Tagged Questions

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

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4
votes
0answers
73 views

Combinatorial prime problem

Update As Barry Cipra noted in the comments, a better framing of the question might be that I'm looking at differences $a−b$ for $5$-smooth numbers $a$ and $b$ satisfying the conditions ...
0
votes
1answer
44 views

Combinatorial prime puzzle

Is it true that no prime larger than $241$ can be made by either acting or subtracting $2$ coprime numbers made up out of the prime factors $2,3,$ and $5?$ Update Above example is clearly wrong, as ...
1
vote
1answer
26 views

looking for specific recreational math puzzle book

Long time ago, I read a (recreational) math puzzle book and I remember was that in the pocket book there was a puzzle where the parents of a worm were deciding how big the blanket for their baby ...
3
votes
2answers
70 views

How to derive an proof for this infinite square root equation?

Here is continuous square root, namely: $\sqrt {1 + a \sqrt {1+b \sqrt {1+c\sqrt {1 +...}}}}$= any integer Find $a,b,c,d,e,f,...$ in general Uh, very interesting algebra pre-calculus problem, yet ...
2
votes
2answers
348 views

John von Neumann- Exercise about a Fly and two Trains [duplicate]

A fly is flying between two trains, each travelling towards each other on the same track at 30 km/h. The fly reaches one engine, reverses itself immediately, and flies back to the other engine, ...
-1
votes
2answers
17 views

City A is 800 miles from city B. City B is 1500 miles from city C. Which of the following could be the distance from city A to city C? [closed]

City A is 800 miles from city B. City B is 1500 miles from city C. Which of the following could be the distance from city A to city C? a) 600 b)1000 c)1200 d)1500 e)2000 f)2500
-1
votes
1answer
40 views

Using the difference equation to find the problem. [closed]

let $a_1 = 2\sqrt 2$ and for any $n>1$ define $a_n = 2^{(n+1)/2}\sqrt{2^n - \sqrt{4^n - (a_{n-1})^2}}.$ Find $a_n$ in closed form and evaluate $\displaystyle\lim_{n\to\infty} a_n.$
1
vote
2answers
108 views

Two math professors problem

My friend asks me a question from internet. The question is as follows Two math professors, professor Uno and professor Dos, play chess at the park while reminiscing about their past. Prof. ...
0
votes
6answers
70 views

How to know a number is divisible by a given number without using a calculator?

My question is simple and comes from my curiousity during studying math. How to know a number is divisible by $7$ or $13$ without using a calculator? For example, how do we decide intuitively that ...
-5
votes
4answers
72 views

Tea with grandmother [closed]

My mother still makes tea with the old saying: one spoon per person and one for the pot. We used to buy a packet of tea every week but since grandmother came to live with us we have to buy two packets ...
7
votes
1answer
39 views

Is every point on a Menger Sponge visible from the outside?

Choose an arbitrary point on the surface of a Menger Sponge. Can you find a straight line starting at that point and extending beyond the sponge that doesn't intersect the sponge anywhere else? That ...
-2
votes
2answers
116 views

I need to fill in all the operations to that 123456789= 1998

i got a problem that 123456789=1998, and i need to fill in the operations between each digit. all of the numbers are single digits so they can not be combined like 2 3 equaling 23. between each digit ...
0
votes
2answers
68 views

About the rationality of $1.1010010001\dots$ [duplicate]

Let's define $\rho=1.1010010001\dots$ which can be expressed by: ...
1
vote
1answer
36 views

Armstrong numbers in base 90

Are there any Armstrong numbers (narcissistic numbers) in base 90? Of course, except the one-digit ones. There don't seem to be. Just curious.
2
votes
0answers
55 views

area estimation with tiling

For any given shape drawn on a graph paper, a kid can calculate the area of any shape by counting the tiles with a simple formula: any edge covering 50% or more, mark the tile; total area = sum all ...
2
votes
1answer
62 views

Brainteaser Switches

You have four switches that could be on or off that are configured in a 2x2 grid. You are given an initial configuration that is random and you are blindfolded. (a) Can you possibly find the ...
4
votes
0answers
52 views

Quantifying infinitely large sums such as $\sum_{x\in\mathbb{R}^+} x$

I thought of this as a student in calculus years ago, and it may be a silly kind of question. I wondered if there were notions of different sizes of infinity a series might sum to, which then lead me ...
1
vote
3answers
50 views

Why is the three utility problem important?

I came across this problem on this website, even though it was fun to answer it there was something sad I realized, and I wanted to ask this from the Math Stack Exchange community. The question: A ...
4
votes
3answers
93 views

How many perfect shuffles are needed to go back to initial state?

