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.

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0
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1answer
36 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 ...
6
votes
1answer
139 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
82 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 $\displaystyle \lim_{n \to \infty} a_n = 0$, ...
3
votes
0answers
57 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
215 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
2k 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
2answers
97 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
51 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
84 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
93 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
39 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
194 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
55 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
98 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
34 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
96 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 ...
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votes
2answers
60 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?
1
vote
2answers
34 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
100 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
154 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
119 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
347 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 ...
2
votes
1answer
81 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
45 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
104 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
82 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
33 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
332 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
119 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
199 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
52 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 $x=\sqrt{1+ 2 \sqrt{1+3 \sqrt{1+\dots\infty}}}$ $x^2= 1+ 2 \sqrt{1+3 \sqrt{1+\dots\infty}}$ ...
2
votes
3answers
115 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 ...
0
votes
1answer
83 views

Infinetly many primes of form $4k+3$ [duplicate]

Prove that there are infinitely many primes of the form $4k + 3$ (where $k$ is an integer). Note that it is a special case of "Theorem 6 (Dirichlet). Let a and b be positive coprime integers. Then ...
0
votes
1answer
72 views

Greatest common divisor of $3$ numbers

Let $a,b, c$ belong to $\mathbb Z$ such that $(a,b,c) \neq (0,0,0)$. Define the [highest common factor] greatest common divisor ${\rm gcd}(a, b, c)$ to be the largest positive integer that divides $a, ...
8
votes
3answers
191 views

Existence of a certain subset of $\mathbb{R}$

To every real $x$ assign a finite set $\mathcal{A}(x)\subset \mathbb{R}$ where $x\not\in \mathcal{A}(x)$. Does there exist $\mathcal{W}\subset \mathbb{R}$ such that: $$1.\;\;\mathcal{W}\cap ...
6
votes
4answers
660 views

Some Questions regarding preparing for Math Olympiads (searched but didn't get answers)

Many questions have been asked on this site regarding preparation for olympiads like the Putnam. I've read those questions and accordingly decided to start with Engel's "Problem Solving" but I have a ...
0
votes
1answer
52 views

Solving $\int\sqrt{1+(-2ax+b)^2}\;dx$

List item What solution $$\int\sqrt{1+(-2ax+b)^2}\;dx$$Unable to develop anything ...$~$:'( I tried completing squares, but can not move much.
4
votes
3answers
67 views

Elementary set theory problem - I get an incorrect result

The problem given is this: $\bigcap_{i \in I}(A_i \cup B_i)$ and $(\bigcap_{i \in I}A_i) \cup(\bigcap_{i \in I}B_i)$ I am asked if they are the same. Here is the reasoning I used: for the first ...
0
votes
1answer
42 views

How many smallest number moves need to measure 6 liter of water?

You are given two (unmarked) containers of capacity 9 liter and 4 liter and a huge tank of water. Need is to get measure of exactly 6 liter, of water. A move is either filling a container completely ...
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votes
3answers
87 views

How to know number of eggs in this problem?

A women took a certain number of eggs to the market and sold some of them. The next day through her poultry industry, the number left over had been doubled, and she sold the same number as the ...
0
votes
1answer
41 views

Combinations with multiple kids

In a certain country, it has been found over many years that $55$% of the babies born there are males. For a family in that country with five children, what is the probability that (i) the two ...
1
vote
0answers
61 views

When does a ball in a game of brick breaker never hit the remaining breaks?

I have a block size 2N*2N and some squares are filled with bricks and some aren't. I have a ball that travels distance 1 in the x and y direction and bounces off with perpendicular direction if it ...
0
votes
2answers
106 views

Using plant to find depth of water (triangles)

John and Chris were out in their row boat one day, and Chris spied a water lily. Knowing that Pat liked a mathematical challenge, Chris announced that, with the help of the plant, it was possible to ...
2
votes
2answers
56 views

2 states, 2 interarrival distribution Renewal Process.

Karlin and Taylor (1975): 18. Consider a stochastic process $X(t)$, $t \geq 0$, which alternates in 2 states $A$ and $B$. Denote by $\xi_1, \eta_1, \xi_2, \eta_2, \ldots,$ the successive ...
0
votes
3answers
78 views

Proving this inequality

I am having trouble with proving an inequality. Assume we have two positive real numbers $a$ and $b$ such that $a+b=1$ and numbers $x > 0$ and $y > 0$. Prove: $$\frac{2}{\frac{a}{x} + ...
1
vote
1answer
28 views

Finding F(x) given any reals x and y

I have a problem and I think I know how to solve it so here it is: Determine $F(x)$ if, for all real $x$ and $y$, $F(x)F(y)-F(xy) = x+y$. I tried a couple of cases and these were my results: When ...
0
votes
1answer
38 views

Linking 5 communities by plane, train, and bus

Every pair of communities in a country is linked directly by exactly one mode of transportation: bus, train or airplane. All three modes of transportation are used in the country; no community is ...
2
votes
2answers
61 views

Based on census data and namm data, how many musicians are there?

There are $115,226,802$ households in the US. $58$% of households have at least $1$ musician. $43$% have $2$ or more musicians. How many musicians are there? Any help would be appreciated...
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12answers
8k views

MENSA IQ Test and rules of maths

In a Mensa calendar, A daily challenge - your daily brain workout. I got this and put a challenge up at work. The Challenge starts with.. ...
0
votes
3answers
59 views

Problem Solving

Here the question on my daughter's 4th grade homework assignment: Sarah is decorating a mosaic board it is 12 inches wide and 16 inches long. Sarah is using square tiles all the same size. What size ...