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

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3
votes
3answers
42 views

How many tokens would person A have under these conditions?

Persons A and B each have a positive integer number of tokens, and the number of tokens B has is a square number less than 100. B says to A, "If you give me all of your tokens, my total number of ...
0
votes
2answers
54 views

Perimeter of Quadrilateral

The lengths of two sides of a quadrilateral are equal to 1 and 4. One of the diagonals has a lengths of 2 and divide the quadrilateral into two isosceles triangles. What is the perimeter of the ...
2
votes
1answer
48 views

How to arrange 1 to 15 such that the sum of any adjacent 3 numbers will be a perfect cube? [closed]

The numbers 1 to 15 should be arranged in a way that any 3 adjacent numbers' sum will be a perfect cube.
10
votes
1answer
158 views

On the theorem “$3$ is everywhere”

In this Numberphile video it is stated that "almost all natural numbers have the digit $3$ in their decimal representation", and a proof of this fact is proposed. A sketch of the proof follows: ...
1
vote
1answer
89 views

How many “m” digit numbers with digits that sum to “N”

How many "m" digit numbers can be formed whose digits sum to "N"? The collection of these numbers can have preceding zeros . The collection of these numbers cannot duplicate multiplicity of digits ...
2
votes
3answers
58 views

Formulize this sequence

There is this function defined as; $$f(x) = 10^x + 10^{x-1} + ...+10^0 $$ Which simply gives the 111.. kind of number, given the length x. What I need to do is a way to formulize this function, ...
2
votes
1answer
63 views

how to compare probability/ratios

For one location, I have: Number of lollipops selling at morning time Number of lollipops selling at afternoon time Selling periods: Every 30 minutes is a period, which sells lollies either ...
3
votes
3answers
40 views

First digits of a cube of a natural number

Can a cube of a number be of form: $2016a_1a_2a_3\dots a_n$? I have no direction, and would love to get a certain direction/proof. Thanks in advance
3
votes
2answers
51 views

I think I've found all roots to $f_k(x)=\sum_{j=1}^k x^j-x^{-j}$ for any $k$ - how to prove it?

Conjecture: The set of unique roots of $$f_k(x)=\sum_{j=1}^k x^j-x^{-j} \;,\;\; x \not=0$$ is given by $e^{i \pi \phi_k}$, where $$\frac{1}{2}\phi_k=\{0, \frac{1}{2}, ...
0
votes
0answers
29 views

Does this graph partitioning algorithm achieve anything interesting?

I was musing over graph clustering and partitioning, and isolating clusters, and came up with an algorithm that I think might do some interesting things. I figured I'd run it past here to get some ...
8
votes
0answers
123 views

Recreational problems in set theory?

Most areas of maths that I can think of have a number of fun, recreational problems that come under their category. Nothing deep: number theoretic stuff in olympiads, integrals, limits, products, ...
1
vote
4answers
41 views

Assumption and simple calculation

I'm having an issue with what seems to be an simple question. Here it is: Two hockey teams, team A and team B played a game, Team A beat Team B by 2 goals. The crowd was pleased as there were 8 ...
0
votes
1answer
36 views

Empirical Formula for Financial problem

I have a financial problem, which is strictly related to math of course. The problem states that on the last year the steel market price was about $450$ \$, and a company, that sells steel, used to ...
0
votes
1answer
25 views

Method to study obvious properties

Most of the time studying mathematics we come across various properties like associative, commutative,...etc. These properties are obvious and sometimes I feel why at all they are given in the text. ...
1
vote
1answer
24 views

Bingo-like Game

In one board game, each player has a unique 4 x 4 grid with squares randomly labeled with each integer from 1 to 16. As the integers 1 to 16 are randomly called, each player puts an "X" in the ...
3
votes
0answers
100 views

Polyhedra with identical faces

The isohedra have identical faces. They have symmetries acting transitively on their faces -- any face can be mapped to any other face to give the same figure. There are also polyhedra where all ...
1
vote
2answers
46 views

Mapping two integers to one: deriving formula

I have an interesting puzzle: Given two non-negative integers, let's call them $x$ and $y$, work out a formula for $z$ as shown in the table below: ...
0
votes
0answers
13 views

