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

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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 ...
-1
votes
2answers
44 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
76 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
46 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
26 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
33 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
51 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
45 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
412 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
45 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 ...
6
votes
2answers
358 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
67 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
84 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
33 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
146 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
138 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
33 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
72 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
187 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
77 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
55 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
2answers
127 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
52 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
19 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
241 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
66 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
26 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
660 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
74 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
86 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
91 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
44 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
55 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 ...
3
votes
1answer
50 views

Numbers interpreted as sets and functions

In set theory numbers are defined as sets $$\emptyset,\{\emptyset\},\{\emptyset,\{\emptyset\}\},\{\emptyset,\{\emptyset\},\{\emptyset,\{\emptyset\}\}\},\dots$$ where $n+1=n\cup\{n\}$ and ...
1
vote
1answer
24 views

Combining $n$-D images to get an ($n-1$)-D one

Our human brains combine two $2$-D images we get from each of our two eyes to get one $3$-D image. Suppose there is a creature in another $4$-D world that can see in $4$-D. How many $3$-D images ...
0
votes
5answers
82 views

Prove that $3n6n3^2+4n8n4^2$ yields a perfect square.

Let $n\geq 0$ be a nonnegative integer. I observed that the expression $3n6n3^2+4n8n4^2$ is always a perfect square where $n$ represents number of "0". And I had verified it by using a calculator ...
0
votes
0answers
61 views

A room contains n people. Everybody wants to shake everyone else’s hand (but not their own).

(a) Suppose that n people require hn handshakes. If an (n + 1)th person enters the room, how many additional handshakes are required? Obtain a recurrence relation for hn+1 in terms of hn. (b) ...
2
votes
0answers
19 views

Can you recommend me a book about integration? [duplicate]

I'm new to this site. I'm an university student in korea and I major in engineering. Recently, I've been quite interested in calculating integration. So nowadays as my hobby, I seek many interesting ...
-1
votes
1answer
40 views

For what reltively prime integers $a$ and $b$ does the expression $2ab$ an even numeric palindrome? [closed]

I currently doing some research on numeric palindromes. And I am stack with the problem: For what reltively prime integers $a$ and $b$ does the expression $2ab$ an even numeric palindrome? Since ...
1
vote
3answers
72 views

Estimate the number of typos there are in a book, based on two editors' finds

This is one question from an interview I have just taken: Suppose there is a book full of typos. Tom and Jerry found $x$ and $y$ typos throughout the book, respectively. There are $z$ typos that ...
5
votes
2answers
335 views

logical problem (how long did you walk?)

My wife is very kind, she always picks me up at work by car and drives me home. Today, I finished at work 30 minutes earlier! So I decided to walk home... on the way I met my wife. She was on her way ...
1
vote
2answers
57 views

How can I know whether to round a quotient up or down (based on whether the number after the decimal point is 5+ or not) with ONLY this information?

Say I have a special calculator that, when it divides one number by another, it gives you the answer in the form of, "quotient r remainder." For example, if you divide 5 by 3, it tells you "1 ...
-3
votes
2answers
46 views

If a machine takes 3min to process 1 byte, how many machines are required to process 1000 bytes in 30min?

We have a machine that takes 3 minutes to process a byte. Now if I send 1000 bytes together the machine will take 3000 minutes to process them serially. If we want to do that in 3 minutes only we need ...
1
vote
1answer
276 views

Prove that if x is irrational, then sqrt(x) is irrational.

I believe the contrapositive method should be correct but i get, The contrapositive of this statement should be, (If $\sqrt{x}$ is rational, then $x$ is rational) Then I end up with ...