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Questions tagged [problem-solving]

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.

1
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1answer
165 views

Uniformly continuous $f$ in $L^p([0,\infty))$

Assume that $1\leq p < \infty $, $f \in L^p([0,\infty))$, and $f$ is uniformly continuous. Prove that $\lim_{x \to \infty} f(x) = 0$ .
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1answer
47 views

Can we find the numbers for which the minimum of the net result is maximum?

A and B play a game.A selects one number from the set {1,2,..,9} at first and supplies it to B.B puts a plus or minus sign before the number(this act is visible to A).The process is repeated twice ...
1
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1answer
637 views

space-time process of an non-homogeneous markov process is a homogeneous markov process

Let $(X_t)_{t\geq 0}$ a non-homogeneous Markov process. I have read several times, that the associated space-time process $(t, X_t)_{t\geq 0}$ is then a homogeneous Markov process. I tried to come up ...
6
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4answers
30k views

What is the highest number that can be got from 4383 by moving exactly 2 matches?

What is the highest number that can be got from 4383 by moving exactly 2 matches? Number 1 has got 2 matches, so I thought it will be 47831 as I remove two matches from second number (3), but it isn'...
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3answers
593 views

grid puzzle about combinatorics

Here is a puzzle about combinatorics. Suppose you have a square grid with $n^2$ points. You want to go from the origin $(0, 0)$ to $(n-1, n-1)$. Assuming you can only go right or up, in how many ways ...
1
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1answer
115 views

Keeping track of constants in messy integrations

I'm currently working through the textbook "Introduction to Electrodynamics" by David Griffiths, and there are some challenging problems in the chapter on electrostatics that involve (relatively, at ...
12
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3answers
870 views

An Integral involving $e^{ax} +1$ and $e^{bx} + 1$

For fun, I was looking at the following Putnam-Style problem the other day on this page: (It is problem B2) Evaluate the integral $$I(a,b)=\int_{0}^{\infty}\frac{e^{ax}-e^{bx}}{x\left(e^{ax}+1\...
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2answers
1k views

In △ ABC, D is the midpoint of AB, while E lies on BC satisfying BE = 2EC. If m∠ADC=m∠BAE, what is the measure of ∠BAC in degrees?

In △ABC, D is the midpoint of AB, while E lies on BC satisfying BE = 2EC. If m∠ADC=m∠BAE, what is the measure of ∠BAC in degrees? I know already that angle A and angle D are congruent because m∠ADC=m∠...
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3answers
182 views

Easy marketing problem

I am a bit weak at math, and I am hoping you can help me find the fastest way to solve a problem. (I hope I came to the right place). This maybe sounds ridiculous, but I want to mathematically solve ...
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0answers
66 views

Minimization of matrix of vectors in polar field

The problem I am facing is the reduction of vibrations of a rotating object. I have a series of vibration measurements taken at 5 different states with magnitude and phase components, and a set of ...
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4answers
1k views

Serious applications of Colouring proofs

Are there any research-level applications of proofs by colouring? This is the kind of proof you use to show that you can't cover a mutilated chessboard with 31 dominoes. Afaik, this technique ...
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2answers
61 views

Equation for simple transform

I have an ordinal list that I am trying to represent mathematically. The list is as follows: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 2000, 3000, 4000, ...
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4answers
2k views

Solving For A Linear Operator [closed]

I'm currently learning about linear operators, and the chapter in my book describing them only has examples with predefined linear operators. One of the first questions asks: ...
3
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2answers
289 views

How to find variable as the denominator

Copper has a density of $8.96 \text { gm per }cm^3$. If a cylinder of copper weighing $24.31 g$ is dropped into a graduated cylinder containing $20.00 mL$ of water, what will be the new water level?
2
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2answers
205 views

Exponents - solving for a constant

There's a constant that is very close to an integer that's referenced here: http://xkcd.com/217/ $$e^{\pi} - \pi = 19.9990999$$ We nerds find this to be cool because it has two mysterious numbers ...
2
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3answers
5k views

The fastest algorithm for asymmetric travelling salesman problem (TSP)

What is the fastest algorithm for asymmetric TSP? Maybe someone knows the fastest solution according to computer calculations. For example, WinQSB calculates 60 cities in 2-3 seconds on Intel Core 2, ...
1
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1answer
95 views

How to Test Arrangements of Buyers & Products in the Most Profitable Way, Given Limitations?

There's multiple products and multiple buyers, each with their own quote for the product, and some not willing to buy the product at all. Some buyers require a minimum dollar amount for the order or ...
2
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2answers
427 views

How to find the lowest cost supplier-product mix?

I was given a Excel spreadsheet with this table: The user wants to find the lowest price mix amongst the various suppliers. The user wants to constrain the number of products that each supplier gets ...
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3answers
7k views

How to solve a problem with chessboard

I am beginning math student and encountered following task which I do not know how to solve: There is chessboard, ie 8x8 tiles. In the top left corner there is pawn. He cannot go diagonally and he can ...
7
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3answers
581 views

How to solve for $x$ in $\frac{200}{x+10} = \frac{200}{x} -1$?

I am really confused how to calculate the following. The answer is $40$, but what are the steps to get $40$? $$\frac{200}{x+10} = \frac{200}{x} - 1.$$ Thank you.
2
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1answer
853 views

Counting digits in an arithmetic sequence

Given $a, d, n, x$. Suggest me a suitable algorithm to compute the number of times the digit $x$ appearing in the arithmetic sequence $a, a + d, a + 2 \times d, \cdots, a + n \times d$. For ...
0
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1answer
33 views

Trouble on writing the function for an account record pagination problem

I have this problem about account record pagination. I have to write the function that describes the total pages needed to contain those account records. This is the problem: ...
3
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3answers
259 views

Large-scale Coordinated Research in Mathematics

I've long dreamt of an occasion where hundreds or thousands of mathematicians work on a single problem in a truly coordinated way. Well, now that I'm nearing my doctoral defense in mathematics, I've ...
2
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1answer
284 views

When should one use a counting argument to prove the existence of an object?

I've wasted a few days trying to prove Thue's lemma with no success! The proof is absolutely easy if you just count. What 'red flags' are useful to give you a warning that counting might be more ...