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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2
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0answers
43 views

On the second part of solution of a question due to Erdos

Problem. Let $a_1<a_2<\dotsb<a_n\le 2n$ be a sequence of positive integers. Then $$ \min [a_i,a_j]\le 6\left(\Big[\frac n2\Big]+1\right), $$ where $[a_i,a_j]$ denotes the least ...
2
votes
1answer
65 views

Find with proof all solutions to $2^n = a! + b!$, where $a$, $b$, $n$ are positive integers and $a \leq b$.

So far I have looked at $n=1$ with $a=1$ and $b=1$ which is $$2^1 = 1! + 1! = 2 $$ and $n=2$ with $a=2$ and $b=2$, $$2^2 = 2!+ 2! = 4$$ and finally $n=3$ with $a=3$ and $b=2$, $$2^3 = 3! + 2! = 8$$ I ...
5
votes
2answers
73 views

How to decide which moduli to check when solving a “polynomial” congruence?

Consider the following problem: Find all integer solutions to $y^2 = x^5 - 4$. The solution goes something like – check modulo 11, where $x^5 \equiv 0, \pm 1$, and then check cases to arrive at ...
1
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2answers
54 views

Why is this the eigenvector?

For the eigenvector how are they getting \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} when you have \begin{bmatrix} 0 & -1 & -1 \\ 0 & -1 & -3 \\ 0 & 0 & -2 \end{bmatrix} ...
2
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0answers
39 views

Asymptotic Behavior of Differential Equation

physicist here. I'm studying some problems that involve the use of differential equations. The professor of the course has indicated that usually variable changes used to simplify the equations come ...
4
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1answer
106 views

How can I maintain notes while self studying Maths?

Thank you for stopping by this thread. I'm an engineering student rekindling an interest in Maths. I just love studying Maths in my free time (and sometimes it trespasses into my non free time). I ...
0
votes
1answer
38 views

Solving triangle

If side $a$ is known and the angles are given as functions of two variables (let's call them $x$ and $y$), what is the easiest way to find $y$ as a function of $x$. To make things easier, let one of ...
0
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2answers
38 views

Strategy to find the most money to use.

As a reward for a week of good behavior, Tommy was given 7 dollars to spend at the canteen. By the time Tommy got to the canteen, there were only chocolate bars, meat pies and pizza pieces left. The ...
3
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0answers
52 views

Please check my problem solved. The task was to calculate $M^{100}$, where M is a $3\times 3$ matrix

Again, o points for this problem. And there's a small mis-type in the beginning where t1=t2=t3=t=1, it's actually -1
0
votes
1answer
71 views

Verification of solution of a contest problem with a limit of nested radicals

They gave me 0 points for this problem. I think it's unfair. What do you think of this proof, is it correct? $\lim\limits_{n\to\infty} \underset{2n\text{ roots ...
1
vote
1answer
70 views

Proving the hat functions are linearly independent

$$ H_i(x) = \begin{cases} (x-x_{i-1})/(x_i-x_{i-1}), & x_{i-1}\le x\le x_i, \\ (x_{i+1}-x)/(x_{i+1}-x_i), & x_i\le x\le x_{i+1}, \\ 0, & \text{otherwise}. \end{cases} $$ How can I prove ...
0
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0answers
8 views

Finding solutions for a complicated derivative that tends to infinity

The original function goes like this: I differentiated the above function with respect to x, and obtained: I want to find the condition(s) which leads the above derivative to infinity. How can ...
1
vote
1answer
16 views

Asymptotic stopping time for a ball-drawing problem

Take two different boxes, one with $N$ red balls and one with $N$ blue balls. Remove balls one at a time from either box with equal probability. When only one color is left, the (expected value of ...
2
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0answers
72 views

How to learn problem solving strategy for Measure Theory?

I have taken both graduate level Algebra and Measure theory courses but found the latter much more difficult for me. I have put a lot effort on learning it by reading a few reference books and ...
1
vote
3answers
46 views

Units of Measure conversion

I was wondering if i could get some help trying to create a simple math formula. I recently was given an interview to work as a tier1 programmer and was asked to make a program. I made the whole thing ...
0
votes
0answers
9 views

Getting number of detractors/passive responses with only NPS and number of responses.

I have survey data that's computed as: NPS = (a - c)/ (a + b + c) where: a = positive resopnse ...
6
votes
3answers
565 views

High-School level probability and logic problem

So the other day I took a math test, (not for class, its just an optional test, so this isn't and kind of cheating) which included all kinds of logical and problem solving exercises, among others this ...
2
votes
3answers
318 views

Is it possible to solve the Zebra Puzzle/Einstein's Riddle using pure math?

