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

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0
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1answer
56 views

What is the algorithm to generate the cards in the game “Dobble” ( known as “Spot it” in the USA )?h

In the game Dobble ( known in the USA as "Spot it" ) , there is a pack of 55 playing cards, each with 8 different symbols on them. What is remarkable ( mathematically ) is that any two cards chosen at ...
34
votes
2answers
2k views

If the decimal expansion of $a/b$ contains “$7143$” then $b>1250$

I recently stumbled upon this really interesting problem: If we have a fraction $\frac{a}{b}$ where $a,b \in \mathbb{N}$ and we know that the decimal fraction of $\frac{a}{b}$ has the numerical ...
2
votes
0answers
8 views

Find least numerator and denominator for a given sequence of numbers in decimal form

Say I have a sequence (s) of digits written as number. (Ex: 1234567890) I need to find out shortest possible pair of numerator (n) and denominator (d) that ,being converted to decimal form of fraction ...
2
votes
3answers
71 views

economist puzzle for

Mr. White and Mr. Black agreed on the plan to average the wealth by pairs of economic classes, but they differed on the order. Averaging means that the total wealth of the two classes is ...
-7
votes
1answer
187 views

Remarkable mathematics in the The Simpsons television show [on hold]

Notice: See this meta post that is currently addressing issues about this question post along with many of the most upvoted questions on MSE that are now closed thanks to unilateral moderator actions. ...
2
votes
1answer
2k views

A recreational math problem, integers in a grid

I was thinking of the following recreational math problem: We have a $4\times 4$ square filled with integers $a_{1,1},...,a_{4,4}$. It has $30$ sub-squares $A_{i,j,k}$, corners of the form ...
31
votes
7answers
18k views

What is the math behind the game Spot It?

I just purchased the game Spot It. As per this site, the structure of the game is as follows: Game has 55 round playing cards. Each card has eight randomly placed symbols. There are a total of 50 ...
4
votes
1answer
1k views

Can you make an equilateral triangle from 3identical trapezoids?

Is it possible to make an equilateral triangle from 3 identical trapezoids? If so, what angles would be needed in the trapezoids?
0
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0answers
5 views

Question regarding Calibration while using Phase Measuring Profilometry (PMP)

We are using PMP to create the 3d model of a real world object in a summer project. However, to actually use PMP we need to relate the camera and the projector parameters and coordinates. To ...
6
votes
2answers
220 views

“Bizarre” continued fraction of Ramanujan! But where's the proof?

$$\frac{e^\pi-1}{e^\pi+1}=\cfrac\pi{2+\cfrac{\pi^2}{6+\cfrac{\pi^2}{10+\cfrac{\pi^2}{14+...}}}}$$ "Bizarre" continued fraction of Ramanujan! But where's the proof? i have no training in continued ...
5
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4answers
1k views

Dates with 8 consecutive digits

In many places, dates are written as DD/MM/YYYY. For example, the 25th of April 1736 is written as 25/04/1736. Dates such as this one that use 8 consecutive digits (not necessarily in order) will be ...
1
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2answers
30 views

Rotation schedule for 6 persons and 2 locations

I like to make a rotation schedule for a dinner party where everyone is new, so the idea is that everyone gets a chance to meet as many new people as possible. Setup: I have 6 persons attending ...
78
votes
5answers
4k views

What is the smallest number of $45^\circ-60^\circ-75^\circ$ triangles that a square can be divided into?

What is the smallest number of $45^\circ-60^\circ-75^\circ$ triangles that a square can be divided into? The image below is a flawed example, from http://www.mathpuzzle.com/flawed456075.gif ...
-3
votes
0answers
15 views

Production efficiency [closed]

I'm trying to answer a question and I don't really know how to work it out. Some insight would really help for those who can answer It.
4
votes
4answers
595 views

A 3rd grade math problem: fill in blanks with numbers to obtain a valid equation

Even though this is a 3rd-grade math problem, people found it extremely hard. Any people have a solution, or algorithm is welcome. I'll try make a program base on the algorithm and see if it's ...
8
votes
2answers
68 views

Calculate moment of inertia of Koch snowflake

That's just a fun question. Please, be creative. Suppose having a Koch snowflake. The area inside this curve is having the total mass $M$ and the length of the first iteration is $L$ (a simple ...
-4
votes
0answers
77 views

What was the first mathematical identity/theorem/corollary/conjecture you proved? [closed]

What was the first mathematical identity/theorem/corollary/conjecture you proved? Let me know when and how.
-5
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0answers
28 views
7
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6answers
172 views

Solve the following equation: $\sqrt {x + \sqrt {4x + \sqrt {16x + \sqrt {64x + 5}}}} - \sqrt x= 1$

A past examination paper had the following question that I found interesting. I tried having a go at it but haven't come around with any solutions. How would one go about tackling it? $$\sqrt {x + ...
0
votes
2answers
298 views

How much the shopkeeper loses?

