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

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3
votes
0answers
18 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
7 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 ...
3
votes
12answers
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, ...
-4
votes
0answers
24 views

Convoluted ways to solve simple questions. [on hold]

I am trying to find complex ways to solve normally simple questions. For example, finding the area of a circle with radius r. Instead of doing $$A=πr^2$$ I would instead do ...
2
votes
2answers
40 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 ...
14
votes
3answers
917 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 ...
-6
votes
0answers
27 views

how do you solve this equation? [on hold]

what is this equations exactly?
0
votes
3answers
23 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 ...
0
votes
1answer
24 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 ...
5
votes
1answer
48 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 ...
0
votes
0answers
35 views

Two Shortest Distance of 20 Address [closed]

Using Google's Distance Matrix API I created a 20 by 20 Matrix (20 Addresses) IE: A1 A2 A3 A4.... A1 0 3 7 1 | Sum of this row... A2 3 0 2 8 | Sum of this row... A3 7 2 0 ...
-4
votes
0answers
52 views

Will this happen, if this happens? [closed]

If a monkey takes over the universe, will all monkeys on Earth die? Answer this question, yes, no, or unable to be determined. I believe that the answer to this question can NEVER be determined, ...
9
votes
3answers
148 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 ...
5
votes
3answers
719 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 ...
5
votes
3answers
111 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 ...
1
vote
1answer
59 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 ...
2
votes
0answers
24 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 ...
3
votes
5answers
88 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 ...
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
31 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
2answers
133 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 ...
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
35 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, ...
-4
votes
1answer
69 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
90 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 ...
0
votes
0answers
47 views

Combinatorial Problem; With a Catch

Good evening, My problem is as follows: You have N points that may be connected by K different lines. Only one line may connect two different points at one time. K will be at least (N-1) and no more ...
0
votes
1answer
28 views

Theoretical insect population growth limit

Fire Ant mounds are rising in my yard: if a mound can have only one queen, and she lays $50$ viable eggs per day, and if $2\%$ of the population dies per day, what is the limit of population growth? ...
7
votes
0answers
138 views

Here is a riddle that I have no idea how to solve.

Okay, so I was trying to solve this riddle found here. It is a diagram of a star with 16 points. Each point corresponds uniquely to a number between 1 and 16. The letters on each point represent a ...
1
vote
1answer
54 views

How can I get the maximum score without iterating all possibilities?

Suppose I have a set of number $S = \{0,\ldots,n-1\}$. I have to find a partition $$P = {\arg \max}_{P \in \mathcal{P} \text{ and } P \text{ is a partition}} \operatorname{score}(P)$$ A partition ...
1
vote
1answer
43 views

FLATLAND's sphere intersection scenario, explored for four dimmensions

I recently finished this wonderful new vintage edition of FLATLAND. http://amzn.com/918775116X In 1884, Edwin Abbott wrote this strange and enchanting novella called FLATLAND, in which a square who ...
4
votes
0answers
89 views

StackEgg optimal algorithm

What is the minimum number of days that is needed to complete the StackEgg game? (It's on the right if anyone didn't notice.) There are four markers (Questions, Answers, Users, Quality) I believe each ...
3
votes
0answers
78 views

Funny translations of mathematical words [closed]

As already noticed in this question there are some mathematical words that literally translated from a language to english (or from english to this language) means something totally different. A few ...
2
votes
0answers
57 views

Does typesetting of mathematical content differ in right-to-left languages?

Languages such as Arabic or Hebrew are written right-to-left. Does the way mathematical content is written differ in those languages? Some simple examples of which I would be interested to know how ...
3
votes
1answer
119 views

A joke proof of a famous mathematician showing that a certain two-digit number is prime

There was a joke (highly sophisticated, non-elementary) proof of a famous mathematician showing that a certain two-digit number (like 43 or 83 but I forgot what) is prime. Could you remind me of a ...
2
votes
1answer
57 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 ...
1
vote
2answers
31 views

What was the average speed for the whole journey?

