fix-point properties to multi-dimensional functions?

$x,y,z\in\mathbb R^3.$ $c:\mathbb R^2\to\mathbb R$. $a,b$ are constants. Function $f(x,y,z)$ satisfies that $\forall z_1,z_2\in\mathbb R$, we have $$\{(x,y)||f(x,y,z_1)=f(x,y,z_2)\}=\{(x,y)||ax+by=c(...
0
votes
2answers
77 views

Tearing paper into three parts with a single cut without folding the paper strip [closed]

How can I divide or tear or cut a single strip of paper into three parts(not necessarily equal) with a single straight cut, and that too without folding the paper strip
1
vote
1answer
64 views

How much faster than a speeding bullet is superman?

I need some help with a problem I want to solve. You have a gunman standing 50 ft away from a human target. According to google, the average bullet travels at 2,500 fps. If my math is correct (...
0
votes
6answers
181 views

For any $k \in \mathbb{N}$, there exist $s \in \mathbb{N}$ such that the expression $9s+3+2^{k}$ is a power of $2$

I have reason(empirical calculations) to think the following statement is true: For any $k \in \mathbb{N}$, there exist $s \in \mathbb{N}$ such that the expression $$9s+3+2^{k}$$ is a power of $2$. ...
0
votes
1answer
49 views

100 people (or some multiple of 100) want to travel from San Diego to LA

100 people (or some multiple of 100) want to travel from San Diego to LA. A trip by car takes C(x) = 100 + 0.6x minutes where x is the number of people who drive. The bus from San Diego to La takes C(...
2
votes
0answers
55 views

Proof verification about a property of the topological space $[0,1]$ Part 2

Suppose $A_1,\dots,A_k$ are connected open subsets of $[0,1]$ such that $[0,1]=\bigcup_{i=1}^k A_i$ and $A_i \not\subseteq A_j$ for each $i\ne j$. By characterization of connected subsets of $\mathbb{...
2
votes
1answer
78 views

Generalizing tug-of-war puzzle

A puzzle at the end of a 3Blue1Brown video asks the following question (paraphrased): From a group of 20 people, you get to send one person to participate in a tug-of-war tournament. You don't care ...
1
vote
1answer
31 views

Finding place of the nine digits

The nine digits 1, 2, 3, ... .., 9 are placed in the nine triangles of the attached figure in such a way that the digits around each circle add up as indicated. Calculate the value of N.
3
votes
2answers
98 views

Dudeney’s solutions to haberdasher's problem exact measures of sections

What is the IG length if the side of the square is 1? I wonder if it is half of the square side. The triangle below represents the haberdasher's problem. version 2 version 1 (added after edit, here ...
1
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2answers
35 views

What are the 'spaces' whose structure is defined by a collection of subsets

I am trying to recount which 'space' structures are defined by a collection of subsets. Given a set $X$ the only two structures I know are: (1) $\mathcal{T}\subseteq \mathcal{P}(X)$ is a topology on $...
0
votes
1answer
37 views

How to calculate the maximum height

I am studying radio galaxies and observing the behavior of fluxes at high frequencies and want to calculate the maximum height of the fluxes at where they best correspond(typically at higher ...
-2
votes
1answer
84 views

chessboard 7x 7

A 7 × 7 chessboard that is painted black and white, with the corners painted black;and we have the operator "inverse", which can be applied to a single row or single column in a table that it change ...
0
votes
1answer
62 views

How many times can I cut a shape in half before getting a new shape?

If you take triangle and slice it from one corner to the opposite base, you get another triangle. That leaves you with two new triangles. If I cut those triangles in half, I'll have four. On the ...
5
votes
3answers
501 views

Is there a bijective, monotonically increasing, strictly concave function from the reals, to the reals?

I can't come up with a single one. The range should be the whole of the reals. The best I have is $\log(x)$ but that's only on the positive real line. And there's $f(x) = x$, but this is not strictly ...
0
votes
0answers
19 views

Addition chain with two sub-optimal sub-addition chains

An addition chain is a finite sequence of positive integers that starts at $1$, so that any element of the sequence is a sum of two previous elements. That is, it is a sequence $(a_1, \ldots, a_k)$ ...
0
votes
1answer
67 views

Theorems & Proof Corrections [discrete mathematics]

So I've recently started a new chapter in my discrete mathematics course on proof methods. I have come across this problem in my textbook but I'm having a very hard time understanding where to start ...
6
votes
1answer
108 views

Is there a solution to this functional equation?

I was going through my old notebooks and I found a sheet of paper with this problem on it. I thought it would be a shame to let such an unreasonably difficult question go to waste, so I decided I ...
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 ...
0
votes
1answer
32 views

How to show this rule works for whole numbers to the fifth power?

Today I was shown a rule about natural numbers raised to the fifth power and an interesting method to generate them through the odd numbers. Start with $1 = 1^5$. Then skip the next $T_1 = 1$ odd ...
10
votes
2answers
454 views

Overlapping circles covering polygon

While working in GeoGebra I noticed something odd. I had a triangle with a point inside and the point was connected to each of the vertices. For each vertice I had drawn the circle passing through the ...
0
votes
2answers
65 views

Determine the form of the sequence {9,144,3600,129600,6350400,…}

I'm having a difficult time figuring out the functional form of this sequence: $$\{9,144,3600,129600,6350400,...\}$$ I'm trying to determine the recursive relationship for a differential equation ...
1
vote
1answer
38 views

Restoring permutation from differences of adjacent elements

Suppose a permutation $\pi \in S_n$ is encoded by a list of integers $P=(p_1, p_2, ... p_{n-1})$, where $p_i = \pi(i+1) - \pi(i)$, i.e. $P$ is the list of differences of adjacent elements. Now, given $...
1
vote
0answers
47 views

Odds of winning a prize in a weighted, random raffle

There is a raffle a state holds annually to assign salmon fishing licenses to fisherman; in a specific stetch of river, to control harvest and limit access, to ensure resource management and a high ...