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

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9
votes
1answer
143 views

Interesting shapes using probability and discrete view of a problem

Suppose we have a circle of radius $r$, we show the distance between a point and the center of the circle by $d$. We then choose each point inside the circle with probability $\frac{d}{r}$ , and turn ...
13
votes
3answers
179 views

Can exist an even number greater than $36$ with more even divisors than $36$, all of them being a prime$-1$?

I did a little test today looking for all the numbers such as their even divisors are exactly all of them a prime number minus 1, to verify possible properties of them. These are the first terms, it ...
3
votes
1answer
81 views

What does it mean to suppress a number in math?

What does it mean to suppress a number in math? I was doing a math problem and it said to "suppress a term of a sequence." Does this mean to decrease or get rid of the term? Problem: Let ...
2
votes
0answers
120 views

Number of ways to color a grid?

I have a $N \times M $ grid and I am trying to calculate the number of ways I can color this grid in maximum $k$ colors (I can use only $2$ colors or all $k$ colors) with the exception that two ...
13
votes
10answers
1k views

Small Representations of $2016$

It's the new year at least in my timezone, and to welcome it in, I ask for small representations of the number $2016$. Rules: Choose a single decimal digit ($1,2,\dots,9$), and use this chosen digit, ...
25
votes
10answers
5k views

Is it possible to draw this picture without lifting the pen?

Some days ago, our math teacher said that he would give a good grade to the first one that will manage to draw this: To draw this without lifting the pen and without tracing the same line more than ...
15
votes
1answer
340 views

New Year Summation 2016: $\displaystyle\sum_{r=3}^{\; 3^2}r^3$

Decode the following summation to welcome the new year! Find integer $n$ such that $$\large\color{darkblue}{\sum_{\qquad \qquad r={\sum_{m=0}^\infty\left(\frac{n-1}n\right)^m }}^{\qquad \qquad ...
5
votes
2answers
68 views

Issues solving equations involving $x^{x^x…}$?

I stumbled across this problem: $x^{x^{x^{...}}}=2$ Obviously, I used the substitution trick and I got $x^2=2$ and thus, $x=\pm\sqrt{2}$. I have tested that this works. However, I tried to ...
10
votes
1answer
102 views

Relationship between primes and practical numbers

This is my first post here. I am a musician, and not a mathematician, but I enjoy doing things to prime numbers and seeing what comes out. I have defined a sequence which takes the following values ...
-1
votes
1answer
237 views

New year incoming, 2016 [closed]

Here we are, another year is going to finish. Then, what are the "good" or "funny" properties you can find about the number $2016$? Or, is there a natural problem having $2016$ as answer? I tried to ...
-9
votes
3answers
176 views

Interesting patterns to the algebraic solutions of polynomials [closed]

In yet another attempt to find the solution to the quintic polynomial, I started looking backwards at the solutions to the quartic, cubic, quadratic, and linear polynomials to see if I could pick up ...
14
votes
4answers
1k views

What's the smallest number that we can multiply with a given one to get the result only zeros and ones?

I have the following set of numbers, $$4, 198, 4356, 10296, 14454, 25542, 31779, 51252, 53946, 99999$$ Let's take $3,4$ as an examples: The smallest number to multiply with $4$ to get the result ...
2
votes
0answers
211 views

How can all players in the Starcraft 2 Grandmaster league win more than they lose?

Starcraft 2 is a competitive online strategy game where players compete in leagues with other players of similar skill. The most difficult and highest league is the Grandmaster (GM) league, which ...
0
votes
1answer
38 views

What is differential time ratio? [closed]

Alright, so I discovered this website detailing some far-out time travel theories. Now, before you say anything let me be clear, I'm not interested in time travel so much as the creative writing ...
2
votes
2answers
72 views

Can this be triangulated?

Given N people with their phones that can sense the signal strength of every other phone knowing what phone it is. Phones don't know their absolute location (underground). There is a formula that ...
47
votes
17answers
2k views

What are some math books written in dialogue or story form, e.g., a teacher explaining to a student?

Good examples would be The Square Root of 2 by David Flannery or Math Girls by Hiroshi Yuki.
0
votes
1answer
78 views

Growth rates slower than logarithmic? [closed]

So far, I've been able to determine growth rates using the following limit:$$\lim_{x\to\infty}\frac{f(x)}{g(x)}$$Which, if need be, can be solved with calculus. From this, I deduced that it is very ...
-2
votes
1answer
35 views

If you invest in an account that earns 4.5% interest compounded continuously.. [closed]

If you invest in an account that earns 4.5% interest compounded continuously, how long will it take to triple your money assumig you leave it in the account? Just another fun question from a website ...
2
votes
2answers
77 views

Otimization on a city with infinite many traffic lights.

