Use this tag when you want to determine the thinking that is needed to solve a certain type of problem, as opposed to looking for a specific answer to a question.

learn more… | top users | synonyms

1
vote
1answer
44 views

If hexagon + triangle = 8, what is the value of a trapezoid? [closed]

If hexagon + triangle = 8, what is the value of a trapezoid? (using blocks) easy problem I'm having a difficult time figuring this out. I know that there are 6 triangles inside of a hexagon so I'm ...
2
votes
1answer
40 views

Competition problem (unknown source)

For what positive $x$ does the series $$(x-1)+( \sqrt[2]{x}-1)+ ( \sqrt[3]{x}-1)+ … + ( \sqrt[n]{x}-1) + …$$ converge?
-2
votes
1answer
44 views

What's the result of this? [closed]

I would like to ask you guys for the result of this equation: $2/2+6(2/2*3)-(9/(8+1)*2)*(2*7+1) = x$ What is x?
0
votes
3answers
38 views

Basic Algebraic Manipulation

How would I solve for $X$ in this instance? I can't figure out how to get the $X$ variables by themselves and the known values on the other side by themselves. $2(4-X)(4-X)+X = 3$
2
votes
4answers
60 views

Calculate the integral using another integral

Need help with this integration: Let $$A = \int_0^\pi \frac{\cos x}{(x+2)^2}dx$$ Compute $$\int_0^{\frac{\pi}{2}} \frac{\sin x \cos x}{x+1}dx$$ In terms of $A$. I tried to do some algebraic ...
0
votes
1answer
37 views

Evaluating the following sum

I have no idea how to solve evaluate this integral: $$\lim_{n\to\infty} \frac{1^a + 2^a + \cdots + n^a}{n^{1+a}}, a > -1$$ I want to set this up as some sort of integration since it is a ...
0
votes
1answer
75 views

probability that a year has 53 mondays

We have the years from 2001, 2002, 2003,... to 2010. Say, a year is chosen at random from the listed years. What is the probability that the chosen year has 53 Mondays ?
0
votes
1answer
27 views

Showing a function is not monotonic.

I need help with what this question is asking. Define $f$ by: $$f(x) = \begin{cases}x^2\sin\frac{1}{x}, & \mbox{if }x\neq 0 \\ 0 & \mbox{if }x=0\end{cases}$$ Let $g(x) = x + 2f(x)$. Show ...
3
votes
1answer
37 views

Prove the following trigonometric polynomial has $2n$ zeros

I am having a lot of trouble with this problem, any help would be greatly appreciated! Prove that the that the trigonometric polynomial $$a_0 + a_1\cos(x)+\cdots+a_n\cos(nx), $$ where the ...
0
votes
0answers
24 views

Given two sets, how can I say statistically if they are similar/different

This is a very open ended question. Suppose I have two sets of data samples of the same form, say [item, rating]. Rating is a value on the interval [0,100] and item is a unique identifier given to a ...
0
votes
1answer
23 views

Radius of Convergence Problem solving

I did this questions using the Ratio Test which showed that the radius of convergence is the same. I'm not sure if that is correct. (I am having my doubts about c_n becoming c_n+1 for the ratio test ...
0
votes
1answer
43 views

Sequences and Series ( Power Series ) question.

I know that the sum from 0 to infinity of part A is the same as the sum to infinity from 1 if you decrease the power by 1. So I'm guessing the series will converge, but I don't know how to find the ...
0
votes
1answer
24 views

Calculating probabilities of events

Was going through past previous exam questions and came across this one: A manufacturer of lie detectors is testing its newest design. It asks 300 people to lie deliberately and another 500 people ...
59
votes
12answers
13k views

Dividing 100% by 3 without any left

In mathematics, as far as I know, you can't divide 100% by 3 without having 0,1...% left. Imagine an apple which was cloned two times, so the other 2 are completely equal in 'quantity'. The totality ...
1
vote
1answer
115 views

How to solve this trigonometric equation / geometric problem

Is there any way to solve this type of equation exactly for x, where a-h are precalculated constants: $a\cos(g x)+b \sin(g x)+c\cos(h x)+d\sin(hx)+ex+f=0$ Or is my only/best option some sort of ...
0
votes
0answers
24 views

Problem involving line segment comparisons

I came across this question, and I find myself having no clue how to proceed. ...
2
votes
2answers
26 views

School Play and Ticket problem.

