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

learn more… | top users | synonyms (2)

0
votes
2answers
44 views

Examples of names for mathematical objects/results with proper nouns

If this question is duplicate, then I apologize. A recent conversation between a few graduate students led to the question of whether there are any mathematical objects or results with proper nouns ...
-3
votes
1answer
41 views

How many months would it take to pay off $\$2224$ computer with $\$250$ a month payment? [on hold]

The question basically tells you it all of what I need to be done... I don't know how much that would be..
0
votes
0answers
120 views

Dates with 8 consecutive digits (not in order)

On many forms, the date has to be written as DD/MM/YYYY. For example, 25 April 1736 is written 25/04/1736. Dates such as this that use eight consecutive digits (not necessarily in order) will be ...
2
votes
1answer
56 views

Compatibility of direct product and quotient in group theory

This question came to me when I tried comparing direct product and quotients of groups with products and quotients of natural numbers. When we divide a number by another and multiply the result with ...
1
vote
0answers
63 views

Is the solution to this elementary number theory problem correct?

Problem: A natural number $n$ is called nice if the following properties hold: • The expression is made ​​up of 4 decimal digits; • the first and third digits of $n$ are equal; • the second and ...
1
vote
0answers
28 views

Shortest smooth paper Möbius Strip

I want to make a familiar Möbius strip of width 1 unit satisfying the physical properties of paper. Assume paper is a ruled surface, and the strip has to be smooth and non-self-intersecting. What ...
313
votes
7answers
12k views

“The Egg:” Bizarre behavior of the roots of a family of polynomials.

In this MO post, I ran into the following family of polynomials: $$f_n(x)=\sum_{m=0}^{n}\prod_{k=0}^{m-1}\frac{x^n-x^k}{x^m-x^k}.$$ In the context of the post, $x$ was a prime number, and $f_n(x)$ ...
2
votes
0answers
40 views

Can i connect these points in a way that satisfies these conditions?

I apologise in advance for the horrible phrasing. If you imagine 3 points like this: You would then draw a path between A and B and another between B and C, such that the length of the line AB is ...
4
votes
2answers
108 views

What is a good approach to demonstrate solvability of this type of puzzle without use of brute-force?

I chanced upon this puzzle in this question on the Anime & Manga site, and, like the OP, tried to solve it without any success. Here is a representation of the puzzle: the blocks may only be moved ...
20
votes
1answer
428 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
vote
1answer
50 views

Is self study of proof-based mathematics difficult?

I heard from a renowned Mathematician that self study of proof based Mathematics is extremely difficult as there is not only right and wrong but also degree's of correctness. So without a teacher ...
84
votes
17answers
14k views

How do you find the center of a circle with a pencil and a book?

Given a circle on a paper, and a pencil and a book. Can you find the center of the circle with the pencil and the book?
0
votes
1answer
38 views

Are there any system(s) of mathematics whose relationship between variables bears difference to that found within mainstream mathematics?

I have been reading up on boolean algebra quite recently, for those not familiar, this type of mathematical system has much to do with the way logic is represented (and is primarily applied to, though ...
-5
votes
0answers
51 views

Uses of numbers in unusual ways [closed]

I am trying to find examples of either mathematical proofs or real world applications of numbers in fairly strange ways and places. Examples like $${x}^{1/\pi}$$ or $$\ln^ex$$
5
votes
14answers
2k views

Measure 11 liters using bottles of 16, 6, and 3 liters

This question has been bugging me for a day and finally I gave up and decided to ask the community for it so here's how it goes: Suppose we have 3 bottles with capacities of $16,6$ and $3$ liters, ...
2
votes
1answer
30 views

Tower of Hanoi variation from Concrete Mathematics - possible arrangements

From Concrete Mathematics, there is a problem that describes a variation of the Towers of Hanoi, where the disks can not move directly from peg $A$ to peg $B$, but must go through a middle peg. ...
6
votes
1answer
156 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
3
votes
3answers
253 views

