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

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0
votes
1answer
39 views

Nice combinatorics puzzle

Priscilla and Suzie are high-school students with an exceptional talent for mathematics. Their mathematics teacher has noticed their talent and now he does his best to encourage the two girls by ...
29
votes
3answers
746 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 ...
17
votes
8answers
1k views

Properties of the number 50

I will shortly be engaging with my 50th (!) birthday. 50 = 1+49 = 25+25 can perhaps be described as a "sub-Ramanujan" number. I'm trying to put together a quiz including some mathematical content. ...
1
vote
1answer
41 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 ...
3
votes
2answers
160 views

How to mathematically color the regions bounded by a parametric curve?

Usually, if an implicit equation $F(x, y) = 0$ defines a curve (or curves) on the x-y plane, then we can use the inequalities $F(x, y) < 0$ or $F(x, y) > 0$ to color the regions bounded by the ...
1
vote
2answers
361 views

Find the angle between two lines using a compass and straight edge.

I've drawn two random, non-parallel, straight lines on a plane. They cross over, forming two angles, $a$ and $b$, where ($a + b + a + b) = 1$ (or $360^\circ$) and $a ≤ b$. (Making $a$ either the acute ...
4
votes
0answers
187 views

Which chapters of Euclid's elements would be helpful for drawing a grid?

I am drawing a $19 \times 19$ grid on my desk. For aesthetic purposes, I don't want to use a ruler. Rather, I want to use Euclidean theorems to 'prove' to myself that such and such line meets at a ...
2
votes
1answer
38 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
32 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 ...
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 ...
4
votes
2answers
561 views

Puzzle on the triangle.

In triangle top four figures that have to be repositioned to form the "triangle" without a unit square. How to explain this? Thank's.
1
vote
3answers
31 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 :: ...
4
votes
3answers
4k views

Formula(/How) to find 2 numbers that add together to give one number and times to give another

I have $2$ numbers $a, b$. I need a formula (or a how to) to find which $2$ numbers $c,d$ will add together to give a and times together to give $b$. So $c + d = a$ $c \cdot d = b$
14
votes
2answers
288 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 ...
4
votes
4answers
1k views

What is the importance of an integer sequence like the happy numbers?

I've been looking at the happy numbers which led me to the OEIS and showed me that there are many documented integer sequences. What I don't understand is the importance of these sequences. To me, the ...
1
vote
2answers
129 views

Determining Formula (Game Mechanics)

WARNING I believe that the data below has errors in the defense strength, so is therefore not solvable. I will update it when I have more information. Thank you. I play a game (Empire: Four ...
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 ...
1
vote
0answers
36 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 ...
9
votes
8answers
5k 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 ...
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
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 ...
6
votes
3answers
138 views

Can someone produce a sudoku puzzle where guessing more than one cell's value at a time is required?

Currently I have a sudoku puzzle solver program and I've tried all the puzzles I can find that are labeled the "hardest" on various sudoku video games and puzzle books. My solver has solved them all. ...
39
votes
19answers
2k views

Literary statements that are false as mathematics [closed]

I recently wanted to use the title of the famous short story "Everything that Rises must Converge" in a poem of mine. However, the mathematician in me insisted on changing it to "Everything that ...
3
votes
0answers
44 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 ...
1
vote
0answers
55 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 ...
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? ...
21
votes
5answers
4k views

Puzzle of gold coins in the bag

At the end of Probability class, our professor gave us the following puzzle: There are 100 bags each with 100 coins, but only one of these bags has gold coins in it. The gold coin has weight of ...
31
votes
1answer
2k views

Minesweeper - Chance of one-click win

I'd like to know if it's possible to calculate the odds of winning a game of Minesweeper (on easy difficulty) in a single click. This page documents a bug that occurs if you do so, and they calculate ...
6
votes
2answers
227 views

Which mathematical game or puzzle did you invent?

A couple of weeks ago, a friend of mine showed me a extension of a game we are all familiar with that he was working on. The game we know is called Tic-Tac-Toe, and he was working on his own version ...
5
votes
0answers
71 views

Algorithm for finding “fact families”

My friend's 3rd grader encountered the following question regarding "fact families" on her math homework: I was in 3rd grade sometime in the 1980s, so I don't believe I ever encountered this term ...
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?
0
votes
2answers
360 views

How much the shopkeeper loses? [duplicate]

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 ...
2
votes
2answers
234 views

The water heater problem ( mathematician or plumber)?? [duplicate]

Isn't it absurd? $\textbf{Problem-}$ Suppose my water heater broke and heat in my apartment raised high. I went to a "person" to ask him to take a look at it, he came to my apartment, used a bunch of ...
3
votes
1answer
113 views

Eight queens problem, wondering about the non-unique solutions

I've done the code that generates all the solutions. But know I am suppose to filter out any redundant solutions based on symmetry and rotations. I have code for vertical symmetry, horizontal ...
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
51 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
5answers
15k views

Probability of winning a prize in a raffle

My work is having it's annual Christmas raffle today. 1600 tickets have been sold, and there are 40 prizes to win. I have bought ten tickets. What are the odds I will win a prize? While an initial ...
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: ...
4
votes
2answers
94 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: $\displaystyle\lim_{h\to0}\frac{e^{(x+h)\ln(x+h)}-e^{x\ln(x)}}{h}$ ...
91
votes
8answers
3k views

Probability that a stick randomly broken in five places can form a tetrahedron

Edit (June. 2015) This question has been moved to MathOverflow, where a recent write-up finds a similar approximation as leonbloy's post below; see here. Randomly break a stick in five places. ...
0
votes
5answers
77 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 ...
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 ...
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 ...
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) ...