Limiting points

For a system of coaxial circles why are there only 2 limiting points? Shouldn't there be infinite limiting points? After all system of coaxial circles are pairs of circles which have same radical ...
1
vote
1answer
65 views

Expected Value for Number of Consecutive Cards of the Same Suit

Here is the setup. Shuffle a deck of 52 cards so their order is random (i.e., determined by a uniformly distributed random variable). Now flip through the cards and find the maximum number of ...
0
votes
1answer
27 views

Using the Fibonacci sequence and deduction to prove… [duplicate]

Using the Fibonacci sequence and induction prove that $$F_{n-1}F_{n+1}-F_{n}^2 = (-1)^n, \space \space n=1,2,3...$$ My efforts so far: The basis holds for $n=1$ Induction step: ...
5
votes
0answers
80 views

Magic square 9, Amazons, and the 2-(81,9,1) design

Consider the following order-7 magic square. The rows, columns, and diagonals all add up to the same sum: 175. Also, all the broken diagonals add up to the same sum, making this a pandiagonal ...
8
votes
0answers
115 views

Limit approximation for $\pi$ in the four fours puzzle?

The four fours puzzle is a recreational math puzzle whose aim is to express whole numbers using four occurrences of the digit 4 and a specified set of operators. A common variety permits the ...
3
votes
1answer
56 views

Golf Problem Math [closed]

Hey guys i cant seem to draw the diagram for this. I dont understand this question at all. I got this triangle but i dont know how to solve it. I only have 2 sides on it and i cant use the sin/cos law ...
0
votes
1answer
29 views

Trignometry Building Problem

Ok guys this is one of the trig recrational problems i was doing and i cant seem to draw the problem right... Please help.. A surveryor standing 69 meters from the base of the bulding measures the ...
2
votes
2answers
58 views

Does probability depend on knowledge?

There is at least $2/3$ probability that this question is rather silly, but being an almost absolute beginner in Probability, I will ask it anyway. Consider the following problem, proposed at AIME ...
0
votes
1answer
73 views

Connection between 7 and 13 [closed]

While there have been many numbers that have been deemed 'lucky' or 'unlucky', 7 and 13 are two of the most prominently known. So, this had led me to wonder if there were any connections between 7 ...
1
vote
1answer
65 views

How many 10-letter words do not contain all the vowels

I can't find where I am overcounting in the problem How many 10-letter words do not contain all the vowels. What I do is to count all the words that have at ...
2
votes
4answers
103 views

Suppose a function is expressed by: $f(x)=f(x+1) - f(x-1)$ and $f(16)=20 , f(20)=16$ What is $f(20162016)$?

Math quiz bee question Suppose a function is expressed by: $$f(x)=f(x+1) + f(x-1)$$ and $$f(16)=20 , f(20)=16.$$ What is $f(20162016)$? Attempt at solution: $f(17)+f(15)=20$ ...
0
votes
0answers
39 views

Does this resilience/resource scheduling analogy make sense?

A firend has recently presented an analogy for the rescheduling of Doctors (big topic in the UK atm) across a 7 day week as opposed to a 5 day week with a skelton staff at weekends - I'm ignoring ...
7
votes
2answers
192 views

Chinese New Year Equation 2016

In the spirit of Chinese New Year, here's a problem to commemorate the year. $\color{black}{\text{Solve the following equation for positive integers $a$ and $b$:}}$ ...
0
votes
0answers
25 views

Is $\sigma(2^r)$ a palindrome (in base $10$) for some $r > 2$, where $\sigma$ is the sum-of-divisors function?

(Note: This post is a bit related to this earlier MSE question.) The title says it all. Is $\sigma(2^r)$ a palindrome (in base $10$) for some $r > 2$, where $\sigma$ is the sum-of-divisors ...
24
votes
1answer
327 views

Is there any palindromic power of $2$?

