# Questions tagged [problem-solving]

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### How to proceed in this Boundary value problem where Eigen values are calculated numerically?

While solving a boundary value problem (background provided in the Context section) I reach the following variable separated two equations ($F(x)$ and $G(y)$) \begin{eqnarray} \lambda_h F''' - 2 \...
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### Simplest diophantine equation with open solvability

What is the simplest diophantine equation for which we (collectively) don't know whether it has any solutions? I'm aware of many simple ones where we don't know (whether we know) all the solutions, ...
87 views

### Coupled (Solid-Fluid) Heat transfer problem in a Heat Sink

I am trying to solve a coupled heat transfer problem between a solid and fluid (I have under braced the governing equations and labelled them). Eqn. (3) is the partio-integral differential equation I ...
319 views

### Covering the disk with a family of infinite total measure - the convex sequel

Let $(U_n)_n$ be an arbitrary sequence of open convex subsets of the unit disk $D(0,1)\subseteq \mathbb{R}^2$ s.t. $\sum_{n=0}^\infty \lambda(U_n)=\infty$ (where $\lambda$ is the Lebesgue measure). ...
496 views

### Covering the disk with a family of infinite total measure

Let $(U_n)_n$ be an arbitrary sequence of open subsets of the unit disk $D(0,1)\subseteq \mathbb{R}^2$ s.t. $\sum_{n=0}^\infty \lambda(U_n)=\infty$ (where $\lambda$ is the Lebesgue measure). Does ...
214 views

### How many arrangements of $n$ points with $k$ edge lengths exist in $d$ dimensions?

[Asking on behalf of a high school mathematics course, but responses written at any level are welcome!] I was recently reading over a nice puzzle called the four points, two distances problem: ...
56 views

### Using weak maximum principle to prove continuous dependence of the boundary data?

I am currently looking at the following ingomogenous Dirichlet problem over an open, bounded domain $\Omega \subset \mathbb{R}^2$ with continuous boundary: \begin{align} \begin{cases} -\operatorname{...
75 views

### Solving an recursive sequence [closed]

I have an recursive sequence and want to convert it to an explicit formula. The recursive sequence is: $f(0) = 4$ $f(1) = 14$ $f(2) = 194$ $f(x+1) = f(x)^2 - 2$
212 views

### Looking for U.K. problem column (?) from 1980s

While digging through some dusty corners of my file cabinet, I found a photocopied sheet of eight (handwritten) problems from 1985 that I recall receiving from my secondary school mathematics teacher ...
57 views

### I need help with snake's position bounds based on center point(rounded) and the length of the snake problem [closed]

First of all, if it's an existing problem just tell me the name, please. To solve the problem a formula/algorythm which receivs a center point of a snake (snake game type (points on a grid connected ...
142 views

### Constructing an n-node DAG, with exactly k paths between node 1 and node n [closed]

Pretty straight forward, yet I didn't find how to approach such a problem. I tried constructing a solution from the reverse problem (Given a DAG count the number of paths between node 1 and node n), ...
498 views

2k views

### Identifying poisoned wines, with a twist

(This is a joint musing with Andrew Gordon and Wyatt Mackey) There is a classic, elementary riddle, discussed before on MO and math.SE: suppose you have 1000 bottles of wine, and one is poisoned. The ...
600 views

### Inequality with symmetric polynomials [closed]

How to prove the inequality $a^6+b^6 \geqslant ab^5+a^5b$ for all $a, b \in \mathbb R$?
521 views

### The derivative of an integral function with indicator and max function as integrand

I encounter the following type of problem: \begin{equation} F(x) = \int_a^b \mathbf{1}_{\{v+x-h(v)\geq 0\}}\max\{h(v)-y-x,0\}dv \end{equation} where $\mathbf{1}_{\{z\geq 0\}}=1$ if event $z\geq 0$ ...
81 views

### Diophantine equation $z=(ax+by+c)/(dxy)$, references? [closed]

I am looking for some sources (books or papers) which discuss the Diophantine equation $$z=\frac{ax+by+c}{dxy}$$ where $a,b,c,d$ are given positive integers. Could anyone give some references? ...
115 views

### Characterize the Monotonicity of a root of a cubic equation

I have a cubic function: \begin{equation*} h(x)\triangleq \eta+x-\frac{V(\eta-x)^3}{c\eta} \end{equation*} we know that $x\in[0,\eta)$ and all letters are positive and $V>c/\eta$. Hence we know ...
282 views

### the sum of fractional parts times the ordinary powers

Is there any way to compute/express $\sum\limits^m_{i=0}\{\frac{q*i}{m}\}(\frac{i}{m})^n$ ? Here $q,m,n$ are natural numbers, one can assume $gcd(q,m)=1$. Furthermore, $n$ can be treated as a ...
375 views

### Division of a square and value of a disk

[Full disclosure] I asked this question on math.stackexchange with little success : https://math.stackexchange.com/questions/1866295/division-of-a-square-and-value-of-a-disk I cam across this problem ...
65 views

10k views

### Contest problems with connections to deeper mathematics

I already posted this on math.stackexchange, but I'm also posting it here because I think that it might get more and better answers here! Hope this is okay. We all know that problems from, for ...
238 views

### Fast removal of weighted edges in a graph in a way such that all shortest paths are preserved

This problem is analogous to fast removal of the minimum number of edges in a weighted graph such that if the graph were to be drawn on paper with edge lengths linear in proportion to their weights, ...
4k views

### Elementary mathematical books

I understand that this is a bit of offtopic but mathoverflow is my last resort, as google did not help. I am about to publish an English translation of my Russian book for high school students. The ...
2k views

### Question about Banach's matchbox problem.

Hi, I've been struggling with this for awhile ( http://en.wikipedia.org/wiki/Banach%27s_matchbox_problem) and I put together this little bit of Python code ...
12k views

### Examples of using physical intuition to solve math problems

For the purposes of this question let a "physical intuition" be an intuition that is derived from your everyday experience of physical reality. Your intuitions about how the spin of a ball affects ...
663 views

### Math Puzzle: calculating the dimensions of variable rectangles in a fixed square

I've got the following problem, I've got a fixed size square and within there are a fixed number of rectangles to be contained within it. I want the rectangles to cover the maximum amount of space ...