# Questions tagged [problem-solving]

The problem-solving tag has no usage guidance.

42
questions

**2**

votes

**0**answers

40 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{...

**0**

votes

**1**answer

70 views

### Solving an recursive sequence [closed]

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

**3**

votes

**0**answers

115 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 ...

**-2**

votes

**1**answer

52 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 ...

**1**

vote

**2**answers

124 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), ...

**15**

votes

**1**answer

483 views

### Characterization of a sphere: every “sub-sphere” has two centers

Let me ask this question without too much formalization:
Suppose a smooth surface $M$ has the property that for all spheres $S(p,R)$ (i.e. the set of all points which lie a distance $R\geq 0$ from $p ...

**5**

votes

**1**answer

165 views

### Classifying functions up to suitable pre-composition and/or post-composition

What's a name for a general technique I've seen used many times?
Given any family $\mathcal{F}$ of functions such that $f:X\to Y$ for all $f\in \mathcal{F}$ when one wishes to study in general for an ...

**16**

votes

**2**answers

982 views

### Is there any published summary of Erdos's published problems in the American Mathematical Monthly journal?

As we know Erdos has proposed a considerable number of problems in the "American Mathematical Monthly" journal. Is there any published summary of Erdos's published problems in the American ...

**1**

vote

**1**answer

55 views

### A problem with elementary inequality involving probabilities and Brier scoring rule

I am trying to prove certain relations between certain values of the so called Brier inaccuracy measure (Brier scoring rule).
Given a vector $p = (p_1, \ldots p_n)$, where $p_1 + \ldots p_n = 1$ and $...

**13**

votes

**0**answers

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 ...

**1**

vote

**5**answers

546 views

### Inequality with symmetric polynomials [closed]

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

**1**

vote

**0**answers

417 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 $z\geq 0$ ...

**1**

vote

**0**answers

80 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?
...

**0**

votes

**2**answers

101 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 ...

**2**

votes

**1**answer

272 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 ...