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

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1
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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
148 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
154 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
83 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
189 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
78 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
62 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
159 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
54 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
242 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
67 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
54 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 ...
23
votes
1answer
666 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
79 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
88 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
92 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
46 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
56 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
27 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
62 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
20 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
74 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
339 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
65 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
50 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
292 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 ...
0
votes
1answer
35 views

If $n=(b_k,b_{k−1},…,b_1)_2$ where $b_i$ are the digits of n in binary, what is the binary expression of $n+1$?

I have a curiosity. If $n=(b_k,b_{k−1},...,b_1)_2$ where $b_i$ are the digits of n in binary, what is the binary expression of $n+1$? Is there a relationship that binds $n+1$ to $b_i$ (ie the digits ...
0
votes
1answer
60 views

Consider the set $Q=\{p+q \sqrt2 : p,q \in\Bbb Q\}$. Prove that if $a\in Q\setminus\{0\}$ then $1/a\in Q$

Given (For all $a,b\in Q$, $a+b\in Q$ and $ab\in Q$) This was a two part question. Part a) is to prove that $Q$ is closed under addition and multiplication. Part b) is prove that if $a\in Q$ and ...
0
votes
0answers
47 views

How many solutions are there to a given instance of the game *LYNE*?

Recently I've been playing a nice little puzzle game called LYNE, which involves building a (special) graph out of a given set of vertices and prescribed valencies, and I've been wondering what could ...
3
votes
1answer
89 views

Are the odds one in a million? [closed]

This is a from a card game call Magic the Gathering And my question is regarding this video during a tournament match (best of 5). One in a million. You dont need watch the video I will explain the ...
0
votes
1answer
28 views

Addition chain search tree pruning by discarding non-minimal chains

An addition chain is an ordered tuple of numbers, starting with $1$, such that each number after $1$ can be expressed as the sum of two smaller numbers in the chain. An example of an addition chain ...
9
votes
8answers
6k views

If yesterday were tomorrow, then today would be Friday.

(S) If yesterday were tomorrow, then today would be Friday. Question: What day is today? This seems to be an old puzzle, and depending on the interpretations, the answers are Wednesday or ...
0
votes
2answers
37 views

Given $A \subseteq \mathbf{Z}$ and $x\in \mathbf{Z}$, we say that $x$ is $A$-mirrored if and only if $−x\in A$. We also define…

Sorry if this question seems kind of long but I am confused for part C. My proof for part C that $M_a$ is closed under addition is as follows: The set $M_a$ is closed. Let $x$ be in $M_a$ and ...
57
votes
0answers
7k views

“The Bachelorette Problem” (slightly adapted from Tao's Google+ account) [duplicate]

The following puzzle being very much recreational for me, I couldn't resist myself from sharing it with my fellow MSE user friends. Let's have a look at it. You are the most eligible bachelorette ...
7
votes
5answers
1k views

Hank and his old car

I'm sort of struggling with this riddle told to me by a friend: Hank owns a car. He has been taking good care of his car; In fact, he has been taking such good care of it that the age of Hank, ...
6
votes
0answers
132 views

Olympic number theory problem: is this solution fine and sufficiently well written?

Determine all the positive integers $m$ such that both the ratios $$ \frac{2(5^m+5)}{3^m+1}, \frac{9^m+1}{5^m+5}$$ are integers. Attempt to a solution: If the ratios are both integers, than their ...
0
votes
0answers
14 views

finding percentge given number range

I have a range from 2.3566e-19 to 0.0010997 I'm trying to get the bottom 10% and the top 10% the formula / numbers I used is below but the answer doesn't look right how can I fix this. ...
1
vote
0answers
68 views

Is the solution to this elementary number theory problem correct?

Problem: A natural number $n$ is called nice if the following properties hold: • The expression is made ​​up of 4 decimal digits; • the first and third digits of $n$ are equal; • the second and ...
0
votes
2answers
101 views

Arranging identical balls in a circle

In how many ways can 4 identical red balls and two identical white balls be arranged in a circle? This is an elementary problem, but many tries have not yet yielded results. I tried by taking the ...
1
vote
0answers
141 views

Crossed Ladders Problem

Two ladders, one 10 meters long and the other 8 meters [long], have been placed in a trench as indicated in the opposite figure. Their point of intersection, M, is 3 meters from the base of the ...
0
votes
0answers
60 views

What are some interesting, atypical mathematical topics that a student who has taken an introductory calculus sequence can learn about?

I understand that usually the next step after $3$ semesters of calculus and $1$ semester of ordinary differential equations (plus one semester of linear algebra, for some) is something like an ...