I may be missing something obvious here, but cant seem to see what. Can anyone give me some insight on how to solve this. 100 tickets are sold for a school play. Tickets for a child cost £1.50 each. ...
1
vote
0answers
23 views

Diffeomorphism/Problem/Euclidean spaces

Problem: Let $f$ : $\mathbb{R}$ $\rightarrow$ $\mathbb{R}$ be a $C^{1}$ function such that |$f'(t)$| $\leq$ $k$ < $1$, $\forall$ $t$ $\in$ $\mathbb{R}$. Define $\phi$ : $\mathbb{R}^{2}$ ...
0
votes
1answer
24 views

Quick Bounds Question [ Sets]

1) Let $S =\{(−1)^n\; \mid\; n \in \mathbb{Z}\}$ . What is the greatest lower bound of $S$? -1 is the Lower bound. But is it also the greatest lower bound? Or does it not exist? Thanks. And also ...
1
vote
2answers
49 views

Amount of Miles

Gary has two cars: His fairly new van and his old clunker station wagon. the wagon currently has 16 times as many miles on it as the van had when the wagon had 3 times as many miles as the van has ...
1
vote
5answers
193 views

First Order Logic

Is it possible to represent the english sentence with numerical value in First order Logic. For example if the sentence is: Nobody has more than one mother. I am wandering who can i show the ...
1
vote
4answers
41 views

How do I work with equations with more than two variables?

I was trying to rewrite this equation in terms of $s$: $$ p = 4s \frac{(s - 1)}{2} + s (2r + 1) $$ After failing at that, I tried with Wolfram Alpha, and got the answer I wanted. But, how did it get ...
1
vote
1answer
271 views

Problem Solving ( Sequences and series)

After injection of a dose $D$ of insulin, the concentration of insulin in a patient's system decays exponentially and so it can be written as $D\exp^{-at}$ where $t$ represents time in hours and $a$ ...
0
votes
1answer
35 views

An unusual inequality

Problem: $(x_i)_{i=1}^n$ is a finite sequence of positive integers. Define $f\big(S\big)=\displaystyle \sum_{i\,\in\, S\,\subseteq\, [n]}x_i$, and suppose $f$ is injective. Prove that: ...
0
votes
2answers
104 views

Finding the Reading Rate

Part 1: If you read 15 minutes per day every day and end up reading 12 books of 200 pages each in 1 year, what is your reading rate in pages per minute? Part 2: If you increase your reading speed so ...
23
votes
7answers
558 views

“Here's a cool problem”: a collection of short questions with clever solutions

This game will be familiar to many mathematicians, and it is always good fun to play. I am looking to find a list of good questions with short, when-you-see-it solutions. The kind of question one ...
2
votes
3answers
673 views

Crossword puzzle- Crossnumber puzzle

The puzzle below is a cross number puzzle, similar to a crossword puzzle except that the entries are numbers. Enter one digit per square. The thick heavy line is a separator. ACROSS: a. A prime ...
0
votes
2answers
43 views

Solving an equation with both linear and exponential terms

Can I find an algebraic solution for the equation below? Thank you. $$ x+e^{x}(x+a)=b $$
2
votes
1answer
38 views

Interesting question about functions

I saw the following question and I would like to share. I don't know the answer. Suppose that the function $f:\Bbb{N}\to\Bbb{N}$ has the property $f(f(n))<f(n+1)$ for any $n\in\Bbb{N}$. Prove that ...
7
votes
1answer
148 views

How to suceed in mathematical olympiads and competitions?

This question may be slightly off-topic but it still relates to Maths so I hope that it does not get taken off. I am a student who is 16 years old, is generally good in Maths and enjoys it and I ...
3
votes
1answer
70 views

Can someone please clarify combinations vs permutations?

I see similar questions asked on here and obviously I did some research and read my book, but it seems like every explanation contradicts another in some way. There are basically infinite scenarios ...
0
votes
2answers
43 views

Ways to add a number using just 1's, 5's, 10's, 25's, 50's

given the set $\{1, 5, 10, 25, 50\}$, in how many ways, can you combine this numbers to get a specific number. For example, 11 can be shaped as $1\cdot11$, or $5\cdot112 + 1\cdot111$, or $10\cdot111 + ...
1
vote
4answers
62 views

Problem of the month. Thinking problem?

Cherise scored 85 on her last math exam of 100 questions. Her teacher has an unusual way of scoring this test. He calculated her score by subtracting 2 times the number of wrong answers from the ...
1
vote
1answer
76 views

How deep would the water be?

