# 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.

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### Every 4-regular simple graph contains a 3-regular subgraph

The following result was conjectured by Berge & Sauer, and proved by Tashkinov [T]. Theorem A. Every 4-regular simple graph contains a 3-regular subgraph. A simple graph is the one with no ...
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### Approximating $\pi$ by an expression of the form $\sqrt{\sqrt{ \cdots \sqrt{ n!! \cdots !}}}$

Here is a problem that appeared as a prize challenge in a periodical for science students, back when I was a student: Find an approximation of $\pi$ formed of the digits $0$ through $9$, each used at ...
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### 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 ...
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### Given that $f(x) :=x^6-6x^5+ax^4+bx^3+cx^2+dx+1$ has its roots as all positive, find $a,b,c,d$

From Larson's "Problem Solving Through Problems" 7.2.10: Given that $f(x) :=x^6-6x^5+ax^4+bx^3+cx^2+dx+1$ has its roots as all positive, find $a,b,c,d$ Thus chapter is about (generalized) ...
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### Minimizing a project costs through dynamic programming

I have a project and I want to minimize the costs. I am responsible for the inspection of 1000 miles of sewer grid in Canada. My goal is to provide time high quality inspection reports. I tried to ...
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This is from a test (I'm not a high school student) given to rising high school juniors. The problem was designed to take less than 20 minutes, preferably 5-15. Judging from its source, this is not a ...
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### What is the probability of two even numbers given one is even?

Your friend has generated two random numbers from $1...10$, independently of each other. What is the probability that both numbers are even given the information that there is an even number among the ...
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### About a problem of field extension in an algebra book by Fumiyuki Terada.

I am reading an algebra book by Fumiyuki Terada. There is the following problem in this book: $E_1, E_2, K$ are fields. $K$ is a subfield of $E_1$. $K$ is a subfield of $E_2$. $p, q$ are ...
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### What are the essential tools and proof techniques for beginning smooth manifolds and differential topology?

I am an undergraduate currently taking a first course in smooth manifolds. I feel that I understand the material intuitively. But, I'm having trouble turning my intuition into proofs. I was hoping ...
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### What could be examples at calculus or introductory analysis level for the idea contained in the statement by David Hilbert?

I read the following quote in the book "As opposed to abstraction the art of doing mathematics consists in finding special cases which contain all the germs of generality. --David Hilbert", however ...
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### Is there a test for tractability of nonlinear differential equations?

After lengthy attempts at tackling the problem one might say that coming up with a closed form solution for a nonlinear differential equation is not possible - that the problem is intractable. But is ...
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### 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 ...
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### 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