Province Ave has infinitely many traffic lights, equally spaced and synchronized. The distance between any two consecutive ones is $1500m$. The traffic light stay green for 1.5 minutes, red for 1 ...
2
votes
5answers
83 views

If $2^{2013}-2^{2012}-2^{2011}+2^{2010} = k \cdot 2^{2010}$, find $k$ [closed]

Hey this is just a question i was having fun with but couldnt solve for some reason. Would love if you can help me solve it thankyou!: If $2^{2013}-2^{2012}-2^{2011}+2^{2010} = k\times2^{2010}$. ...
4
votes
1answer
68 views

Difference Puzzles

I have a puzzle calendar that features 20 or so different types of puzzles. Some are pop culture references and some are logical. Anyway I can do most of the logical ones without breaking a sweat in ...
42
votes
2answers
1k views

Xmas Greeting 2015

Simplify the expression below into a seasonal greeting using commonly-used symbols in commonly-used formulas in maths and physics. Colours are purely ornamental! $$\large \begin{align} \frac{ ...
1
vote
3answers
80 views

Integrating $f(x)=\int|\cos(x)|dx$ and then solving $f(x)=\frac {2x}{\pi}$?

I realised the other day that by applying absolute value signs to the cosine function and then integrating, I would get an almost sine function that doesn't have negative slope. And then I also ...
5
votes
1answer
33 views

Manipulation with strings riddle.

Starting with the "string" $PI$, can I or not transform it into the "string" $PK$ by applying the following rules (each rule can be used any number of times, in any order, and $x$ and $y$ represents a ...
13
votes
3answers
144 views

Generating numbers by repeated doubling and digit reversal

Let $S$ be the smallest set of positive integers satisfying the following conditions: $1 \in S$, If $n \in S$ then $2n \in S$, If $n \in S$ then the digit reversal of $n$ is also in $S$. We assume ...
1
vote
2answers
51 views

Does an infinite iteration of a function still have my solution and why does it work?

I found the other day that you could find some solutions to an equation in the form $$f[f(x)]=x$$As a matter of fact, I found some solutions to$$f[f(f(\cdots f(x)\cdots))]=x$$ The solution, if one ...
1
vote
0answers
27 views

Has a simple optimal or provably near optimal strategy been shown for backgammon bearing off?

I aplogize in advance for the somewhat long post. I've tried to split it into manageable paragraphs. So in backgammmon, in the so-called "end-game", both players have their pieces in their respective ...
4
votes
0answers
279 views

Evaluating $\int_{0}^{\infty} \left[\left(\frac{2015}{2015+x}+\cdots +\frac{2}{2+x}+\frac{1}{1+x}-x\right)^{2016}+1 \right] ^{-1}\mathrm{d}x$

I need to evaluate $$\int_{0}^{\infty} \left[\left(\frac{2015}{2015+x}+\cdots +\frac{2}{2+x}+\frac{1}{1+x}-x\right)^{2016}+1 \right] ^{-1}\mathrm{d}x $$ I've been told that the way forward is ...
5
votes
3answers
132 views

Dwarfs over a bridge

300 dwarfs go over a bridge in the middle of the night. The bridge is rickety and manages at most two dwarfs at a time. With them is a lantern that they must provide at each transition. Dwarfs need ...
4
votes
2answers
93 views

How can one find the zeroes of $f(x)=ae^{bx}+cx+d$?

A certain physics problem I have been working on has turned into a math problem. Particularly, I want to find the solutions of some equation of the form $$f(x)=ae^{bx}+cx+d = 0$$ where $a, b, c,$ ...
2
votes
2answers
50 views

Multidimensional Riemann integration and notion of volume or Lebesgue theory and notion of measure

I have finished 9 chapters of "Introduction to Analysis" by Maxwell Rosenlicht (1968). The last chapter treats about "Multiple Integrals". I find the notation a bit complicated. Also, author ...
5
votes
1answer
357 views

Dividing numbers with dots?!

OK. This intrigues me. I recently came across this video. Which presumably tells you how to divide 133,342 with 121 only using hand drawn dots! Fair enough but I don't think this works for every ...
1
vote
3answers
36 views

How many definitions of a list of 30 would I need to know so that I could answer at least 10 from any 18?