Cover a cicular hole with planks

A friend of mine asked me the following question. Whats the minimum number of rectangular planks of unit width (and infinite length) needed to cover a circular hole with diameter $n$? ...
0
votes
0answers
14 views

Mathematics in Football- Foul play and goal-scoring opportunity

I am reading an article talking about the mathematics in football (link: https://plus.maths.org/content/ball ). In the second part, it asks if a player should risk being sent off in order to gain the ...
1
vote
3answers
29 views

Units of Measure conversion

I was wondering if i could get some help trying to create a simple math formula. I recently was given an interview to work as a tier1 programmer and was asked to make a program. I made the whole thing ...
14
votes
3answers
959 views

A fun problem by Arnold using the Poincaré recurrence theorem

I came across this problem by V. I. Arnold while studying his classical mechanics book. Consider a sequence where the $n^{th}$ term is made up by considering the first digit of $2^n$, the first ...
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 ...
0
votes
1answer
30 views

Contraharmonic mean given harmonic mean

Given that two positive integers, $X$ and $Y$, have a harmonic mean of $6.875$, what is their contraharmonic mean. Harmonic mean is $(2XY)/(X+Y)$ and contraharmonic mean is $(X^2 +Y^2)/(X+Y)$. I began ...
2
votes
2answers
43 views

How to find the number of values for $x$ and $y$?

I have come across numerous questions where I am asked for example, if $x$ and $y$ are non-negative integers and $3x + 4y = 96$, how many pairs of $(x,y)$ are there? Usually, I just use trial and ...
4
votes
1answer
648 views

Social Golfer Problem - Quintets

I wrote an article on the Social Golfer Problem, which has questions like: Each day, 16 people play Munchkin in foursomes simultaneously. How many days can they play with no two people playing with ...
8
votes
7answers
2k 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 ...
0
votes
3answers
5k views

How do you find the altitude in a pyramid? (SAT math question)

The pyramid shown above has altitude h and a square base of side m. The four edges that meet at V, the vertex of the pyramid, each have length e. If e = m, what is the value of h in terms of m? A) ...
2
votes
1answer
58 views

Number of algebraic solutions to a formula related to a square tiling problem

How can many different sets of prime-factors fit together so well in this formula? I am curious about the number of solutions to the following equation: $$ r_3 = \sqrt{2}\; \frac{ 1 + r_1 (r_2 ...
22
votes
2answers
1k views

What is the millionth decimal digit of the $ 10^{10^{10^{10}}} $-th prime?

What is the millionth decimal digit of the $10^{10^{10^{10}}}$th prime? (This prime, with more than $10^{10^{10}}$ decimal digits, is far larger than the largest "known" prime.) The answer should ...
1
vote
1answer
96 views

Cutting chocolate diagonally

Given is chocolate with rectangular pieces of size $a \times b$. If cut diagonally, how many pieces will it be split into? If knife passes exactly by co-catenating we assume there is no damage to ...
3
votes
4answers
670 views

Conway's game of life variations

Is there any known two-dimensional Conway's game of life variation where each cell can not be just on/off but able to hold more states, maybe 4 or 5?
5
votes
1answer
59 views

How many rectangles or triangles.

I have come across numerous questions where I am given the picture such as the above one been asked "how many rectangles are there?". I have even come across some slightly different images that ...
9
votes
3answers
155 views

Sum of digits of $11\dots 11^2$ where $11\dots 11$ is a 1992 digit number with all digits $1$ [duplicate]

I read this on a non-math forum where the OP says this is a question for Grade 6 elementary school students. Grade 6 elementary school level is somehow ambiguous but clearly this means no advanced ...
0
votes
1answer
250 views

Finding probability that a person gets $7$ when rolling a pair of dice

*I STILL DON'T GET THE ANSWERS PROVIDED. PLEASE HELP! In a game, the participant rolls a pair of dice. If the result is a $7$, he wins. If the outcome is a number $n$ different from $7$, he continues ...
1
vote
1answer
60 views

If every row in a square grid corresponds to a column, then every column corresponds to a row.

