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

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2
votes
2answers
39 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
101 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
122 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
51 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
35 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? ...
8
votes
1answer
279 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
0answers
60 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
68 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
99 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
97 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
68 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
155 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
79 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
54 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
42 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
536 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
76 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 ...
3
votes
4answers
176 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
181 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
21 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
43 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
53 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
66 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> ...
9
votes
0answers
241 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 ...
3
votes
3answers
95 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
89 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 ...
47
votes
10answers
1k views

Fake induction proofs

Question: Can you provide an example of a claim where the base case holds but there is a subtle flaw in the inductive step that leads to a fake proof of a clearly erroneous result? [Note: Please do ...
2
votes
2answers
60 views

Are there integers a, b, c, d generating four right triangles with integer sides?

To make this more precise, we are looking for four (ETA: distinct) positive integers $a$, $b$, $c$, and $d$, such that $\sqrt{a^2+b^2}$, $\sqrt{b^2+c^2}$, $\sqrt{c^2+d^2}$, and $\sqrt{d^2+a^2}$ are ...
0
votes
1answer
35 views

How to get real value after discount.

Suppose my item real value is 100. and i have given discount 10 % to my customer. Now the changed value of item id 90. If i set value 110 and give 10% discount then i got result 99. but i need result ...
2
votes
1answer
34 views

Would the powerset of $\mathbb{Z}$ also not denumerable?

Would the powerset of $\mathbb{Z}$ also be not denumerable?, Since Cantor's theorem says that the $\mathbb{N}$ is denumberable but the powerset of $\mathbb{N}$ is not denumberable because there does ...
0
votes
2answers
98 views

How would you prove that $2^{n-1} > n!$?

How do i prove that $2^{n-1} < n!$ for all $n \ge 1$ This is my proof: Base case: Let n=1 then $2^{1-1} =1$ is the same on the right side so it holds Inductive step: let $k \le 1$ we assume that ...
0
votes
1answer
57 views

How to tell if a function and a composite function is onto or one to one

For each of the following, f : A → B, g : B → C. Which one are true and which ones are false? So far i have, f is onto but g ◦ f is not onto. (False) f is 1-1 but g ◦ f is not 1-1. (False) g is onto ...
1
vote
2answers
37 views

How to prove if $A \times C \subseteq B \times D \implies A \subseteq B$

My proof Given $(x,y) \in A \times C \implies x \in A$ and $y \in C$ since $A \times C \subseteq B \times D$ then $(x,y) \in B \times D$ then $x \in B$ and $y \in D$ since $x \in A$ and $x \in B$ ...
0
votes
2answers
57 views

How to prove intersections and subsets of sets

Simple proofs for these are pretty straight forward such as proving if two sets are equal then they are subsets of each other or if you want to show one set is a subset of the other just show that ...
0
votes
0answers
32 views

How can you prove that a collection of union set is equal to the set of natural numbers?

For example $\bigcup_{n\in \mathbb{N}}A_n=\mathbb{N}$ My proof, to prove that two sets are equal i must show that they are subsets of each other. I understand how to show $\bigcup_{n\in ...
2
votes
1answer
53 views

Find $a_{n}$ if $(a_{n})$ is a sequence such that $a_{1} := 1$ and $\frac{1}{a_{n+1}} = \frac{2}{a_{n}} + 3$ for $n \geq 2$?

This problem is weird. By the initial condition $a_{1} = 1$ we have $a_{2} = \frac{1}{5}$ and so on. But is there really a pattern for $a_{n}$? I guess this problem is that kind of problems that ...
1
vote
2answers
46 views

Find an integer $k$ such that $a_{k} = 2^{261}$?

Let $a_{1} := 2$ and $$a_{k} := \frac{2^{(k+1)(k+2)/2}}{\prod\limits_{j=1}^{k-1}a_{j}}$$ for all integers $k \geq 2.$ The problem is to find an integer $k$ such that $a_{k} = 2^{261}.$ The ...
15
votes
2answers
326 views

Do any of these sequences have infinitely-many distinct iterates under run-length substitution?