While studying for my English exam, I noticed that the way the definitions portion of the final is set up posed an interesting problem. While I will study all the definitions, I thought trying to ...
1
vote
1answer
25 views

Number of way that set of point can be colinear

Assume I have $n$ points in a plane. and I want arrange them in the way that for any point at least I can find two other points that are all the three points are collinar. I want to know how many way ...
1
vote
1answer
80 views

How can we draw $14$ squares to obtain an $8 \times 8$ table divided into $64$ unit squares?

How can we draw $14$ squares to obtain an $8\times8$ table divided into $64$ unit squares? Notes: -The squares to be drawn can be of any size. -There will be no drawings outside the table.
4
votes
1answer
108 views

What is the minimum number of squares to be drawn on a paper in order to obtain an 8x8 table divided into 64 unit squares? [closed]

What is the minimum number of squares to be drawn on a paper in order to obtain an $8\times8$ table divided into $64$ unit squares. Notes: -The squares to be drawn can be of any size. -There ...
3
votes
0answers
65 views

Compute shooting targets for the gunmen

This is an extension of the well known "3 gunmen puzzle": N gunmen with hitting probabilities in (0,1] take turns to shoot at each other. Firing order is fixed (gunman 1 shoots first, then gunman ...
10
votes
5answers
550 views

Formulae of the Year $2016$ [closed]

Soon it's the year $2016$. Time to ponder how we can arrange the digits in 2016 to form a valid equation. Use any symbols you like (please explain the less obvious ones). Keep digits in the same order ...
3
votes
0answers
345 views

An interesting way to visualize the Mandelbrot Set. Proofs? Simplifications? Extensions?

This is a multi-part Question. Please chime in with any interesting insights in addition to Answers. I have noticed some interesting properties of Mandelbrot series that lead to a different way to ...
2
votes
0answers
58 views

Could you suggest books, papers or problems that could be used as good “general” motivating examples of calculus application?

I would like to stress the kind of reference I am looking for... In statistics there are lots of motivating (and sometimes unexpected) examples that are interested for everyone such as Birthday ...
1
vote
2answers
128 views

I want to write a Christmas message only with particular zeta values. It is possible?

I want to write a Christmas message to leave as a comment thanking the people who in the next 24th December will solve some of my problems: I wish you Math Christmas and a Happy New Year ... ...
5
votes
2answers
48 views

Deleting one digit yields a divisor

Let $N$ be a positive integer with $d\geq 4$ digits, none of which is zero. Suppose that erasing some digit of $N$ yields another number $M$ which happens to be a divisor of $N$. Examples : 1375 ...
4
votes
0answers
35 views

Hamiltonian path on a chessboard with prescribed endpoints

On an 8 x 8 chessboard consider two squares to be adjacent if and only if they share a common side. All paths below will consist of steps which join one square to an adjacent one. Under these ...
0
votes
1answer
57 views

2-player game, putting coins on a round table [duplicate]

Two players place coins of identical size (say quarters) on a round table. Each player has to place exactly one coin on the table without overlap with the coins already on the table. The first player ...
4
votes
1answer
88 views

Fun Q6: Side length of the pentagon in a five sided star?

Consider a regular pentagon of side length $a$. If you form a 5-sided star using the vertices of the pentagon, then you'll get a pentagon inside that star. What is the side length of that pentagon? ...
0
votes
0answers
38 views

Solutions of diophantine equation: $s^2 = (ad)^2+ (bc-ad+4ac)^2$

Given diophantine equation: $$s^2 = (ad)^2 + (bc-ad+4ac)^2$$ $s,a,b,c,d$ are all variables. They are all odd. a and b are coprime. c and d are coprime. How do you parametrize all the solutions? ...
2
votes
1answer
49 views

Count the pair of numbers that satisfy the set

I have an operation $f$ which takes two numbers $A$ and $B$ and returns a symmetric difference of digits of these two numbers. For example having $453$ and $1134$ the operation will produce a set ...
1
vote
1answer
19 views

Pinpointing a hidden submarine moving at constant speed

A submarine is moving along the line at a constant speed $s$, starting from position $a$. Thus its position is $a + st$. $t$ does not necessarily start from zero, it starts from some value $k$ ...
-1
votes
2answers
87 views

3 girls and 4 boys were standing in a circle . What is the probability that two girls are together but one is not with them?

Question: 3 girls and 4 boys were standing in a circle . What is the probability that two girls are together but one is not with them ?
14
votes
1answer
131 views

Numbers whose powers are almost integers

Some real numbers $\alpha$ have the property that their powers get ever closer to being integers -- more precisely, that $$ \lim_{n\to\infty} \alpha^n-[\alpha^n] = 0 $$ where $[\cdot]$ is the ...