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

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0
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1answer
30 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
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2answers
30 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
22 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
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0answers
25 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
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1answer
51 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
44 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
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2answers
318 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
53 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
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1answer
35 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
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1answer
42 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
39 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
16 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
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1answer
39 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
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0answers
17 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
50 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
219 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 ...
3
votes
0answers
46 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
100 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 ...
10
votes
4answers
216 views

Tricky 3d geometry problem

We have a cube with edge length $L$, now rotate it around its major diagonal (a complete turn, that is to say, the angle is 360 degrees), which object are we gonna get? Astoundingly the answer is D. ...
2
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0answers
51 views

What is the best way to master my algebra skills without taking an algebra class?

I was in advanced math my entire life. I got through all the math I needed for my original degree. 8 years later here I am changing degrees and I need more math. I just took calculus I and I passed ...
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1answer
22 views

How to prove by induction with a set of equivalence sets?

For example Prove by induction that the operation of raising to the power m$\in$ $\mathbb{N}$ is well defined in $\mathbb{Z}_n$ $\forall$m$\in$ $\mathbb{N}$ $\forall$[x]$\in$ ...
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votes
2answers
28 views

how to prove that $x^2 + y^2 =1$ is injective and surjective depending on the restrictions?

Suppose we have $S=\{(x,y) \in [-1,1]\times[0,1]: x^2 + y^2 = 1\}$ I know this is a function since the domain(s)= $[-1,1]$ and I know this should be surjective and injective since the restriction ...
0
votes
2answers
36 views

There's addition, multiplication and exponentiation. Is there another “level” after exponentiation? [duplicate]

I guess they all can be broken back down into addition but I just have always had this burning question if there was some other mystery operator after exponentiation.
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votes
1answer
68 views

Puzzle: Players A,B,C,D are in a line

Players A,B,C,D stands in a line. Players A, D do not move. round 1: player B moves one distance closer to the midpoint of A,C round 2: player c moves one distance closer to the midpoint of B,D ...
0
votes
1answer
34 views

How to find a relation when given the distinct equivalence classes?

For example I am not sure how to approach this type of problem. I know that the equivalence classes partition $A$. Suppose $[a]= \{1,4,5\}$, $[b]=\{2,6\}$ and $[c]= \{3\}$. $[a]\bigcap[b]= ...
0
votes
1answer
18 views

How to show that a relation is an equivalence relation given a defined relation

I understand for the most part the conceptual aspects of an equivalence relation. A relation is considered a equivalence relation if it satisfies reflexive, symmetric and transitive properties but Im ...
2
votes
1answer
31 views

Puzzle requiring minimizing participant's points

Yesterday on Puzzling SE a puzzle was posted, see here I didn't get the solution posted there so I am rewriting it for discussing it here. 121 women are competing in the heptathlon in Olympic ...
0
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0answers
59 views

New Scientist Enigma 1779

I drew four right-angled triangles. The hypotenuse of my first triangle was also the shortest side of my second triangle; the hypotenuse of my second triangle was also the shortest side of my third ...
0
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0answers
41 views

maximize partitioned area puzzle…

I took the time to draw this out. It's pretty simple and also very chicken scratch. I apologize for the crudeness and chicken scratch. The part of this that throws me off is the partitioned part. ...
5
votes
1answer
33 views

How many n-bit strings have at most m subsequent 0s?

The title already is the complete question, but I would like to add some details to make clear what I mean. A $n$-bit string is an element of $\{0,1\}^n$. All possible 3-bit strings are: 0: 000 1: ...
2
votes
4answers
132 views

If I hear thunder 5 seconds after I see the lighting, can I calculate the distance to where lighting occurred?

My kid asked me this the other day, and it got me thinking that it is really impossible to calculate. We know the speed of sound (340.29 m/s) and speed of light (299,792,458 m/s) and I can calculate ...
0
votes
2answers
39 views

A question about mathematical algorithm in Digital Systems.

My question is related to math technique that must be used to solve a question in Digital Systems subject. and I know Its not so related to this forum, but I couldn't find another related place in ...
2
votes
1answer
140 views

Mathematical Formulas for Game Battle Calculations

I am from a programming background and trying to write a game for fun. I am trying to write a battle calculator and which ever way I think about it I seem to run into trouble. Basically the scenario ...
6
votes
2answers
343 views

Does there exist a power of 2 which is the concatenation of two powers of 2?

