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

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0
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52 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 ...
4
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4answers
1k 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 ...
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1answer
38 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
76 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 ...
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1answer
86 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
77 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
32 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?
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1answer
15 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 ...
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5answers
933 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
106 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 ...
0
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1answer
134 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
162 views

A mathematical puzzle [closed]

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
30 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
116 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
80 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 ...
3
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1answer
93 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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0answers
40 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
41 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
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2answers
129 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 ...
1
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1answer
78 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
90 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
44 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
68 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
282 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
35 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
2k 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 ...
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3answers
1k 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
49 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 ...
0
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1answer
45 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
89 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
170 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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5answers
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
119 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
70 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 ...
2
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0answers
33 views

How to maximize the minimal amount not payable with the exchange of at most two coins?

Background I've been thinking about payments which you can do using at most two coins. This includes three possible cases: You pay by giving one coin of the value you owe (for example, if you have ...
3
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5answers
144 views

Can every perfect square exist as the sum or difference of two perfect squares?

I believe this is trivial and I'm over-complicating it. But can every squared integer be expressed as the sum of two squared integers OR the difference of two squared integers? And is there a proof ...
0
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1answer
33 views

What are the steps to function design?

So I'm trying to write a program, and I want to use math functions to help it. In this example, I'm trying to change the color of a line based on the position of each pixel on the line. Anyway, I ...
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0answers
37 views

Interesting horserace counting problem

So for a horserace with no drawing horses there are n! Results. How many results will there be if the horses can draw?
2
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2answers
145 views

Helping 7th grade with math question… I'm stumped.

First salesperson says 7 baubles together with 5 gewgaws is the same value as 6 trinkets Second salesperson says 4 baubles with 9 trinkets has the same value as 5 gewgaws Third salesperson says 6 ...
2
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1answer
85 views

What is the _simplest_ way to solve problems of this kind?

Two doors with talking doorknockers - one always tells the truth and one always lies. One door leads to death other to escape. Only one question may be asked to either of the door knockers. What would ...
2
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2answers
39 views

I have an equation I would like solving.

I need to solve the following problem Decorator A is painting a large wall. At her current rate, she will complete the wall in 1 hour and 40 minutes. Decorator B is painting a similar wall, ...
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1answer
100 views

9 hens lay 9 eggs in 9 days… [closed]

9 hens lay 9 eggs in 9 days. How many eggs will 3 hens lay in 3 days??? it's a tricky question asked by a friend and can you solve it and explain your answer.
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2answers
121 views

Mathematics problems clock

Long ago, I had an idea of creating (actually, labeling) a clock that will have, instead of the numbers 1,…,12, important mathematical problems whose solution turned out to be that number. Such a ...
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0answers
50 views

Combinatorial Problem; With a Catch

Good evening, My problem is as follows: You have N points that may be connected by K different lines. Only one line may connect two different points at one time. K will be at least (N-1) and no more ...
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1answer
35 views

Theoretical insect population growth limit

Fire Ant mounds are rising in my yard: if a mound can have only one queen, and she lays $50$ viable eggs per day, and if $2\%$ of the population dies per day, what is the limit of population growth? ...
8
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1answer
276 views

Here is a riddle that I have no idea how to solve.

Okay, so I was trying to solve this riddle found here. It is a diagram of a star with 16 points. Each point corresponds uniquely to a number between 1 and 16. The letters on each point represent a ...
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0answers
60 views

How can I get the maximum score without iterating all possibilities?

Suppose I have a set of number $S = \{0,\ldots,n-1\}$. I have to find a partition $$P = {\arg \max}_{P \in \mathcal{P} \text{ and } P \text{ is a partition}} \operatorname{score}(P)$$ A partition ...
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1answer
67 views

FLATLAND's sphere intersection scenario, explored for four dimmensions

I recently finished this wonderful new vintage edition of FLATLAND. http://amzn.com/918775116X In 1884, Edwin Abbott wrote this strange and enchanting novella called FLATLAND, in which a square who ...
4
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0answers
99 views

StackEgg optimal algorithm

What is the minimum number of days that is needed to complete the StackEgg game? (It's on the right if anyone didn't notice.) There are four markers (Questions, Answers, Users, Quality) I believe each ...