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

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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 ...
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1answer
156 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. ...
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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 ...
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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 ...
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0answers
15 views

Production efficiency [on hold]

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.
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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.
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0answers
28 views

Long easy algebra [closed]

x-51+27.3-98+83-2.16-23+54.21-63= 617,820
8
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2answers
65 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 ...
7
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6answers
168 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 + ...
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3answers
70 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 ...
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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 ...
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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?
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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 ...
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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 $g\approx \pi^2 \approx 9.87$ ...
4
votes
4answers
576 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 ...
0
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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
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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
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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 ...
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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, ...
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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
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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 ...
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 ...
4
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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 ...
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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 $y^2$ ...
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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?
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2answers
111 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 ...
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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 ...
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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 ...
3
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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
74 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 ...
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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 ...
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0answers
34 views

Shortest smooth paper Möbius Strip

I want to make a familiar Möbius strip of width 1 unit satisfying the physical properties of paper. Assume paper is a ruled surface, and the strip has to be smooth and non-self-intersecting. What ...
2
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0answers
40 views

Can i connect these points in a way that satisfies these conditions?

I apologise in advance for the horrible phrasing. If you imagine 3 points like this: You would then draw a path between A and B and another between B and C, such that the length of the line AB is ...
4
votes
2answers
118 views

What is a good approach to demonstrate solvability of this type of puzzle without use of brute-force?

I chanced upon this puzzle in this question on the Anime & Manga site, and, like the OP, tried to solve it without any success. Here is a representation of the puzzle: the blocks may only be moved ...
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1answer
56 views

Is self study of proof-based mathematics difficult?

I heard from a renowned Mathematician that self study of proof based Mathematics is extremely difficult as there is not only right and wrong but also degree's of correctness. So without a teacher ...
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1answer
69 views

Are there any system(s) of mathematics whose relationship between variables bears difference to that found within mainstream mathematics?

I have been reading up on boolean algebra quite recently, for those not familiar, this type of mathematical system has much to do with the way logic is represented (and is primarily applied to, though ...
2
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1answer
32 views

Tower of Hanoi variation from Concrete Mathematics - possible arrangements

From Concrete Mathematics, there is a problem that describes a variation of the Towers of Hanoi, where the disks can not move directly from peg $A$ to peg $B$, but must go through a middle peg. ...
2
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1answer
62 views

Compatibility of direct product and quotient in group theory

This question came to me when I tried comparing direct product and quotients of groups with products and quotients of natural numbers. When we divide a number by another and multiply the result with ...
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3answers
266 views

Cover a cicular hole with planks

A friend of mine asked me the following question. Whats the minimum number of rectangular planks of unit width (and infinite length) needed to cover a circular hole with diameter $n$? ...
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0answers
23 views

Mathematics in Football- Foul play and goal-scoring opportunity

I am reading an article talking about the mathematics in football (link: https://plus.maths.org/content/ball ). In the second part, it asks if a player should risk being sent off in order to gain the ...
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14answers
1k views

Measure 11 liters using bottles of 16, 6, and 3 liters

This question has been bugging me for a day and finally I gave up and decided to ask the community for it so here's how it goes: Suppose we have 3 bottles with capacities of $16,6$ and $3$ liters, ...
2
votes
2answers
44 views

How to find the number of values for $x$ and $y$?

I have come across numerous questions where I am asked for example, if $x$ and $y$ are non-negative integers and $3x + 4y = 96$, how many pairs of $(x,y)$ are there? Usually, I just use trial and ...
14
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3answers
980 views

A fun problem by Arnold using the Poincaré recurrence theorem

I came across this problem by V. I. Arnold while studying his classical mechanics book. Consider a sequence where the $n^{th}$ term is made up by considering the first digit of $2^n$, the first ...
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3answers
35 views

Units of Measure conversion

I was wondering if i could get some help trying to create a simple math formula. I recently was given an interview to work as a tier1 programmer and was asked to make a program. I made the whole thing ...
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1answer
34 views

Contraharmonic mean given harmonic mean

Given that two positive integers, $X$ and $Y$, have a harmonic mean of $6.875$, what is their contraharmonic mean. Harmonic mean is $(2XY)/(X+Y)$ and contraharmonic mean is $(X^2 +Y^2)/(X+Y)$. I began ...
5
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1answer
71 views

How many rectangles or triangles.

I have come across numerous questions where I am given the picture such as the above one been asked "how many rectangles are there?". I have even come across some slightly different images that ...
9
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3answers
161 views

Sum of digits of $11\dots 11^2$ where $11\dots 11$ is a 1992 digit number with all digits $1$ [duplicate]

I read this on a non-math forum where the OP says this is a question for Grade 6 elementary school students. Grade 6 elementary school level is somehow ambiguous but clearly this means no advanced ...
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 ...
5
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3answers
113 views

Move the last two digits in front to multiply by $6$

Here is the problem: Can you determine the smallest natural number $N>0$ not divisible by $10$, such that when you move the last two digits of $N$ to the front, shifting the other digits two ...
1
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1answer
65 views

If every row in a square grid corresponds to a column, then every column corresponds to a row.

I am looking for a proof of the following: A square grid is filled out with symbols from some alphabet, with one symbol in each square of the grid. Each row of the grid is the same as some column ...