# Tagged Questions

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

I cam across this problem and I really don't know how to solve it. So you start with a square that has value 1. You divide this square in 4 so that each new square has a new value, as given by the ...
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### How far away is that cloud?

A few weeks ago I was on an airplane and to pass the time started thinking about this problem. Using the following information, I wanted to know how far away a cloud I could see was. Under some ...
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### Puzzle - zero knowledge proof

I am solving the following problem : I have edge-matching puzzles, where all pieces are squares and the grid has $n$*$n$ format. There is no global image to guide a puzzle solver. Despite the puzzles ...
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### Solving a system of equations

I'm trying to prove the existence of a solution to the system of equations $$c_i = \gamma x_i + (1-\gamma) \frac{x_i^2}{\sum_{j=1}^\infty x_j}$$ for $i\in\{1,2,....\}$ where $\sum c_i=1$. I am also ...
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### Arbitrary ratio sequences on a partition of $\mathbb{R}$ (Partition regularity of fixed ratio sequences)

Background: This question arose purely recreationally and doesn't really fit into any context that I know of. Let $A \sqcup B = \mathbb{R}$ be a partition of the ...
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### How to deal with a mathematical problem if I don't know the answer?

The problem is I'm looking on shortest path between points problem and the intuition tells me that the shortest path between points happens when paths don't cross. It's a step one. Then for all sub-...
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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
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### Shortlist of problems in linear algebra

A while ago I remember seeing a very nice shortlist of problems in linear algebra. It was a list of about 40-50 problems. The idea was that if you solve them, you learn linear algebra very well and ...
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### Iterations $n, n^n, (n^n)^{(n^n)},…$

(Note: I'm reposting this, as I posted the original too late in the evening to gain anyone's notice.) A contest problem (#2 on the 2010 Virginia Tech Math Competition) proffers the solver the ...
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### A question on combinations of a set of numbers

I have the set of the first $n$ primes $\{2,3,5,\ldots,p_n\}$. There are $n^n$ ways of selecting $n$ numbers from this set. Each combination has a number ($C_k$) associated with it and it is the ...
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### Problem on the digits of $n!$

let $m$ be a natural number, is it always possible to find an $N\in \mathbb{N}$ such that $m$ or more "$0$" digits (excluding the terminal ones) appears amongs the decimal digits of $n!$ if $n\ge N$
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### A challenging non homogenous fractional inequality.

The following problem is a challenging generalization of several difficult inequalities, where none of the usual methods used in inequalities seems to work. I would like to know if someone has a ...
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### Is it possible to bruteforce a differential equation

Is there any method to solve differential equations which involves just a number of basic functions combined into various permutations (with various factors) which are then fed into the differential ...
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Let us consider a centred square integrable stochastic process $\{X_t:t\in [0,2]\}$. Also let the eigen values and the eigen function of the kernel of the covariance operator of $X_t$ are $\lambda_1\... 0answers 63 views ### Reference request - Problem book by subject I'm looking for good problem textbooks for self-study. I know only of two of this sort: "Introduction to Measure Theory" by Terry Tao, and "Problems in Algebraic Number Theory" by Esmonde and Murty. ... 0answers 22 views ### 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 ... 0answers 51 views ### Is the matrix with these coefficients invertible? Let$0 \leq x_{i-1} < x_i < x_{i+1} \leq 1$. Let$p, q$be functions that depend on that such that$p$is positive and$q$is non-negative. Let$c_i = a_{i+1,i} = a_{i,i+1}$. Let all other ... 0answers 54 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 common ... 0answers 170 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 ... 0answers 38 views ### Get function definition from an equation My question: I have to find a function$g$fulfilling the equation $$2\frac{t_k \cdot t_0 - 1}{t_k-t_{-1}} = g(t_k) + g(t_{k+1}) + t_{k+1}\cdot g(t_k)g(t_{k+1})$$ Whereby$t_{n+1}=t_n + h$with$t_0, ...
Determine $\phi(x,0)$ for $A(x)=\begin{pmatrix} -1 & \cos(x) \\ 0 & -1\end{pmatrix}$, where $\phi(x,0)t_{0}$ is a solution of $\frac{d}{dx}t(x)=A(x)t(x)$. I am not entirely sure as to how ...
I am working on a computer program and at some point I need to isolate an x and a z. I am basically trying to isolate x and z in these two equations: 1) $xn_{x} + yn_{y} + zn_{z} = n_{d}$ 2) \$\sqrt{(...