The other day, in a popular-science book, I saw: Given 32 cards ($c_i$ for $i=0..31$), cut the deck into two parts and shuffle them the American way (riffle shuffling). The deck now looks like: ...
1
vote
1answer
45 views

Find the number of people in the family

PRE-RMO 2014 question 14 (set-A) One morning,each member of Manjul's family drank an 8-ounce mixture of coffee with milk. The amounts of coffee and milk varied from cup to cup, but were never zero. ...
1
vote
5answers
77 views

Game Theory - First move vs second move advantage?

This question came up in a lunchtime discussion with coworkers. None of us are professional mathematicians or teachers of math, and we weren't sure how to get the answer. I apologize in advance if my ...
0
votes
1answer
36 views

Calculate winner of soccer match

I am writing a program that simulates a soccer tournament between countries using their FIFA rankings. I am looking for a function that takes two country rankings and outputs a number between (about) ...
19
votes
1answer
390 views

Infinite staircase to a circle

Suppose you start at $(0,0)$ on the unit disc and repeat the following procedure again and again: Face east and walk half-way to the circumference. Face north and walk half-way to the circumference. ...
0
votes
0answers
17 views

External tangent to the circle

http://www.artofproblemsolving.com/Wiki/index.php/2006_AMC_12A_Problems/Problem_19 I don't understand why L1 'clearly' bisects the angle formed by L2 and the x-axis. Is this a standard result ...
1
vote
0answers
54 views

measuring the curvature of a pringle

Assuming for the sake of argument that a pringle shaped potato chip has a constant negative curvature, (which according to http://math.stackexchange.com/a/617610/88985 it is not ) see also picture ...
1
vote
0answers
58 views

Big list of fun mathematical book to “play” with classmates

I am searching for some fun maths books "have fun" (mathematically) with my classmates. To give you a better idea of what I'm looking for, I'll mention some books that I find suitable: Roger B. ...
4
votes
2answers
122 views

I have used Cauchy and Jensen. It is not helping me very much. Advice on solving this problem.

Let $a$, $b$ and $c$ be positive real numbers with $abc=1$. Prove that $$ \frac{a^{n+2}}{a^n+(n-1)b^n}+\frac{b^{n+2}}{b^n+(n-1)c^n}+\frac{c^{n+2}}{c^n+(n-1)a^n} \geq \frac{3}{n} $$ for each ...
3
votes
1answer
50 views

If the permuted set of $(1,2, \dots n ) $ is such that sum of any two adjacent numbers is a square. Find the generalized form of $n$.

$ \text{Let}$$ P(n) \text{be permutation of}$$ (1,2 \dots n)$$ \text{such that if}$$ P(n)={a_1,a_2, \dots a_n} $$ \text{then} $$(a_i+a_{i+1})=k^2$$ \text{where}$$ k\in \mathbb{N}$ and $i \in {1,2,3, ...
4
votes
0answers
86 views

Can -9 to 9 be placed in 41 lines of zero?

The cubic curve $2x^3-4x^2y+2xy^2-8x+y^3-y$ can be used to get lattice points allowing the placement of the numbers $-8$ to $8$ so that all 32 triplets that sum to 0 will be a straight line of three. ...
1
vote
0answers
51 views

Are there tricks to solve seating arrangement problems?

How are seating problems solved in general? I am stuck on this one for example. There are 8 houses in a line and in each house only one boy lives with the conditions as given below: Jack is not the ...
1
vote
1answer
37 views

7th grade percentage question

In the year $2010$, John's monthly salary was $\$3500$. John's monthly salary in $2010$ was $25\%$ more than it was in $2009$. Calculate his monthly salary in $2009$. Many of us debated the answer ...
6
votes
0answers
69 views

Name of a certain set

I want to know if there is any already-standard way to refer to the sets described as follows. For a set $X$, let $-X = \{-x: x \in X \}$; call it the negative of $X$. Take the set of all primes in ...
2
votes
3answers
100 views

Is there a shortcut for raising 2 to the power of a number (e.g. $2^{27}$)?

