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

2
votes
1answer
59 views

A problem with polynomials.

This is a problem from a test in my course in analytic functions. I didn't manage to solve it. Could you please give me a hint? The problem is: Calculate the third root of the sum of the coefficients ...
0
votes
1answer
60 views

Problem with an equation.

I have this equation: v*t-(u*g*t^2)/2 = d And I'm having trouble solving it for t. Mathematica gave me two results, ...
1
vote
1answer
716 views

Solving modular inequalities/constraint solving

A few of my current programming problems boil down to solving inequalities over modular domains and possibility could benifit from knowledge of efficient maths/algorithms rather than brute force ...
3
votes
1answer
141 views

Linear Algebra problem: intersection of a subspace with a cone.

In $\mathbb{R}^n$, consider the closed cone $$C^+ = \{ (x_1, \ldots, x_n) : x_i \geq 0,~~i= 1, \ldots, n\}.$$ Let $S \subseteq \mathbb{R}^n$ be a subspace (of any dimension) such that $S \cap C^+ = ...
6
votes
3answers
240 views

Is there an efficient algorithm to find a length maximizing combination?

The problem is the following Given $v_1, \, v_2, \, \ldots, \, v_n \in \mathbb R^m$; find $\epsilon_1, \, \epsilon_2, \, \ldots, \, \epsilon_n \in \{0,1\}$ such that $$\left\vert \sum_{i=1}^n ...
5
votes
3answers
682 views

Secret Number Problem

Ten students are seated around a (circular) table. Each student selects his or her own secret number and tells the person on his or her right side the number and the person his or her left side the ...
8
votes
5answers
787 views

How many rationals of the form $\large \frac{2^n+1}{n^2}$ are integers?

This was Problem 3 (first day) of the 1990 IMO. A full solution can be found here. How many rationals of the form $\large \frac{2^n+1}{n^2},$ $(n \in \mathbb{N} )$ are integers? The possible ...
13
votes
1answer
306 views

How many $N$ of the form $2^n$ are there such that no digit is a power of $2$?

How many $N$ of the form $2^n,\text{ with } n \in \mathbb{N}$ are there such that no digit is a power of $2$? For this one the answer given is the $2^{16}$, but how could we prove that that this ...
1
vote
4answers
271 views

solve complex equation

$x^8 = \frac{1+i}{\sqrt{3} - i} = \frac{\sqrt[8]{\frac{2}{\sqrt{2}}}(\cos \frac{\pi}{4} + i \sin{\frac{\pi}{4}})}{2 \cos \frac{\pi}{6} + i \sin \frac{3\pi}{2}}$ What's the way to solve this kind of ...
3
votes
3answers
292 views

What is the answer to this hard problem for 4th graders?

Here is the problem. Peter's password for his mail is a 6 digit number. The first two digits are his house number. Next to them is the sum of the digits of his phone number. Next to them is the sum of ...
3
votes
4answers
7k views

Probability of winning a prize in a raffle

My work is having it's annual Christmas raffle today. 1600 tickets have been sold, and there are 40 prizes to win. I have bought ten tickets. What are the odds I will win a prize? While an initial ...
0
votes
2answers
587 views

What is the difference between Centroid of area and Bisector of area?

We got this fuzzy course in the university, there was a problem which it's result led to multiple overlapping fuzzy values. in order to conclude a value out of that there was different approaches ...
-1
votes
1answer
173 views

How to answer to this algebra problem?

Thanks for your attention to this question, here is the problem: Compute the number of positive integers $x$ less than or equal to $1000$ that satisfy the following condition: $$x! \text{ is ...
1
vote
2answers
191 views

Pack box inside “smaller” box

Now, there is a puzzle that is quite well known as far as I know, concerning the packing of rectangular boxes in 3-dimensional space. You also have a measurement of a box as the sum of the hight, ...
5
votes
2answers
85 views

Help with a geometry problem

The problem says: A triangle has its lengths in an arithmetic progression, with difference d. The area of the triangle is t. Find the dimensions. the solution says: the notation can be even better if ...
14
votes
2answers
1k views

Asking 2011 Putnam B6

I wish to ask today's Putnam problem B6: Suppose $p$ is an odd prime. Prove that for $n\in \{0,1,2...p-1\}$, at least $\frac{p+1}{2}$ number of $\sum^{p-1}_{k=0} k! n^{k}$ is not divisble by $p$. ...
0
votes
2answers
238 views

Counting functions

How many functions are possible from the set $A=\{0,1,2\}$ into the set $B =\{0,1,2,3,4,5,6,7\}$ such that $f(i) \le f(j)$ for $i \lt j$ and $i,j \in A$? I am not sure which counting model ...
1
vote
2answers
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
votes
2answers
371 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 ...
2
votes
2answers
218 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 ...
1
vote
1answer
177 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 ...
174
votes
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 ...
4
votes
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 ...
1
vote
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 ...
3
votes
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 ...
10
votes
2answers
287 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 ...
14
votes
2answers
466 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
votes
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 $[X]^n$ ...
2
votes
1answer
231 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 ...
1
vote
2answers
598 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
votes
1answer
569 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
votes
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 ...
2
votes
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
votes
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
vote
1answer
152 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 $\lim_{x \to \infty} f(x) = 0$ .
1
vote
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 ...
1
vote
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 ...
4
votes
3answers
686 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
401 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
vote
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 ...
11
votes
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 ...
-1
votes
2answers
526 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 ...
1
vote
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 ...
1
vote
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
votes
4answers
674 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 ...
0
votes
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, ...
3
votes
4answers
680 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
votes
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?
3
votes
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 ...
2
votes
2answers
136 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 ...