I struck with this tricky math question A girl went to a shop and bought a Rs.$200$ show piece. She gave a Rs.$1000$ note to shopkeeper. Shopkeeper didn't have any change so he went outside and ...
0
votes
2answers
24 views

How can I find the length of a function $f$ between two points $x_1,x_2$ [closed]

Let's say I have some function $f$ and two values $x_1,x_2$, with $x_1 < x_2$. Is it possible to find the length of any arbitrary function $f$ between these two points? Assume that ...
8
votes
8answers
3k views

If yesterday were tomorrow, then today would be Friday.

(S) If yesterday were tomorrow, then today would be Friday. Question: What day is today? This seems to be an old puzzle, and depending on the interpretations, the answers are Wednesday or ...
3
votes
2answers
463 views

Horse Race Math question

There are 25 horses. You can take 5 of the horses at a time and race them. Each horse always finishes the race in the same amount of time, and there are no ties. The only information you get from each ...
1
vote
2answers
29 views

If you fold a rectangular piece of paper in half [duplicate]

If you fold a rectangular piece of paper in half and the resulting rectangles have the same aspect ratio as the original rectangle, then what is the aspect ratio of the rectangles?
0
votes
0answers
42 views

Moscow Institute of Physics and Technology Mathematics Competition Question

As mentioned in the title, does anyone know where can I obtain past question papers from Moscow Institute of Physics and Technology? Any link will be greatly appreciated. The following is one of ...
0
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2answers
50 views

Irrational approximations of gravitational acceleration [closed]

Earth's gravitational acceleration is approximated somewhere around $g\approx 9.8\ m/s^2$ on Earth's surface. A friend of mine pointed to me an interesting approximation $g\approx \pi^2 \approx 9.87$ ...
5
votes
1answer
177 views

Coding Theory Problem to save Humanity

For starters, this problem doesn't originate from me, it's a friend's coding theory problem and I got interested, thinking about it, but I can't think of any as I only have very basic coding theory ...
0
votes
1answer
37 views

Really easy percentage % question?

So I have an exam coming up. Just trying to calculate the bare minimum I need to pass (although I am aiming for much higher). I need 40% to pass the subject. So from a previous exam worth 30%, I ...
4
votes
1answer
73 views

Is there a nice recurrence relation for $n^n$

I know there is a nice equation for $n!$, but is there one for $n^n$? I was thinking you could get it with the fact $n^n=a^{n\log_an}$ but I can't seem to make the needed jump. Edit: It was suggested ...
9
votes
1answer
83 views

Interesting properties of the function $(a,b)\mapsto a/(a-b)$

Consider the extremely simple function $$f(a,b)=\frac a{a-b}.$$ This gives the coordinate where the line through $(0,a)$ and $(1,b)$ meets the $x$-axis. I noticed that the function $f$ has some ...
0
votes
1answer
29 views

Calculate total arc length of spherical cap of a specified circumference

For the past day, I have been trying to calculate the arc length of a sphere from a pole to a longitudinal cross-section with a specified circumference. I have diagrams and equations belo w. However, ...
1
vote
0answers
20 views

Rotation of 15 people at five tables

I have five tables of four people each. At each table is a table leader who remains stationery. How do I rotate the 15 participants so that they get to meet new people each time they rotate?
0
votes
1answer
12 views

Finding amount of Days it will take for a Dam to empty

So say I have a dam, with a max capacity of 3,538,000 acres FT of water. It's currently storing 1,796,250 acre FT of water. Water is flowing IN at a rate of 1,050 cubic-FT per second, and out flowing ...
7
votes
0answers
112 views

Name of a certain set

I want to know if there is any already-standard way to refer to the sets described as follows. For a set $X$, let $-X = \{-x: x \in X \}$; call it the negative of $X$. Take the set of all primes in ...
9
votes
5answers
873 views

A seemingly easy combinatorics brain teaser

So I have a brain teaser that goes like this: There's a school that awards students that, during a given period, are never late more than once and who don't ever happen to be absent for three ...
2
votes
5answers
535 views