A coworker of mine posted a problem in our local communication software that seems to be a simpler variation of the Zebra Puzzle/Einstein's Riddle. I know how to solve it intuitively, by using ...
0
votes
2answers
42 views

Finding the probability of a complex event…

My apologies - I'm not a math professional, but the guys in my office (a bunch of web programmers) just came across across a logic problem that we've been discussing. We have a solution, but now ...
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0answers
40 views

Combination problems

During numerous math contests I have come across questions such as: I have __ shirts, __ shoes and ___ pants... How many combinations of the __ are possible... As well as many other combination ...
3
votes
1answer
101 views

What are some good problem solving techniques for Math Olympiad style tests? [duplicate]

I am taking part in a Math Olympiad style test at my school in a few weeks. This test is mainly problem solving based and tests you on topics such as counting techniques, algebra, geometry as well as ...
1
vote
1answer
25 views

Where do I begin to solve this ODE?

I've a problem: $ye^{xy}+4y^3+(xe^{xy}+12xy^2-2y)y'=0 $ I can't begin to solve it because I don't know where to start. Help me, please. Thanks!
1
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1answer
94 views

How is problem solving ability on an olympiad level relevant to mathematical graduate study/research?

I am starting on math later than many of my peers and hence have little to no experience in competitive problem solving. Is this a disadvantage during the study of the more abstract mathematics that ...
5
votes
5answers
1k views

Dates with 8 consecutive digits

In many places, dates are written as DD/MM/YYYY. For example, the 25th of April 1736 is written as 25/04/1736. Dates such as this one that use 8 consecutive digits (not necessarily in order) will be ...
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0answers
73 views

Ideas for math problem solving class for undergraduate students in university

In our university there is a huge gap between two group of students. a group of them came from Math Olympiad competitions and have a very strong background from high school but others, they have just ...
1
vote
2answers
57 views

How can I reduce the occurrence of algebra mistakes in my solutions?

Apologies is this is the wrong forum; point me to the right one if that's the case. In this particular case, I'm studying limits (in an intro Calc course, and on Khan Academy) but the question ...
0
votes
2answers
32 views

How to find average walking time per day

I have calculated that the total walking time for a person is 2990702 minutes in 801 days. I want to know his average walking time per day in minutes. I dont know if I need to convert minutes into ...
0
votes
2answers
27 views

Number of ways to ride from one city to another

I stucked with some combinatorial problem: There are 3 highroads between city A and city B. Highroads are intersected with 4 countryroads. What is the number of ways to make a tour from A to B, if we ...
1
vote
1answer
29 views

Help finding the inverse of an exponential function

$$f(x)=6^{3x+9}-2.$$ I got to one step, but I became lost. I understand that I'm converting it into logarithmic form, but I don't understand what the next steps are. \begin{align*} ...
2
votes
1answer
36 views

If for every k the interval $[a,ak]$ contains $n$ specials numbers how many special numbers $[az,akz]$ must contain?

The purpose of my question is to determine if a specific kind of reasoning is true or false. Let's say that for every positive natural number $a$, there is a at least $n$ "special numbers" in the ...
1
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0answers
28 views

Can we choose $g$ so that $\|(g\widehat{(f^{3})})^{\vee}\|_{L^{p}} \leq C \|g_{1}f\|_{L^{2}}^{r} \|(g_{2}\hat{f})^{\vee}\|_{L^{s}}$?

Let $f, f^{2}, f^{3}\in L^{q}(\mathbb R)\cap C_{0}(\mathbb R)$ where $ q\geq p, \ \text{and}$ and $C_{0}(\mathbb R)$ is the class of continuous functions vanishing at infinity. My Questions: ...
0
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0answers
16 views

What is the fastest way to calculate the character of a fundamental representation?

Suppose we know the Cartan matrix $C$ of a Kac-Moody algebra $\mathbb g$: $$ C=\left(\begin{array}{cccc} 2 & -1 & 0 & 0\\ -1 & 2 & -1 & -1\\ 0 & -1 & 2 & 0\\ 0 ...
7
votes
1answer
111 views

A “Theorem Style” Problem Book in Differential Geometry

I am trying to teach myself differential geometry using Lee's Introduction to Smooth Manifolds. To test my understanding, and learn the subject better, I am looking for a good problem book in ...
1
vote
1answer
74 views

Coin Flipping Game - Expected Number of Tails

Can someone help me with this problem? In this game, let $S_{t}$ denote your earnings at time $t$. Your initial earnings is one dollar ($S_{0} = 1$). For each subsequent time, $t = 1, 2, ..$, flip a ...
3
votes
1answer
62 views

Trying to solve $A^TA = B$ where $B$ is known

Have a matrix A that's 4x3 and a matrix B that is known. They relate by the following equation: $$ A^T A = B $$ Trying to find A, given B, such that $A^TA$ is as close to B as possible. I've tried ...
0
votes
1answer
21 views

How to stabilize cyclic tridiagonal matrix algorithm?

