# 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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### Expected radius of throwing a dart at a dartboard

I am doing a problem that states: If you are throwing a dart at a circular board with radius $R$, what is the expected distance from the centre? If $x$ is the expected radius, then it would be the ...
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### How to find good maths problems [closed]

Pls can you tell some good ways to find math problem and think deeply about simple things ... I want to think more but need some good problems to work on ... Not that collartz conjecture , or twine ...
4 votes
1 answer
90 views

### List all topologies of $X = \{1,2,3\}$ up to homeomorphism.

Problem 2-2 in Lee's Introduction to Topological Manifolds reads: Let $X = \{1, 2, 3\}$. Give a list of topologies on $X$ such that every topology on $X$ is homeomorphic to exactly one on your list. ...
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### Solving $\frac{1 - \cos(y/2)}{\pi d} \cdot 180c=y$ for $y$

I have been trying to solve a problem that came to me randomly about a week ago, and I am very close to solving it but have reached a roadblock when re-arranging the final equation to solve it. I do ...
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2 votes
1 answer
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### Find the potential $\Phi$ and the field $\mathbf{F} = \nabla \Phi$ for a two-dimensional dipole at the origin. [closed]

I'm struggling with one of the problems from mathematical analysis II course. The problem is next: Find the potential $\Phi$ and the field $\vec{\mathbf{F}} = \nabla \Phi$ for a two-dimensional ...
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### I need help with this propositional logic problem

I study compound statements, and I encountered this problem in the book: The problem I tried a solution: Let p be proposition "The first door leads to freedom" and let q be proposition "...
3 votes
3 answers
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24 votes
3 answers
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### What's the area of the triangle in this geometry problem? I think I can solve it, but it's way too convoluted...

I am trying to solve this geometry problem from an exam. The exam is supposed to be 3 hours long and this is supposed to be 1 out of 10 problems. So given that, the solution should be something quick, ...
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4 votes
2 answers
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### Probability of 3 Aces, Last Picked is an Ace

"Aaron picks an integer $k \in [1,52]$. Then, he draws the first $k$ cards from a standard, shuffled 52-card deck. Aaron wins a prize if the last card he draws is an ace and if there exists ...
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6 votes
1 answer
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### A literally challenging math book

The only way to learn mathematics is to do mathematics. - Paul Halmos Most books about uni-level mathematics follow a strict scheme of giving you the content and letting you practice with it with ...
2 votes
1 answer
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### Combinatorial Probability Question Similar to Sheldon Ross's A First Course in Probability 10th ed Chapter 2 Problem 7

I wrote a combinatorial probability question, and I am not sure if my solution is correct. It is just a slight rewording of a problem from Sheldon Ross's A First Course in Probability 10th ed. Chapter ...
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### $x$, $y$, $z$ positive and $\frac{y}{x-z} = \frac{x + y}{z} = \frac{x}{y}$, find numerical value of $\frac{x}{y}$

$x$, $y$, $z$ positive and $\frac{y}{x-z} = \frac{x + y}{z} = \frac{x}{y}$, find numerical value of $\frac{x}{y}$ The solution in the textbook seems straight forward. Because they are equal ...
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### Normality of the derived family of a normal family.

I am trying to solve a problem from complex analysis which is concerning normal families.The problem is the following: Show that,if $\mathcal F\subset \mathcal H(\Omega)$ is a normal family of ...
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### Some maths journals for tough Olympiad and real analysis problems? [closed]

I wanted to know some maths journals and problems magazines like that in crux mathematicorum, American mathematical society, Romanian maths magazine etc. I want to know even more journals with ...
-1 votes
1 answer
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### How to solve this equation $8 \left(3^x+5^x+7^x\right)=5\cdot 2^x+2\cdot 4^x+17\cdot 6^x$? [closed]

I use Mathematica to solve this equation $$8 \left(3^x+5^x+7^x\right)=5\cdot 2^x+2\cdot 4^x+17\cdot 6^x$$ and get three solutions $x=0\lor x=1\lor x=2.$ I don't know how to solve by hand. How can I ...
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### Buffon's needle in one dimension

I want to solve Buffon's Needle problem but first I was trying to tackle a simpler case. So: consider an infinite line with points each $t$ units. Let's say that we have a "needle" of length ...
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1 vote
1 answer
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### Number of dinners

How many dinners consist of 2 optional appetisers, 3 main courses and 4 optional beverages? My result is $2\cdot 3\cdot4 + 2\cdot3 + 3\cdot4 + 3 = 45$. Where the first product $2\cdot3\cdot4$ ...
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### $\int_D 1$, where $D:=\{(x, y, z) \in \mathbb{R}^3 : x^2 + y^2 = r^2, (r, z) \in C\}$. (Problem 3-29 in "Calculus on Manifolds" by Michael Spivak)

The following problem is a problem in the section "FUBINI'S THEOREM". Problem 3-29. Use Fubini's theorem to derive an expression for the volume of a set of $\mathbb{R}^3$ obtained by ...
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1 vote
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### define $a@b=\frac{b^2+3a}{a+33b},$ calculate (1@2@...@100)×3303

Find the following question in a middle school math competition: define $a@b=\frac{b^2+3a}{a+33b}$, then what is $(1@2@3@\cdots@100)\times3303$? If we assume that $1@2@3=(1@2)@3$, the code below is ...
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### Linear Systems of Diff Eq - unsure how to solve

here is the problem I am trying to solve: "Consider a system of two well-stirred and interconnected tanks that are filled to capacity. Tank 1 holds 40 liters of water, initially containing 20 kg ...