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

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26
votes
3answers
635 views

Guessing the length of a playlist on “shuffle random?”

The other night I was hanging out with some friends and someone put on a playlist on shuffle random, where the songs are drawn uniformly at random from a fixed playlist. The person who put the ...
1
vote
1answer
37 views

Does this game have infinite expected payout?

Consider the following game: Suppose the initial value of the pot is $ S $. Our player Josephine then rolls a fair $n$-sided die. If the roll is not $1$, then the pot is multiplied by that roll, and ...
2
votes
1answer
35 views

Puzzle: Determining the structure of a bipartite graph

Consider the bipartite graph $G = (X, Y, E)$, with $|X| = |Y| = n$. We can think of $X$ and $Y$ as clusters of $n$ switches on either end of a long hallway. Each switch on one end of the hallway has ...
0
votes
1answer
31 views

$f(x)=y$ while $g(y)=x$; Is it possible to find two not reverse functions that behave such at least for a given set of inputs and outputs?

I want to know if it is possible to program such a code that could determine two distinguish, not inverse, functions, say $f$ and $g$, that is true for the below statements at a given input and output ...
1
vote
3answers
29 views

understanding how multiplying a number by itself and than using the result for division gives you a consistent result

hey guys i am basically a programmer and just came across a peice of mathematical calculation that i was curious to understand , have a look below :: ...
14
votes
2answers
280 views

Is there something interesting about $373857714078$? [closed]

On a site, someone asked which number is most interesting and I answered, "Every number is interesting. Give me a number and I shall tell you why it is!". Now some guy took it literally, and gave me ...
1
vote
0answers
35 views

Sum numbers game

$2n+1$ numbers are lined up as follows: $n$ , $n-1$ , $n-2$ , $\cdots$ , $2$ , $1$ , $2$ , $3$ , $\cdots$ , $n-1$ , $n$ At each step, one can choose any number in the line and add it to each of ...
0
votes
0answers
18 views

Iterated digit product

A very interesting calculator at http://www.micmaths.com/defis/defi_01.html repeatedly calculates the product of the digits of a number and stops when it reaches a single digit. It asks what is the ...
2
votes
1answer
67 views

The Rubik Square permutation groups

This post was inspired by this webpage of mathematical challenge due to Mickaël Launay (French). Let $G_n$ be the subgroup of $S_{n^2}$ generated by the red arrow permutations as for the following ...
3
votes
2answers
78 views

If $\frac{(b−c)}{a} + \frac{(a+c)}{b} + \frac{(a−b)}{c}=1$ and $a-b+c \neq 0 $, then prove that $\frac 1a = \frac 1b + \frac 1c$

The question given is If $\dfrac{(b−c)}{a} + \dfrac{(a+c)}{b} + \dfrac{(a−b)}{c}=1$ and $a-b+c \neq 0 $ then prove that $\dfrac 1a = \dfrac 1b + \dfrac 1c$ I tried to take $abc$ on the right ...
1
vote
3answers
39 views

Intersections of trigonometric functions and $x$

I was fiddling with my calculator and disovered something odd: $\sin x$ only intersects $x$ (as it seems) at $x=0$. Why is that? Furthermore, what is the significance of the intersection of $\cos x$ ...
3
votes
0answers
43 views

Examples of calculus on “strange” spaces

I am interested in examples of calculus on "strange" spaces. For example, you can take the derivative of a regular expression[1][2]. Also the concept extends past regular languages, to more general ...
0
votes
0answers
27 views

Right answer probability [duplicate]

I thought I'm familiar with probability, but this question got me a little stuck: If one choose an answer to this question completely random, the probability of choosing the right one is: A) ...
1
vote
0answers
35 views

Prime numbers and the folding in RNA structure

In [1] Ian explain an experiment of Sluyser and Sonnhammer: It seems that they encode the sequence of prime numbers as following manner, first compute the binary expression of prime number and its ...
1
vote
0answers
19 views

Get the number of digits $n$ is accurate to $p$

I am writing a little something on the accuracy of of approximations of certain numbers. Currently, I'm looking for a way to find the number of digits a number $n$ (the approximation) is "good for" ...
1
vote
1answer
28 views

A variant of the Vandermonde determinant

A very hard proof that $\sum_{i=0}^n i = \frac{n(n+1)}2$ (in comparison with the elementary level of the identity) is to compare degrees in the Vandermonde identity, which you prove playing around ...
0
votes
0answers
32 views

How many possible Connect 4 end boards are there?