In networking, when dealing with subnetting, you convert the net mask to binary and count the number of ones (for the example in the question there would be $27$ $1$'s) and to figure out how many ...
2
votes
1answer
4k views

Probabalistic proof of green-eyed dragons logic puzzle

I came across the "green-eyed dragons" puzzle (alternatively known as the "blue eyed villagers" puzzle). The typical proof uses a straightforward inductive strategy. I came up with a probabalistic ...
0
votes
1answer
103 views

Loonies and Toonies Combinatorics

How many ways can you make $n$ Canadian dollars using only loonies (Canadian \$1 coins) and toonies (Canadian \$2 coins) such that the numbers of loonies and toonies are different from one another? I ...
8
votes
1answer
195 views

How to prove that $\frac{1}{x_1}+\frac{1}{x_2}+…+\frac{1}{x_n}-\frac{1}{x_1x_2…x_n}\in \mathbb{N}\cup \{0\}$

Question: Show that for every natural number $n$ there exist $n$ natural numbers $ x_1 < x_2 < ... < x_n ,$ such that $$ ...
1
vote
0answers
83 views

Why is $2^{16} = 65536$ the only power of $2$ less than $2^{31000}$ that doesn't contain the digits $1$, $2$, $4$ or $8$ in its decimal representation

$65536$ is the only power of $2$ less than $2^{31000}$ that does not contain the digits $1$, $2$, $4$ or $8$ in its decimal representation. http://en.wikipedia.org/wiki/65536_%28number%29
1
vote
1answer
107 views

How to find Fantasy Football Playoff Probabilities

A friend of mine came to me a few hours ago wondering what the probability of him making the playoffs were in our fantasy football league. I originally thought it wouldn't be too hard to figure out, ...
1
vote
1answer
43 views

Average rate of speed relative to a given point

For this question I am mainly concerned about points A and B on the image below and the image below hopefully helps illustrate my question. If point B is fixed and A has to move in a strait line in ...
0
votes
2answers
57 views

The water heater problem ( mathematician or plumber)??

Isn't it absurd, I mean doesn't it make probability 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 ...
1
vote
0answers
22 views

Maximum number of non-zero entries ,such that no two non-zero entries are on the same row or column.

In an M x N matrix such that all non-zero entries are covered in "a" rows and " b" columns. Then the maximum number of non-zero entries ,such that No two non-zero entries are on the same row or column ...
1
vote
0answers
23 views

Which $L \subset [0,1]$ equal the set of limits of a sequence of a sequence in $[0,1] \setminus L$?

I was glanced at this question here and it cause me to wonder the following: Question: Is there a simple description of the subsets $L \subset [0,1]$ with the property that there exists a sequence ...
1
vote
1answer
26 views

What's known about magic cubes of order 4?

An earlier question asked for a demonstration that there is no magic cube of order 4. The question was closed and deleted. I think it's worth having some information on magic cubes on m.se, so I'm ...
0
votes
0answers
76 views

Why does $\infty !$ equal $\sqrt{2\pi}$? [duplicate]

It seems at least counterintuitive. Is this related to the way we do non-classical summations?($\displaystyle\sum_{k=1}^{\infty} k=\zeta(-1)=-\frac{1}{12}$ etc)
0
votes
2answers
47 views

3 Knights and Knaves

I have been struggling with this problem: Knights always tell the truth but knaves never tell the truth. In a group of three individuals (who we will label as N1, N2, and N3) each is either a knight ...
1
vote
4answers
94 views

Example of a non-trivial function such that $f(2x)=f(x)$

Could you give an example of a non-constant function $f$ such that $$ f(x) = f(2x). $$ The one that I can think of is the trivial one, namely $\chi_{\mathbb{Q}}$, the characteristic function on the ...
0
votes
1answer
21 views

Possible Number Combos That I can not figure out [closed]

I am wondering, I have 4 QB's, 8 RB's, 12 WR's, 4 TE's, 4 K's, 4 Def, I can only play 1 QB, 2 RB's, 3 WR's, 1 TE, 1 K, 1 DEF for a total of nine players. How many different combinations do I ...
7
votes
0answers
61 views

For what numbers is $a_{b}= b_{a}$? (Reference?)

A student recently asked me about solutions to the equation $$a_{b} = b_{a},$$ where the subscript notation $a_{b}$ denotes interpreting the digits of $a$ in base $b$. It turns out there are tons of ...
0
votes
0answers
11 views

Finding where plots may cross with octave / matlab

I have several data points that are plotted below and I would like to find the frequency value when the amplitude value crosses 4. I've included an example along with the data points in the example ...
0
votes
1answer
82 views

how $2x=x$ , related to differential calculus [duplicate]

can anybody please tell me what's happening here ? $$1^2=1$$ $$2^2=2+2$$ $$3^2=3+3+3$$ $$x^2 = x+x+\cdots+x \mbox{ ($x$ times)}$$ differentiating both the sides $$2x = 1 + 1 + \cdots+1 \mbox{ ...