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
187 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
33 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
55 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 ...
21
votes
7answers
473 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
2answers
71 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
37 views

Solving an equation with both linear and exponential terms

Can I find an algebraic solution for the equation below? Thank you. $$ x+e^{x}(x+a)=b $$
1
vote
1answer
33 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
2answers
83 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
0answers
45 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
33 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
57 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
71 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
37 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
38 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
58 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
65 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
32 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
119 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
61 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
51 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
196 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
563 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
92 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
42 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
70 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
36 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
58 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
54 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 ...
1
vote
0answers
36 views

How can I finish formulating this problem?

I'm a software engineer with a very limited background in maths, and I'm trying to teach myself to think more mathematically as I try to learn more about maths. I'm currently trying to formulate a ...
1
vote
0answers
185 views

Maximizing the number of groups

The problem is as follows, There is a restaurant which has N number of chairs each chair has a unique number written on it so the array of chairs is like [1,2,....N-1,N] , there are G number of groups ...
0
votes
1answer
27 views

Lifetime of exponential variable of a battery

Suppose that the operating lifetime of a certain type of battery is an exponential random variable with parameter $\theta=2$ $($measured in years$)$. Find the probability that a battery of this type ...
1
vote
0answers
54 views

Natural Numbers Equation

I am trying to find the $(k_1,k_2,...,k_N)$ tuples solutions to an all natural numbers equation in the following form : Given $n\in\mathbb{N}^{*}$, $N\in\mathbb{N}^{*}$ and $n_i\in\mathbb{N}^{*}\leq ...
1
vote
1answer
31 views

Random variable of a store

The weekly profit in thousands of dollars of Miller's Office Supply Store is random variable X whose cdf is given as follows: $F(x)=0$ for $x<0$; $F(x)=(3/32)(2x^2-x^3/3)$ for $0 \leq x \leq 4$; ...
2
votes
3answers
46 views

The game of craps and dice

The game of craps involves the repeated tossing of a pair of dice. In the game of craps, Nancy throws a five on ther first tos of a pair of dice. ["Five" means that the sum of the number ofr dots on ...
0
votes
2answers
39 views

Problem Solving Question? Sum of the squares

The sum of the squares of two numbers is 247 and the product of the two numbers is 21. How would I find all possible values for the sum of the two numbers?
0
votes
2answers
31 views

Solving an equation

Integrating gives $$\ln\frac{250-X}{40-X} = 210kt+c_1\qquad\text{or}\qquad \frac{250-X}{40-X}=c_2e^{210kt}.\tag{10}$$ When $t=0, X=0,$ so it follows at this point that $c_2 =\frac{25}{4}$. Using ...
0
votes
1answer
42 views

Help , Word Problem

Bob and Bob played golf against each other in a tournament. A marshall keeping their score had a difficult time because both players were named Bob. The scores the marshall recorded were the correct ...
4
votes
2answers
101 views

Primes $p$ such that $p^2$ divides $x^2 + y^2 + 1$

Call a prime $p$ awesome if there exist positive integers $x$ and $y$ such that $p^2$ divides $x^2+y^2+1$. Observation: $2$ is not awesome, because $x^2+y^2+1\not\equiv 0$ (mod $4$). But $3$ is ...
0
votes
2answers
59 views

How to solve age word problems?

Roy is now 4 years older than Erik and half of that amount older than Iris. If in 2 years, roy will be twice as old as Erik, then in 2 years what would be Roy's age multiplied by Iris's age? Is ...
0
votes
1answer
85 views

Math Question on Guess and Check strategy

We always liked poking around Grandpa's attic whenever we had a family reunion. We found all sorts of neat stuff up there. Once we found a bunch of baseball cards, so Grandpa said, "Just divide 'em up ...
1
vote
1answer
64 views

very simple math question

I have this very simple math question: Each person starts working life on a salary of $5000$ dollars and then benefits form an annual increment of $250$ dollars over $40$ years of his career. My ...
0
votes
2answers
36 views

Mod Problem solving

I can't do this last question of my homework that's due in tomorrow. Can anyone hint me on what to do? Suppose $p$ is prime and $k$ is a positive integer Show that if $p$ is odd and $x$ is an ...
0
votes
2answers
79 views

Playing Detective

Four suspects were assembled in the director's office, having been accused of a devious crime: turning off the light switch during Mr. Buehler's business presentation. It was known that only one of ...
0
votes
0answers
36 views

The trace of a wedge product of matrices

I'm trying understand a computation on Besse's book (p. 371). I already know the curvature operator $R:\bigwedge^2\to\bigwedge^2$ may be written in block diagonal form relative to the direct sum ...
2
votes
1answer
31 views

Calculate the area of this object problem

Stuck on the last questions of my homework that's due in tomorrow. Somebody help. I think it's to do with integration but i can't do it. Can anyone give me a hint?
9
votes
1answer
282 views

Prove that this particular sequence contains an infinite number of sixes

Given the sequence $$2,7,1,4,7,4,2,8,\ldots$$ which begins with $2, 7$ and is constructed by multiplying successive pairs of its members and adjoining the results as the next one or two members of ...
5
votes
1answer
63 views

Is this a problem that has already been solved?

I have a question paper with $n$ True/False questions and I don't know the answer to any of those questions. My objective is to find the answer key of the question paper. All I have is a machine which ...
4
votes
3answers
74 views

Difficulty in solving challenging trig equation

Find $\theta$ on $[0, 2\pi)$ such that $$\cos{\theta}^{\sin{\theta}^{\cos{\theta}^{\dots}}} = 2 + 2\sec^2{\theta}\tan^2{\theta} - \sec^4{\theta} - \tan^4{\theta}$$ I'm not sure on how to tackle this ...
1
vote
2answers
41 views

Find square roots upto infinte times

Evaluate : $\sqrt{1+ 2 \sqrt{1+3 \sqrt{1+\dots\infty}}}$ Is it possible to solve in the following way : Let $x=\sqrt{1+ 2 \sqrt{1+3 \sqrt{1+\dots\infty}}}$ $x^2= 1+ 2 \sqrt{1+3 \sqrt{1+\dots\infty}}$ ...
1
vote
2answers
64 views

Is this Chinese card game solved?

There is a card game here in China, use a standard 52 card deck of cards. Draw four cards and use any elementary operators $(+,-,\times, \div)$, and only use each card value once to get a result of ...