If you search google you can find that there are over 4.5 trillion board combinations, but if i understand correctly there are two differences between this and what I am asking. First this figure ...
2
votes
1answer
100 views

Closed form for $\sqrt {-1\sqrt {-2 \sqrt {-3 \sqrt {-4 \ldots}}}}$ [closed]

Does $\sqrt {-1\sqrt {-2 \sqrt {-3 \sqrt {-4 \ldots}}}}$ converge? Is there a closed form for it?
2
votes
1answer
50 views

Fibonacci spiral in octopus tentacles.

How you happened to notice the presence of the Fibonacci spiral in nature it is really evident. For example, unlike octopuses, squid and cuttlefishes, the nautilus kept its stunning shell, which is ...
3
votes
1answer
29 views

Summation functions for wall clock, 10AM, 11AM and 12PM tips needed

For a recreational purposes I'm fine tuning my wall clock sheet and like to ask about tips how to esthetically modify the summation function for 10, 11 and 12. Below is the image of the final result: ...
0
votes
0answers
31 views

Proving a quadrilateral is an isosceles trapezoid

Warning: You'll probably need pencil and paper to follow this. Recently I came across the following problem in a middle/high school geometry textbook: $\ast$ Suppose $\ QUAD\ $ is a quadrilateral ...
0
votes
5answers
76 views

If I have 10 different pairs of socks and have washed 10 socks, what are the chances that none will match?

I have 10 pairs of different types of socks. I randomly (let's just assume it was true randomness) washed 10 individual socks. It turns out none of them match! What are the chances of this? I've ...
4
votes
5answers
146 views

What fraction of a sphere can an external observer see?

Here is a geometry problem. Let there be a ball of radius R and let's call it the Moon. Let there be an external observer: A. A is at a distance d to (the surface of) the Moon. [Edit] A is a ...
2
votes
1answer
41 views

Is there anything I could read that talks about dimensionality of prime/composite numbers?

Is there anything out there that talks about how primes are one dimensional numbers and composites can only be in dimensions greater than 1? What I mean is, 4 would be a two dimensional number (2x2) ...
1
vote
1answer
67 views

Finding integer solution to solve a puzzle

I have been given the following puzzle: find the smallest number that it's right most digit is 2, and if you remove that digit and place it on the left most side of the number it will double its ...
4
votes
2answers
92 views

How to compute the derivative of $x^x$ using the definition

I want to prove that $\displaystyle\lim_{h\to 0}\frac{(x+h)^{x+h}-x^x}{h}=x^x(\ln(x)+1).$ If I write $x^x$ as $e^{x\ln(x)}$ I get: $\displaystyle\lim_{h\to0}\frac{e^{(x+h)\ln(x+h)}-e^{x\ln(x)}}{h}$ ...
3
votes
0answers
42 views

What are some simple (or elegant) functions that satisfy these conditions? [closed]

I wish to have a function that maps [0,1] to [0,1]. I also require that f(0) = 0 and f(1) = 1. Also, I would like the function to be of sigmoidal shape, such as this: The above function is ok, ...
1
vote
3answers
40 views

Plotting a part of curves (with possible solution as an attempt)

I may mess up with this question! I plotted them using http://www.desmos.com/calculator How to plot only a part of some curves? For example: Plot of $y=x^2$: But if i want to plot the ...
-1
votes
1answer
36 views