I've received a task which is: Solve equation by cyclic tridiagonal matrix algorithm: $$ \frac{\partial{f}}{\partial{t}} = \lambda*\frac{\partial{f}}{\partial{x}}, \\ x\in[0,1]\ t\in[0,1] \\ ...
2
votes
1answer
64 views

Problem Books with Problems less “intense” than Putnam Problems

As the title indicates, I'm looking for a few suggestions on problem books. The problems should be a bit less demanding than Putnam problems. Like the Putnam, however, the prerequisites should be ...
3
votes
2answers
25 views

Calculating the value of numbers with different operations

Calculate the value of: $$-14 + 49 \times 21 - 63 + 56 \div 35 \div 28 \times 70 - 42 \div 7$$ I noticed the numbers are a factor of $7$, so I took out $7$ as a common factor: $$7[-2 + (7 \times 3) ...
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0answers
16 views

Scheduling problem

Consider the following setting: $N$ jobs, each has a starting time, which is assumed to be a natural number and all N numbers are distinct, e.g., the 1st job has starting time at 5, the 2nd is 6, the ...
3
votes
0answers
40 views

Good problem books at a relatively advanced level?

I have been searching for problem books on advanced topics. By advanced I am referring to the undergraduate level and above. I am looking for something analogous to the olympiad type problem books ...
1
vote
1answer
41 views

Series solution

Given the differential equation $2(1-x)y''-3y'+\frac{y}{x}=0$ and in standard form: $y''-\frac{3}{2(1-x)}y'+\frac{1}{2x(1-x)}y=0$ I want to find the series solution for the larger root $σ = 1$ of ...
2
votes
1answer
69 views

Rank of a symmetric matrix. (ISI Sample Paper)

I have rephrased the question as follows : Here, $\langle v,w\rangle=v^tw$ is the usual dot product. Let $A$ be an $n \times n$ symmetric matrix. Let $l_1, l_2, \ldots , l_{r+s}$ be $(r + s)$ ...
5
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0answers
49 views

How to find a list of summands and factors adding up to a total?

I am neither a mathematician nor do I have an idea on how to write down my problem in accurate mathematic formulas. Please feel free to edit my question into shape and remove this paragraph. Also I am ...
0
votes
2answers
39 views

Homework Problem About Finding a Value of $k$ for Which the Given System of Equations Has No Solutions

While working through the third of three packets I'm going through to review for a pre-test for an independent-study calculus class, I came across the following problem: For what value of $k$ ...
2
votes
1answer
72 views

mod operation proof

Prove: $ ab\,\bmod\,d = ((a\,\bmod\,d)\,(b\,\bmod\,d))\,\bmod\,d $ where $a$, $b$ and $d$ are non-negative integers. Reference : http://en.wikipedia.org/wiki/Modulo_operation#Equivalencies Context ...
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1answer
54 views

Find all continuous functions $f:\mathbb{R}\to\mathbb{R}$ satisfying $\frac{f(x+3)}{3+f(x)}=\frac{4+x^2}{x^2}$

Find all continuous $f:\mathbb{R}\to\mathbb{R}$ satisfying $$\frac{f(x+3)}{3+f(x)}=\frac{4+x^2}{x^2}.$$ I believe the original question was $$\frac{f(x)}{3+f(x)}=\frac{4+x^2}{x^2},$$ which has a ...
1
vote
1answer
49 views

Polygon center which always lies inside the polygon (with no hole)

Is there is any type of centre (of polygon) which always lies inside the polygon (with no hole)? Note: Here our polygon may be any type of polygon (convex or concave) but ...
1
vote
1answer
64 views

Can you generate math problems that are solveable?

If you take Linear Programming, it problems are formulated like this: You know that Cabinet X costs 10 cents per unit, requires 6 square feet of floor space, and holds 8 cubic feet of files. ...
0
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1answer
36 views

Odds of Winning Office NCAA Pool

I have 6 coworkers competition in a NCAA bracket. I'm trying to find out how to calculate who has the best chance of winning. For example currently the score card looks like: Player 1. Current Right ...
2
votes
1answer
74 views

Solving an equation for x, characteristics

I am trying to plot characteristics on Matlab for a hyperbolic pde. I need to compute \begin{equation} x=\frac{t}{(1+x^2)}+x_i \end{equation} for every spatial step. Any help with how to do this? ...