Let $$S = \{x \in \{1,2\}^\mathbb{N}: \ \text{every run in }x\text{ has finite length}\}$$ and define $$T: S\to \mathbb{N}^\mathbb{N} $$ such that for any $x\in S$, ${T}x$ is the sequence of ...
0
votes
1answer
83 views

How to prove that there are no integers a,b such that $b^2=4a+2$

How to prove that there are no integers a,b such that $b^2=4a+2$ This seems like a very simple prof but when i tried to work through it i keep on hitting walls. I tried to prove this by ...
0
votes
1answer
38 views

Anyone know of a good composite number counter?

I am looking for a chart that would show how many composite numbers there are under "n" broken out by how many factors they have. Has anyone seen a chart like this? Example information I am looking ...
0
votes
1answer
46 views

Implications of redefining base natural logarithm constant e

Disclaimer: I'm no math expert! I understand that the constant $$e$$ is expressed as follows: $$e = \sum_{n=0}^{\infty} \frac1{n!} = 1 + \frac1{1*1} + \frac1{1*2} + ...$$ What would be the ...
1
vote
1answer
43 views

Name of this type of plot? Does anyone know how to produce it

Does this type of polar plot have a name? Does anyone know how to produce it in octave 3.8.1 which is compatible with matlab? Link to site
0
votes
1answer
22 views

Price Difference Question. Unable to derive 3rd equation

A man buys Rs.7 apples. When after a few days the price of the apple goes down by Rs.2, he buys 6 more apples. Both the amounts were in whole numbers, were two digits and has the same digits. Find ...
-2
votes
1answer
48 views

When A was half B's age, B was one fourth A's age.

The question goes like this : A told B, "When I was half your present age, you were one -fourth my present age". If A is currently 60 yrs, how old is B ? I am unable to form equations for the ...
1
vote
0answers
20 views

Discrete Model Finding Stability

For the discrete model $$x_{t+1} = (\lambda +1)x_t +x_t^3$$ Draw a bifurcation diagram (expressing the equilibrium vs $\lambda$ for values of $\lambda$ near zero. I have the bifurcation diagram. It ...
2
votes
1answer
83 views

Convergence in probability iff convergence for every bounded continuous function

I'm trying to show the following: $X_n \overset{p}{\to}X \iff f \circ X_n \overset{p}{\to} f \circ X$ for every continuous, bounded function $f$. I can show ($\Rightarrow$) already using the usual ...
8
votes
5answers
237 views

What multiples of $d$ are still multiples of $d$ when they have their digits reversed?

I teach at a school for 11 to 18 year olds. Every term I put up a Challenge on the wall outside my classroom. This question is one that I have devised for that audience. I think that it is quite ...
4
votes
0answers
56 views

Conway's Game OF Life maximum periods on a set x by x game board.

I have taken interest in Conway's Game of Life and want to know if you guys can help me with a mathematical problem :) That is what this website is for right? You need to be familiar with the rules ...
4
votes
5answers
108 views

Find all possible values of $ a^3 + b^3$ if $a^2+b^2=ab=4$.

Find all possible values of $a^3 + b^3$ if $a^2+b^2=ab=4$. From $a^3+b^3=(a+b)(a^2-ab+b^2)=(a+b)(4-4)=(a+b)0$. Then we know $a^3+b^3=0$. If $a=b=0$, it is conflict with $a^2+b^2=ab=4$. If $a\neq0$ ...
0
votes
1answer
33 views

How to prove that A $\subseteq$B $\implies$ |A|$\le$|B|?

How to prove that A $\subseteq$B $\implies$ |A|$\le$|B|? I know that for |A|$\le$|B| there has to be a function f:A $\mapsto$B which is an injective function. But i get stuck because the sets A and B ...