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

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1
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0answers
58 views

sum of integers of two exponents equal

For what values of n, such that $n \in \mathbb{Z}^+,$ does the sum of digits $(214)^n$ and $(2014)^n$ equal? So I found $1$, which is fairly obvious, there are supposed to be more?
0
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2answers
135 views

How do you solve “sum of ages” puzzles?

Ma and Pa and brother and me. The sum of our ages is eighty-three. Six times Pa’s age is seven times Ma’s age, and Ma’s age is three times my age. What is Pa’s age? What is Ma’s age? What is my ...
0
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1answer
56 views

Placing bricks on Board

Situation: I have a $8\times 8$ board (sic), but two squares from it's one diagonal are removed (Black colored squares are removed) I'm given with plenty of(Rectangular) bricks having dimensions $...
0
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3answers
139 views

The fly flying between two trains

I know this question has been posted many times, but I don't understand it. Two trains travel on the same track towards each other, each going at a speed of 40 kph. They start out 180km apart. A fly ...
13
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1answer
318 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 absolute differences $|a−b|$ or totals $a+b$ for $5$-smooth numbers $a$ and $b$ satisfying ...
0
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1answer
76 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
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1answer
63 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
118 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
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1answer
773 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
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2answers
224 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
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6answers
181 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 ...
8
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1answer
82 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 ...
0
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2answers
85 views

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

Let's define $\rho=1.1010010001\dots$ which can be expressed by: $$\rho=\frac{1}{10^{0}}\underbrace{+\frac{1}{10^{1}}}_{\text{power}+1}\underbrace{+\frac{1}{10^{3}}}_{\text{power}+2}\underbrace{+\frac{...
1
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1answer
60 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
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0answers
96 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
76 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
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0answers
217 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 ...
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3answers
80 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
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3answers
126 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
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1answer
72 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. ...
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4answers
558 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
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1answer
147 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) ...
20
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1answer
497 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. ...
1
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0answers
170 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 ...
4
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2answers
175 views

If $abc=1$, then $\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} $

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 ...
6
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2answers
97 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
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0answers
97 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
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0answers
309 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
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1answer
47 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 ...
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0answers
157 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
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3answers
3k 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 ...
4
votes
4answers
7k 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
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1answer
146 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
231 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 $$ \frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}-\frac{1}{x_1x_2......
6
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1answer
179 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
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1answer
1k 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
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1answer
55 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 ...
2
votes
2answers
400 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 ...
1
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0answers
82 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
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0answers
48 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
72 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 ...
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2answers
137 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 ...
2
votes
4answers
254 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
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1answer
27 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
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1answer
95 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 ...
1
vote
2answers
188 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 note: this is an example and the amplitude ...
1
vote
1answer
103 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{ ...
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1answer
50 views

How do I calculate surface area given a three dimensional coordinates of a face?

I have three dimensional coordinates of a face, how do I calculate surface area?
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2answers
195 views

Construct numbers using digits $123456789$ and the operations $+,-,×,÷$

From an old book I found the following question. Use the digits $1,2,3,4,5,6,7,8,9$ and the operations $"+,-,×,÷"$ with $( )$ for construct the result $100.$ During the computations the order of $...
1
vote
1answer
34 views

Mathematical reasons for hull design relative to sustainable angle of heel

I've recently been doing a comparative study of ancient Sumerian mythology relative to the book of Genesis. I am curious if there is a way to explain mathematically why a circular, square (cubic) or ...