I am curious whether there exists a power of $2$, $z = d_1d_2\ldots d_n$ (where $d_i$ is the $i$-th digit of $z$), such that $z_1 = d_1d_2\ldots d_j$ and $z_2 = d_{j+1}d_{j+2}\ldots d_n$, $1\le j\le ...
0
votes
0answers
56 views

Marbles that are distinguishable and indistinguishable at the same time

Thinking about a question and my answer to it and another question I asked earlier. I've come up with the following problem: Consider two otherwise very similar marbles, a red one and a blue one. Let ...
0
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2answers
32 views

Combinatorics arrangement question

Taken the word to be "Logarithm", how many ways can this word be arranged alphabetically? For example "Ail" is valid but "mhi" is not. I know how to find how many words can be arranged using e*n!, but ...
1
vote
1answer
45 views

Possible permutations of a grid

I hope this is the correct place to post this, as I don’t study maths. But I do need help calculating the possible permutations of a grid based game I’m currently programming. This isn’t to help out ...
1
vote
2answers
30 views

Perception of time: 1 day to John is X days to Sally

I'm a ruby programmer writing a calculator for a fun blog post. I want to quantify the perception of time between two individuals. John has lived 236676.87 hours Sally has lived 438290.5 hours 1 ...
1
vote
1answer
138 views

Proving the Sine Rule with one line.

Working on a general proof of the Law of Sines for ALL Euclidean triangles. Right triangles are easy. Acute triangles are just two proofs of the right triangle. But this is not sufficient for me. I ...
2
votes
3answers
53 views

Give an example of four different subsets A, B, C and D of {1, 2, 3, 4} such that all intersections of two subsets are different.

My work, Suppose E={1,2,3,4} then power set of E is P(E)={ {}, {1}, {2}, {3}, {4} {1,2}, {2,3}, {3,4}, {1,3}, {1,4}, {2,4}, {1,2,3},{2,3,4}, {1,2,4}, {1,3,4}, {1,2,3,4} } Shows the possible subsets ...
0
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0answers
31 views

Ball-of-wacks combinations

The six-color version of the ball-of-wacks consists of thirty rhomboidal pieces, which can be combined to form a rhombic triacontahedron. There are six colors, each with five pieces. One challenge ...
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2answers
49 views

partnership problems [closed]

A,B and C started a business by investing Rs 7,000, Rs 5,000 and Rs 3,000 respectively. If they earned a profit of Rs 9,000 , find the share of A ? Note: Rs = Indian Rupees
2
votes
1answer
178 views

What is an ordinary differential equation equation that is yet to be solved?

In another word, the ODE i am talking about is very special that an special method must be developed in order to solve solely that ODE approximately in infinite series. An standard method mean it ...
0
votes
1answer
73 views

How do you solve for x in this equation? $4^x=2^x+6$

$4^x=2^x+6$ Given that $x$ is in the form "log base $a$ of $b$" and both $a$ and $b$ are prime numbers, what is the ordered pair $(a,b)$: I have no idea how to solve this, I've been staring at it ...
0
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1answer
38 views

Assuming that a player makes every statistically optimal decision in Blackjack, at what payout ratio will they break even, on average?

In Blackjack, the player chooses whether to draw another card(s), or to stop drawing and make the dealer draw. Some decisions are better than others. For example, if the player's cards add up to 8 or ...
1
vote
1answer
70 views

Determining Formula (Game Mechanics)

WARNING I believe that the data below has errors in the defense strength, so is therefore not solvable. I will update it when I have more information. Thank you. I play a game (Empire: Four ...
0
votes
1answer
43 views

Proving Finite Union of Disjoint Closed Intervals is Closed?

Forgive my poor LaTeX, I'm very new to it (as in, reading guides as I go just to write this). In my Elementary Real Analysis course, we're asked to prove a finite union of closed sets is itself ...
0
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0answers
16 views

Multidimensional Multiplication Table

Has anyone done any math concerning multidimensional tables? I am just looking for the correct search term to do some more research in. Essentially what I am looking for would be a table that you ...
3
votes
4answers
233 views

How should you prove product rules by induction?

For example: $$\prod_{i=2}^n\left(1-\frac{1}{i^2}\right)=\frac{n+1}{2n}$$ For every $n$ greater than or equal to $2$ my approach for this was that I need to prove that: $$ ...