Last weekend I went to London ... I calculated my average speed going to London was 30 mph On the return journey the traffic was terrible and I calculated an average speed of 20mph What was the ...
0
votes
0answers
38 views

Geometrical properties of tetrahedra under rotation

Consider two tetrahedra which share the same point of origin but differ in both scale and rotation over the X-axis. Can someone explain why the following points meet with these parameters? Both have ...
9
votes
4answers
349 views

Big List of examples of recreational finite unbounded games

What are some examples of mathematical games that can take an unbounded amount of time (a.k.a. there are starting positions such that for any number $n$, there is a line of play taking $>n$ times) ...
4
votes
1answer
65 views

Maximum number of points you can put on grid $ n\times m$ with no equidistant?

Assume we have a grid of $n\times m$ points. and the distance between two rows or two columns is 1 ( unit ). I have a couple of questions related to this grid:- What is the list of possible length ...
-1
votes
0answers
67 views

diophantine-equations

Why there are no solutions in positive coprime integers for the following diophantine equation $$2x^3 + y^2 = z^k$$ where, (x,y,z) are (pairwise) positive coprime integers, and k is positive integer ...
2
votes
4answers
158 views

Recurrence relation for right-angled triangles stuck-together

Given the image: and that $x_0 = 1, y_0=0$ and $\text{angles} \space θ_i , i = 1, 2, 3, · · ·$ can be arbitrarily picked. How can I derive a recurrence relationship for $x_{n+1}$ and $x_n$? I ...
1
vote
2answers
159 views

The Probability Riddle

While working on a mathematical model we have come across a problem that seems easy yet has a bunch of intelligent, mathematically trained people start doubting themselves :). Riddle us this... ...
0
votes
1answer
17 views

Is a series that contains the index term a function of the same series without the index term?

Can it be shown that $U_{2} = \sum_{i=1}^{n} [i*g(Y_{i})]$ is a function of $U_{1}=\sum_{i=1}^{n} g(Y_{i})$ ? My intuition tells me that this is not true because of the changing (for lack of a ...
1
vote
1answer
32 views

Why is 438579088 a perfect digit-to-digit invariant?

A PDDI (perfect digit-to-digit invariant) is a number which is also the sum of each of it's digits raised to them self. My main problem with the number 438579088 being a PDDI is the 7th number - 0. ...
3
votes
1answer
47 views

Tiny arithmetic trigonometry anomaly

$1.96\sin(149^\circ) + 1.00842\sin(203^\circ) + 0.61446\sin(285^\circ) = 0.02193075901$ But if I calculated each of the terms separately, then add them together, I get a result that is a tiny bit ...
1
vote
1answer
43 views

Propability of M-faced dice rolling a greater result than an N-faced dice ( M<N) and expected value of the absolute difference?

Hello I have a game-mechanic which goes like this: Two-sides are rolling numbers. The defender rolls between [1,Armor_Value] , attacker rolls between [1,Damage_Value]. If the attacker_roll> ...
8
votes
0answers
163 views

Mathematical properties of two dimensional projection of three dimensional rotated object

Please be gentle as I do not have any degree in maths. By using a compass/straighedge method to construct Metatron's cube, a regular dodecahedron can be inferred from intersecting points. I'm looking ...
6
votes
2answers
176 views

Mystical looking graphs (three-dimensional rotating hearts)

Plop the following into Google: $$ 2-\sqrt{1-x^2-(y-|x|)^2}\cos(30(2-x^2-(y-|x|)^2)),\tag{1}\\ \text{$x$ is from $-1$ to $1$, $y$ is from $-1$ to $1.5$, $z$ is from $1$ to $2$} $$ Here is the result ...
3
votes
3answers
90 views

Choosing new teammates

My sister gave me a combinatorical riddle. It doesn't appear to be hard, but I ask you if my thoughts are right, just for certainty. Here it is. Assume you belong to a group of $100$ people, and ...
2
votes
6answers
85 views

Prove that the series $\sum_{1}^{\infty}\frac{k}{(k+1)(k+2)(k+3)}$ converges and find its limit

I try to split the summand into differences, but that seems to be a futile way in our case right here, because the numerator is $k$, instead of a given number. A closely-related series, say ...