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

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-2
votes
1answer
40 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
19 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
59 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
225 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
49 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
106 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
232 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
votes
0answers
58 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 ...
-1
votes
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]$\in$ ...
0
votes
2answers
30 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
41 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.
-2
votes
1answer
70 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
40 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
24 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
32 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
votes
0answers
61 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
votes
0answers
50 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
39 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
214 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
44 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 ...
3
votes
1answer
153 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
354 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
63 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
votes
2answers
34 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
64 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
31 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
144 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
71 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
votes
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 ...
-1
votes
2answers
61 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
181 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
75 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
votes
1answer
46 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
86 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
48 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
votes
0answers
17 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
236 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: $$ ...
1
vote
3answers
65 views

Different Types of Waves

I am making a basic 2D rigid body simulator as a hobby. It involves springs. Naturally, I need to render them. Rigid body simulators, such as Algodoo, render them simply like this Another (more ...
0
votes
1answer
21 views

Finding argmin$_{n \in \mathbb{N}} |2^{n/12} - 5|$ non-computationally

The problem is to find the integer $n$ such that $|2^{n/12} - 5|$ attains its minimum. Since it is clear that $24 \leq n \leq 35$, by computation one easily gets $n = 28$. However, how to find this ...
0
votes
2answers
51 views

what is$ f^{(n+1)}(x)$ as a function [closed]

Define $f^{(n+1)}(x)$ in function form. Is it $f(f^{(n)}(x))$ or is it $f^{(n)}(x)*f(x)$. Or is it something else completey. Thank you so much. I'm actually studying functions and this was something ...
22
votes
1answer
653 views

Moriarty's calculator: some bizarre and deceptive graphical anomalies

Background: This is a problem I first came across a few years ago in a calculus textbook (a James Stewart one), where it addressed some of the pitfalls of using graphing calculators. The original ...
3
votes
1answer
67 views

What gambling/board game or real life thing can (surprisingly) be modelled as a linear programming problem?

So I've taken Linear Programming 101. I've read my textbook, took the test and all that, and - besides all the theory, the nice algebraic interpretations, etc - I've encountered a lot of textbook ...
0
votes
1answer
80 views

Does there exist some infinite series such that even today we still can't test out if it converges or diverges? [duplicate]

I'm a college fresh man on my winter vacation and I'm previewing the part in my next term's Mathematical Analysis that deals with the infinite series. I have therefore learned some tricks for deciding ...
-3
votes
3answers
90 views

Problem About Equality: Is 2=1? [closed]

As we know that $$\frac{1}{0} = ∞ \implies \frac{1}{∞} = 0 \implies 1 = 0.∞$$ Now let $x=0$ and $y=0$ then $$x+y=0 \implies \frac{x+y}{1}=0 \implies \frac{x+y}{0}=1$$ and $x+y=0$ so $$\frac{0}{0}=1$$ ...
0
votes
1answer
41 views

Why do repeated trigonometric operations approach seemingly arbitrary limits?

So I was messing around on my iPhone calculator trying to find the the precision of the calculator by finding at what point sin(x) was equal to x. I found myself repeating the sine function ...
0
votes
0answers
28 views

Number of Words

In an alphabet there are 3 consonants and 5 wovels. 1 letter words are meaningless. The words that have two consonants together are meaningless. The words that have 3 vowels together are meaningless. ...
5
votes
1answer
69 views

Is there always a solution for this packing problem with collision constraints

I have six boxes with different sizes. Two boxes are red, two boxes are blue and two boxes are green. There is only one dimension that matters. Let $r$ and $r'$ be the size of red boxes. Similarly ...
0
votes
1answer
42 views

Prove or disprove: for every $f,g : \mathbb R\to\mathbb R$ even, the composition $h= f\circ g$ is even.

Proof: Given $f,g:\mathbb R\to\mathbb R$ even then $f(-x)=f(x)$ and $g(-x)=g(x)$ then $h=f \circ g$ then $h=f(g(x))=f(g(-x))$ then $h=g(-x)=g(x)$ since $x \neq -x$ the composition of two even ...
0
votes
1answer
53 views

Give an example of a function that is not strictly increasing. Draw its graph and prove that the function is not strictly increasing

I picked x^4 to be a function which is not strictly increasing for all real numbers. Since to be not strictly increasing means that for the function y=f(x) x1 < x2 then f(x1)< f(x2) but ...