Need Help Evaluating This Indefinite Integral

I would appreciate any help finding a possible closed form solution of this integral. $$\int\sqrt{\cosh(u)-\cos(v)}\cdot e^\frac{u}{2}~du$$ Any help would be greatly appreciated! The solution for ...
1
vote
1answer
58 views

What are some good mathematical journals? [closed]

I would like to study mathematics when I'm older, but I want to read some of the current literature to learn what mathematics is truly about, maybe direct my studies into some particular field. What ...
1
vote
0answers
60 views

Efficient elevator strategy

Suppose an institution building has 12 floors and there are a total of 8 lifts. Now lets say a situation arises at peak times where almost all the lifts are crowded and people randomly enter any lift, ...
18
votes
2answers
711 views

Puzzle: Cracking the safe [duplicate]

A safe is protected by a four-digit $(0-9)$ combination. The safe only considers the last four digits entered when deciding whether an input matches the passcode. For instance, if I enter the stream ...
3
votes
1answer
44 views

Is it possible to create horizontal lines of arbitrary length in match-three games?

Bejeweled. Candy Crush. A match-three game always follows the same basic rules, with each one adding its tweaks to gameplay. A mathematician would describe the state of one such game as a ...
2
votes
1answer
25 views

Imitating smaller Rubik's cubes with bigger ones.

Let's assume we have a 4x4x4 Rubik's cube. With this cube we can imitate a 2x2x2 by considering all 2x2x2 corner cubes as 1 block. Similarly, we can solve it like a 3x3x3 by first solving the 2x2 ...
8
votes
1answer
161 views

Reference Request: what are some books on mathematics you can read without pencil and paper

I am going overseas for the summer, I need a book or two so I can learn about mathematics (overviews, engineering applications, history, connection with other branches of science) without actually ...
7
votes
2answers
162 views

USSR Exam problem

I obtained this problem from here. A car starts from point $A$ towards $B$ at the same time as a motorcycle starts from $B$ to $A$ (but with a lesser speed). At the moment they meet, a second ...
0
votes
0answers
16 views

Trajectories in orthogonal systems

Please forgive any awkward phrasing or misuse of terminology. My education isn't entirely formal. Question Am I right in guessing these orbits trace lissajous-ish figures on hyperspheres? ...
2
votes
1answer
96 views

How many triangles in picture? Formula or algorithm for this?

How many triangles are in this picture? Is there any formula or computer software to calculate this? Also: I know programming so I can program something to solve this if someone can point out an ...
2
votes
2answers
96 views

Can every statement be solved by mathematical induction ? (see details below)

I have the following equation system : $$\sum_{i=1}^n a_i^2 = n $$ $$\sum_{i=1}^n a_i=n$$ here the solution is only $a_i$ =1 . Can it be solved by mathematical induction ? I have tried , but have ...
6
votes
1answer
75 views

A runs 7/4 times as fast as B. If A gives B a start of 84m, how far must the winning post be…?

The problem statement in the book is: $A$ runs $7/4$ times as fast as $B$. If $A$ gives $B$ a start of $84$m, how far must the winning post be so that $A$ and $B$ might reach it at the same time? ...
1
vote
0answers
52 views

The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time. How much a day does the clock gain?

The question in the textbook is: The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time. How much a day does the clock gain? My method: The correct ...
0
votes
2answers
575 views

Give the answer of following question [closed]

Puzzle 🔵🔴⚪ +🔵🔴⚪ +🔵🔴⚪ =⚪⚪⚪ Can you tell the numbers represented by....BLUE, RED, white?
2
votes
0answers
31 views

making integers from a given set

this Q is very easily generalizable. For example consider $1,2,3$ and $4$. We have $1=1, 2=2, 3=3, 4=4, 5=4+1, 6=2\times 3, 11=4\times 3-1$. You can only use each number once. 37 is the first number ...
2
votes
0answers
15 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 ...
39
votes
0answers
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 ...
0
votes
2answers
120 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 ...
0
votes
0answers
6 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 ...
1
vote
2answers
51 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 ...
10
votes
2answers
90 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
votes
6answers
201 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 + ...