Higher Dimenional Tic Tac Toe

Here we have a problem that seems very intuitive, but is hard to define mathematically. In Tic Tac Toe, we can find an equivalent of the game in any number of dimensions, it seems. The trick is to ...
2
votes
1answer
68 views

Number of algebraic solutions to a formula related to a square tiling problem

How can many different sets of prime-factors fit together so well in this formula? I am curious about the number of solutions to the following equation: $$ r_3 = \sqrt{2}\; \frac{ 1 + r_1 (r_2 ...
4
votes
0answers
90 views

Mathematical Thinking - How does it work? [closed]

Not only am I hoping you can answer my question, but perhaps refine my question itself. Unfortunately it is something I do not know how to ask, but I will give it my best attempt. Either I ask it, or ...
27
votes
3answers
1k views

Which is bigger: $9^{9^{9^{9^{9^{9^{9^{9^{9^{9}}}}}}}}}$ or $9!!!!!!!!!$?

In my classes I sometimes have a contest concerning who can write the largest number in ten symbols. It almost never comes up, but I'm torn between two "best" answers: a stack of ten 9's (exponents) ...
12
votes
1answer
295 views

Algebraic structures associated to flexagons?

Flexagons strike me as objects that would admit investigation in a first course in modern algebra. I'm surprised to be unable to find a reference discussing flexagons using modern algebra language. ...
-1
votes
0answers
41 views

Write the word or phrase that best completes the statement or answers the question. [duplicate]

Write the word or phrase that best completes the statement or answers the question. $$\cos^2\theta-\sin^2\theta=1+\sin\theta$$ i have tried manipulating the equation by substituting $x^2$ and $y^2$ ...
0
votes
1answer
121 views

Latest episode of the big bang theory, vanity card.

I usually don't read these, but this time I did, and this was the card: Does the last mathematical symbols have any meaning? I get that the equal 150.6+V, is there any more meaning behind this?
0
votes
2answers
112 views

A mathematical puzzle

I am given a set $S$ of sorted numbers and I have to find value of $rndm(S)$ $$\Large rndm(S)=\sum_{s\text{ is a subset of }S}\max(s)-\min(s)$$ Where $\max(s)$ represents the maximum value in set ...
1
vote
1answer
353 views

Arithmetic progressions of perfect powers

Find the largest positive integer $n<100$, such that there exists an arithmetic progression of positive integers $a_1,a_2,...,a_n$ with the following properties. $1)$ All numbers ...
1
vote
2answers
106 views

How can I find $(x,y)$ so that $x^y=y^x$, $x\neq y$? [duplicate]

I have found that there are two $(x,y)$ that fulfill the property that $x^y=y^x$, $x\neq y$: $(2,4)$ $(4,2)$ From this: How can I find more, if any? How can I prove that there are no other ...
0
votes
0answers
27 views

Calculating without determinant the volume of a parallelepiped in the vector space $\mathbb{R}^{3}$ over $\mathbb{R}$?

Let $a_{1}, a_{2}, a_{3} \in \mathbb{R}^{3}(\mathbb{R})$ form a linearly independent set. It is well-known that the parallelepiped $P$ having $a_{1}, a_{2}, a_{3}$ as adjacent sides has volume equal ...
3
votes
1answer
55 views

Explaining to an alien on the phone which is our LEFT and our RIGHT.

I hope this question has some sort of meaningfulness. Suppose you are on the phone with an alien which is on his planet. For some reason he know which are our UP and DOWN and our FRONT and BACK. It's ...
2
votes
1answer
75 views

Is a mapping a homeomorphism

I'm considering the mapping $\Psi: C^2([0,1])$ to $C^1([0,1])$ via: $f(x) \mapsto f(x)+x\cdot f'(x)$. Is this mapping a homeomorphism? It should be continuous given that, for any sequence $(f_n) \in ...
1
vote
3answers
67 views

Can there be an infinitely long line, that you could get infinitely closer to the end of? [closed]

You might be thinking that this was a ridiculous question, because you cannot get infinitely close to the end of a line. But.... 0.9 repeating goes on infinitely, with each 9 after the decimal place ...
117
votes
12answers
17k views

How can a piece of A4 paper be folded in exactly three equal parts?

This is something that always annoys me when putting an A4 letter in a oblong envelope: one has to estimate where to put the creases when folding the letter. I normally start from the bottom and on ...