My question is in the title: Is it possible to find $n≥4$ such that $2^n$ is a palindromic number (in base $10$)? A palindromic number is a number which is the same, independently from which ...
0
votes
1answer
13 views

Write bounds for a quantity in terms of bounds on another quantity

I have an expression that gives me the bounds for a certain variable X in terms of another variable Y. How can I write these ...
1
vote
1answer
58 views

Taking away pocket money [closed]

This is my fist post on Mathematics, so I hope my question isn't too trivial - you won't need a degree to answer this one! - but it's messing with my head.... Allow me to explain..... I'm helping my ...
5
votes
1answer
52 views

Factor the matrix (scalar $\times A$) into permutations of $A$

Here's an example of $A . B = scalar \times C$, done with magic squares. The last square does not have a consecutive range of digits. Drop the magic square requirement. In $2\times2$ matrices we ...
1
vote
1answer
75 views

Puzzle. Transfer maximal coal using a train [duplicate]

We need to transfer coal from point $A$ to point $B$ using a train. There is $9000$ tonne at point $A$. The distance between point $A$ and $B$ is $3000$ km. Train can carry only $3000$ tonne included ...
1
vote
2answers
42 views

Area of piece of paper folded around straight line of orientation $\theta$

Imagine drawing a straight line $l$ through the center of a square piece of paper with area $1$. Now fold the paper along that line. Q: What is the function for the area covered by the folded ...
1
vote
4answers
74 views

Finding the height of a Building at Night

EDIT: Method $1$ is false, as pointed out by Hetebrij. If it is night, how would one find the height of the building? By assuming I am trying to find the height of a building at night, I am ...
0
votes
0answers
23 views

Property of all k-dimesional shapes

A close friend showed me an intuitive pattern that given a k-dimensional convex polytope P, if one doubles every sidelength to generate a $P'$ it is possible to fit $2^k$ copies of $P$ within the ...
-3
votes
1answer
61 views

Counting and Abstract Problem Solving [closed]

Suppose that you have a bucket holds fiv-sev c, and one holds tw-one c. How could you use them to measure out thre c of water?
1
vote
2answers
51 views

Connecting up boxes mathematically (Puzzle)

How would you connect each black box once to each colored box without any lines overlapping, this is racking my brain so please help. Note that you can move the boxes where ever you want. Maybe ...
1
vote
0answers
34 views

square monotonic numbers

A monotonic number is a number in which the digits are in non-decreasing order. I found by computer that most of these numbers are squares of these numbers $$3 \ldots 34,3 \ldots 35,3 \ldots 37,3 ...
4
votes
2answers
118 views

recommend math books [closed]

So i completed an year ago my schooling and i am pretty good at maths well at my level and i am very interested in maths and want to learn as much maths as possible and i like stuff like number ...
0
votes
1answer
36 views

Is there a function that allows you to generate the highest multiple of a number below a certain boundary?

Say for example, that I want the highest multiple of 36 below 100. Is there a function that allows me to generate this with two arbitrary numbers?
-3
votes
5answers
97 views

Catherine is now twice as old as Jason but 6 years ago she was 5 times as old as he was. How old is Catherine now? [closed]

This is an IQ question. "Catherine is now twice as old as Jason but 6 years ago she was 5 times as old as he was. How old is Catherine now?" How to solve such questions? I think their combined age ...
2
votes
0answers
145 views

How to find Misiurewicz Points without solving huge polynomials? (Mandelbrot Set)

Here is a plot of 17,723 Misiurewicz Points. The code below generates a set of polynomials u[m,n], the roots of which have periodicity (m-n) starting at iteration n. I stopped at 17,723 points ...
5
votes
1answer
295 views

How do find the numerical average of $x^x$ from $(-4,-2)$ without x-values that give a complex output?

I wanted to find the approximate average of all real points in $(x)^{x}$ from $[-4,-2]$. This means I am ignoring all real inputs that give a complex output and need average to be a real number. To ...
4
votes
3answers
252 views

Lifting a toilet seat without breaking urine stream

Yes, I know the title is bizarre. I was urinating and forgot to lift the seat up. That made me wonder: assuming I maintain my current position, is it possible for the toilet seat (assume it is a ...
3
votes
0answers
71 views

Making $66$ with $1,1,1,1,1$

How can one make $66$ with only $1,1,1,1,1$? You cannot combine these two numbers to make a new number, such as this: $66=11 \times (1+1+1)!$. This was inspired a game of dice that I used to play, ...
5
votes
1answer
273 views

Hillary Clinton's Iowa Caucus Coin Toss Wins and Bayesian Inference

In yesterday's Iowa Caucus, Hillary Clinton beat Bernie Sanders in six out of six tied counties by a coin-toss*. I believe we would have heard the uproar about it by now if this was somehow rigged in ...