I am looking for a proof of the following: A square grid is filled out with symbols from some alphabet, with one symbol in each square of the grid. Each row of the grid is the same as some column ...
5
votes
3answers
854 views

Dates with 8 consecutive digits

In many places, dates are written as DD/MM/YYYY. For example, the 25th of April 1736 is written as 25/04/1736. Dates such as this one that use 8 consecutive digits (not necessarily in order) will be ...
3
votes
5answers
89 views

Can every perfect square exist as the sum or difference of two perfect squares?

I believe this is trivial and I'm over-complicating it. But can every squared integer be expressed as the sum of two squared integers OR the difference of two squared integers? And is there a proof ...
31
votes
7answers
4k views

Where is the flaw in this argument of a proof that 1=2? (Derivative of repeated addition)

Consider the following: $1 = 1^2$ $2 + 2 = 2^2$ $3 + 3 + 3 = 3^2$ Therefore, $\underbrace{x + x + x + \ldots + x}_{x \textrm{ times}}= x^2$ Take the derivative of lhs and rhs and we get: ...
5
votes
3answers
112 views

Move the last two digits in front to multiply by $6$

Here is the problem: Can you determine the smallest natural number $N>0$ not divisible by $10$, such that when you move the last two digits of $N$ to the front, shifting the other digits two ...
2
votes
0answers
26 views

How to maximize the minimal amount not payable with the exchange of at most two coins?

Background I've been thinking about payments which you can do using at most two coins. This includes three possible cases: You pay by giving one coin of the value you owe (for example, if you have ...
0
votes
1answer
31 views

What are the steps to function design?

So I'm trying to write a program, and I want to use math functions to help it. In this example, I'm trying to change the color of a line based on the position of each pixel on the line. Anyway, I ...
1
vote
0answers
35 views

Interesting horserace counting problem

So for a horserace with no drawing horses there are n! Results. How many results will there be if the horses can draw?
2
votes
1answer
74 views

What is the _simplest_ way to solve problems of this kind?

Two doors with talking doorknockers - one always tells the truth and one always lies. One door leads to death other to escape. Only one question may be asked to either of the door knockers. What would ...
2
votes
2answers
135 views

Helping 7th grade with math question… I'm stumped.

First salesperson says 7 baubles together with 5 gewgaws is the same value as 6 trinkets Second salesperson says 4 baubles with 9 trinkets has the same value as 5 gewgaws Third salesperson says 6 ...
3
votes
1answer
180 views

Truchet tiles on a flattened cube

We have 2 Truchet tiles and a flattened cube as shown. We randomly place copies of the tiles into faces of the flattened cube. Find the probability that the circular arcs on the Truchet tiles ...
2
votes
2answers
37 views

I have an equation I would like solving.

I need to solve the following problem Decorator A is painting a large wall. At her current rate, she will complete the wall in 1 hour and 40 minutes. Decorator B is painting a similar wall, ...
-3
votes
1answer
71 views

9 hens lay 9 eggs in 9 days… [closed]

9 hens lay 9 eggs in 9 days. How many eggs will 3 hens lay in 3 days??? it's a tricky question asked by a friend and can you solve it and explain your answer.
-1
votes
2answers
93 views

Mathematics problems clock

Long ago, I had an idea of creating (actually, labeling) a clock that will have, instead of the numbers 1,…,12, important mathematical problems whose solution turned out to be that number. Such a ...
2
votes
5answers
467 views

Higher Dimenional Tic Tac Toe

Here we have a problem that seems very intuitive, but is hard to define mathematically. In Tic Tac Toe, we can find an equivalent of the game in any number of dimensions, it seems. The trick is to ...
47
votes
10answers
1k views

Arc length contest! Minimize the arc length of $f(x)$ when given three conditions.

Contest: Give an example of a continuous function $f$ that satisfies three conditions: $f(x) \geq 0$ on the interval $0\leq x\leq 1$; $f(0)=0$ and $f(1)=0$; the area bounded by the graph of $f$ and ...