The lake created by Hoover Dam on the Arizona-Nevada border has a capacity of 31,250,000 acre-feet. If the whole lake suddenly flooded the Mojave Desert (area 15,000 sq. miles) how deep would the ...
0
votes
1answer
49 views

Sliding Question

At the local playground, three boys like to go down the a very wide slide. After going down the slide, they turn around and climb back up the slide rather than walking around to climb the ladder. The ...
0
votes
2answers
44 views

Finding the distance between the point $(3,7)$ and $x = 0$

In the paper of maths, there was an M.C.Q.S.: The distance of the point $(3,7)$ from $x = 0$ is $3$ $7$ $10$ $8$ So can anyone tell me what was the correct answer and how to ...
2
votes
2answers
73 views

Find $\max_{\sigma \in S_n}\sum_{i=1}^n|\sigma(i)-i|$ where $S_n$ is the group of permutations on $n$ letters (Greedy algorithm shows up?)

Find $\max_{\sigma \in S_n}\sum_{i=1}^n|\sigma(i)-i|$, where $S_n$ is the symmetric group of permutations of $n$ symbols. So, the story goes like this: When I first saw the problem, I thought the ...
2
votes
2answers
99 views

Solving inequalities with absolute values

This is the question: $$ \left| \frac{x+2}{3(x-1)} \right| \leq \frac{2}{3} $$ And this is my working out, first I squared both the numerator and denominator, then solved it as if it was a normal ...
0
votes
1answer
33 views

Is it possible to always get the optimal formula regardless of the derivation method?

Today I've tried to solve a geometric problem (collision point between two circles in a specific situation). I found a working solution but I'm not sure if it was optimal (maybe my solution took more ...
5
votes
1answer
124 views

If $(n_k)$ is strictly increasing and $\lim_{n \to \infty} n_k^{1/2^k} = \infty$ show that $\sum_{k=1}^{\infty} 1/n_k$ is irrational

Prove that for a strictly increasing natural sequence $(n_k) $ satisfying $\lim_{n \to \infty} n_k^{1/2^k}=\infty$, $\sum_{k=1}^{\infty} 1/n_k$ is irrational. This is another problem "problems in ...
1
vote
2answers
65 views

$\forall x \in \mathbb{R}$ show that $x=\sum_{n=1}^\infty k_na_n = \prod_{n=1}^{\infty}m_na_n$ …

Yet again, another cool problem from the book "problems in mathematical analysis" by Piotr & Witkowski: Prove that if $a_n \neq 0$, $n=1,2,\cdots$ and $\displaystyle \lim_{n \to \infty} a_n = 0$, ...
2
votes
0answers
52 views

Problem on the digits of $n!$

let $m$ be a natural number, is it always possible to find an $N\in \mathbb{N}$ such that $m$ or more "$0$" digits (excluding the terminal ones) appears amongs the decimal digits of $n!$ if $n\ge N$
7
votes
2answers
210 views

Every $x \in (0,1]$ can be represented as $x = \sum_{k=1}^{\infty} 1/{n_k}$, such that $n_{k+1}/n_k\in \{2,3,4\}$

Show that every $x \in (0,1]$ can be represented as $x = \sum_{k=1}^{\infty} 1/{n_k}$, where $(n_k)$ is a sequence of positive integers such that $n_{k+1}/n_k\in \{2,3,4\}$. Please do NOT reveal the ...
6
votes
2answers
735 views

Express y in terms of x

Question: $$ \text{It is given that } y= \frac{3a+2}{2a-4} \text{and }x= \frac{a+3}{a+8} \\ $$ $$ \text{Express } y \text{ in terms of } x. $$ From using $x$ to solve for $a$, I discovered that ...
2
votes
0answers
93 views

Please help me remembering a problem on $n!$ [closed]

I couple of years ago a friend of mine gave me a problem about the digits of $n!$, I never solved it and I also forgot what the question was. It asked you to prove some fact about the digits of $n!$ ...
0
votes
0answers
45 views

Minimal digit cost problem

Every now and then I try to solve programming/math (well, preferably programming :D) problems wich can be found all over the internet. Currently I am trying to solve old problems from a yearly ...
2
votes
2answers
73 views

Accumulation points of $\{ \sqrt{n} - \sqrt{m}: m,n \in \mathbb{N} \}$

This is my first post on MSE, so, pardon me if I'm not used to the site's rule yet. I'm trying to prepare myself for competitions in the future and I'm trying to improve my problem solving skills. ...
0
votes
1answer
40 views

Two players $A,B$ throw two dice…

Two players $A,B$ throw two dice. A throw first, and they throw it in turns (i.e. $A,B,A,B,A...$). If $A$ gets sum of $10$ at the dice he wins, if $B$ gets $9$ - he wins. What is the probability ...
2
votes
1answer
66 views

Finding when the distances to three cities again have different digits

Very confused on this question. How would you solve it, and what would be the answer(s). Recently I was driving down the freeway and spotted the following freeway sign with the distances to three ...
-2
votes
2answers
74 views

Math problem puzzle

My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 120 years. Can you tell me my age in years ? It's ...