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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50 views

How to find the the probability that both of them draw exactly one common card?

Harry and Ron play a game of cards. They only have half a standard pack of cards. Harry draws two cards and replaces them back. Ron again repeats the same process. How to find the the probability that ...
3
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2answers
369 views

$W$ white balls, $B$ black balls, adding $K$ of the resultant color each iteration

The problem is stated as follows. We have a box with $W$ white balls and $B$ black ones. Repeat $N$ times: each iteration a ball is taken out (uniformly), and put back along with $K$ (constant) more ...
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2answers
217 views

$k$ balls into $n$ bins: how to formally account for “time”

We throw balls into the bins until no bin is empty. What is the expected time until no bin is empty? The solution goes: Let $Y$ be the random variable that counts the time until no bin remains ...
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1answer
176 views

Finding positive real numbers $x$,$y$ and $z$ IMO Shortlist 1995 A4

How can we find all of the positive real numbers like $x$,$y$,$z$, such that : 1.) $x + y + z = a + b + c$(here $a$,$b$ and $c>0)$ and 2.) $4xyz = a^2x + b^2y + c^2z + abc$ ?(Both the conditions ...
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4answers
11k views

The Mathematics of Tetris

I am a big fan of the oldschool games and I once noticed that there is a sort parity associated to one and only one Tetris piece, the $\color{purple}{\text{T}}$ piece. This parity is found with no ...
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2answers
376 views

Counting ordered triples of non-negative integers not greater than 100

Can we find the number of ordered triples $(x,y,z)$ of non-negative integers satisfying (i) $x \leq y \leq z$ (ii) $x + y + z \leq 100$? Source:Regional Mathematics Olympiad India (2003) Thank you.I ...
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4answers
177 views

Looking for a simple problem for math demonstration

I'm holding a 3-5 minute speech next week on mathematical problem solving, and how it makes me happy, to 15-20 non-mathematicians. As a part of it, I had thought about demonstrating two problems, but ...
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1answer
144 views

What does the underscore stand for in the following analogies?

This is taken from the Miller Analogies Test. No explanation or context is given. My assumption is that the underscore stands for the same operation/number/whatever in both, but I don't know what it ...
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2answers
286 views

Zombie Survival: What is the optimal way to place seven entities on an infinite grid to reduce number of adjacent pairs?

I am designing a zombie-survival type scenario in a tabletop RPG game. My system is going to work in such a way that the players take damage at the start of their turns based on how many adjacent ...
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2answers
465 views

The Farmyard problem

Problem: There is a farmer who has a $1\text{ mile}\times 1\text{ mile}$ square piece of land. He knows that there is a completely straight pipe underneath some part of his property, but it could ...
2
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1answer
88 views

Is this relation transitive if $n=m$?

If $X$ is a set and $n \in \mathbb N$, then $[X]^n$ will denote the set of all subsets of $X$ with exactly $n$ elements. For a set $X$ and natural numbers $n$ and $m$ define a relation $R$ on $[X]^n$ ...
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1answer
230 views

Pile of cards(Tournament of Towns)

I have been trying this problem for a while.But somehow, my proof(I tried an inductive approach) appears to be break down at some point.Here it is: There is a large pile of cards.On each card one of ...
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2answers
588 views

A Combinations Problem Involving Days Of the Week

I'am reading through Engineering Math by Ken Stroud/Dexter Booth and in page 274 under Combinations. Here's the situation. Assuming that you have a part-time Job in the weekday evenings where you ...
2
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1answer
567 views

Average and minimum Values of $|\sin x+ \cos x + \tan x + \cot x +\sec x +\csc x|$, $\forall x \in \mathbb{R}$

A problem was asked at Putnam Competition in 2003 (Problem 3), about finding the minimum Value of $|\sin x+ \cos x + \tan x + \cot x +\sec x +\csc x|$ where $x$ is Real. the question paper and ...
2
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1answer
129 views

A sequence of functions $f_n \in L^1(\mathbb{R}) \cap L^2(\mathbb{R})$

Consider a sequence of functions $\{f_n \}\in L^1(\mathbb{R}) \cap L^2(\mathbb{R})$ , convergent to $f$ in $L^1(\mathbb{R})$ and to $g$ in $L^2(\mathbb{R})$. Prove that $f=g$ a.e. What I understood ...
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0answers
410 views

Is the measurability of the set E required for this problem to be right or have a solution? [closed]

This is one problem from my text book and since this book is new edition, I have been finding many typos or errors in this book. So I am not sure if this problem has an error that it should have ...
4
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1answer
187 views

Problem about absolute continuity of a function

$f:\mathbf{R} \to \mathbf{R}$ is an increasing function with $\lim_{x\to -\infty}f=0$ ,$\lim_{x\to \infty}f=1$, and $\int_{R}f'=1$. Prove that $f$ is absolutely continuous on every interval ...
1
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1answer
150 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
41 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 ...
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1answer
201 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 ...
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3answers
666 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 ...
3
votes
3answers
394 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 ...
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1answer
96 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 ...
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3answers
616 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 ...
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2answers
524 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 ...
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3answers
150 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
56 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 ...
4
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4answers
666 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
56 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
674 views

Solving For A Linear Operator

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
276 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?
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2answers
1k views

What is the algorithm for long division of polynomials with multiple variables?

I was helping a high-school student last night whose teacher had given as a homework problem the division $$\frac{15x^4-y^2}{x^2+y};$$ I tried a heuristic involving splitting off a difference of ...
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2answers
135 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 ...
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3answers
2k 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, ...
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1answer
83 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
126 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 ...
3
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3answers
1k 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
261 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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0answers
102 views

Feasibility of a cryptography transformation

This is a follow-up of the question: Transformation We are given $$g^{1/(x+m)},$$ (it is not possible to find $\frac{1}{x+m}$ due to the Discrete log problem), can we find a $k$ such that ...
2
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1answer
262 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
30 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: ...
2
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3answers
243 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 ...