# 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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### Calculate number of sides of cylinder so each side is a certain width

I'm working on a video-game and as part of the level, I need to create one half of the room curved. For the cylinder, all sides should be of width 450cm, and the cylinder will have radius of 1475cm, ...
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### Balkan Olympiad in Mathematics 2001 [closed]

Where can I find the solutions of the problems from the Balkan Olympiad in Mathematics 2001, Belgrade?
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### Finding the least number of dots to add into a 10x10 grid

I have a 10x10 grid where are some dots. What is the least number of dots that I need to add in order to have 3 dots in every row and column have odd number of dots in every row and column have ...
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### Regarding a Markov chain example state space $\{0,1\}$

I have trouble formulating a question. The set up is $(X_n)$ is a Markov chain with the state space $\mathcal{S} = \{0,1\}$. We know $X_0 =1$ and $X_2=1$ and the transition probability matrix, $p$. ...
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### Finding other point's values on a line knowing one point and distance between two others

So I have a normal line that has points $A, B, C$ and $D$ on it (same order). The distance between $A$ and $D$ is $392$. Point $B$ is equal to $293$. $$CD = 2AB = 4BC$$ Picture of the problem (drawn ...
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### Prove that $(a-b)^n\mid (a^n-b^n) \iff n=1$ under given conditions

Suppose that $a,b,(a-b)$ are pairwise co-prime (i.e. $a\perp b\perp (a-b)\perp a$), and that $\frac{a}{2}<b<a$, where $a$ and $b$ are both positive integers greater than $2$. Let $n$ be odd. ...
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### Paradox of Random Natural Numbers

I've got a question about a game taken from a book called Rachunek prawdopodobieństwa dla (prawie) każdego by Jacek Jakubowski and Rafał Sztencel. Adam and Bolek have a machine that generates a pair ...
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### Cuboid room, hooks and strings proof

I'm trying to do the following problem: In a cuboid shaped room a hook is placed in the centre of each wall, the floor, and the ceiling. Every pair of hooks has either a piece of red or blue ...
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### Need to solve for t but can not work out how to get t on one side

I have a object in free fall with $g$ = acceleration, $y$ is the position above the ground and $t$ = time. I worked out that to find the speed at and $t$ is $dy = g . t$ So to get the position $py$ ...
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### Find numbers that fit each riddle look for more than one answer [closed]

There are two $2$ digits numbers. The first number is greater than $50$ and ends in $0$. When you subtract one number from the other number the difference is $29$
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### A quicker generalized method to finding a curve tangent to another curve?

Let's say we have a curve of $\sin(x)$ and we have to find a curve tangent to this in form of $c(x-d)^{1/3}$. This curve should have the same tangent line as $\sin(x)$ at any point around $(a,\sin(a))$...
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### Solving a Chessboard problem using the Invariance principle

Problem Statement There is an integer in each square of an 8 x 8 chessboard. In one move, you may choose any 4 x 4 or ...
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### Optimization-like question

Let's say I have a formula like $ax + by + cz = N$. $a, b, c$, and $N$ are known and cannot be changed. $x, y$, and $z$ are known and can be changed. The problem is that the equation is not true! My ...
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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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### How is a general case equivalent to a special case and how showing a special case demonstrates a general case, in the proof of pythagoras theorem?

"The general theorem expressed by $\lambda a^2 = \lambda b^2 + \lambda c^2$ is equivalent not only to the special case $a^2 = b^2 + c^2$ but to any other special case. Therefore, if any such ...
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### Where can I find a lot of good exercises on the wave equation?

I find myself in the situation of needing to understand the wave equation inside and out -- I've studied it, obviously, and have been looking for resources for some time. So far in my search I'm ...
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### Solving problems of the form $x^c - c^x = d$ in the complex plane.

Is there a known procedure for solving for $x$ in $x^c - c^x = d$ with known $c, d \in \mathbb C$?
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### Publishing journals in mathematics. [closed]

I want to ask if I am to publish any research paper on trigonometric function. Where is the best place to do that and what field of mathematics can it be categorized?
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### Applying invariance principle on a problem on sequence of positive integers

The problem statement: Start with the positive integers 1,...,4n-1. In one move you may replace any two integers by their difference. Prove that an even integer ...
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### Determine the angle of 3 drawn lines from each corner of 3 congruent squares

Three squares are drawn next to each other. Three lines are drawn from a corner as illustrated. Determine the sum of the three angles exposed (the exact number of degrees or radians):
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### Problem solving: How far is the maximum distance?

The tires located on the front of the car wears out after $25000$ km, while the tires on the back wears out after $15000$ km. How far can you maximum ride with new tires if you can swap the tires ...
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### Christmas problem, the salesman with the nuts [closed]

At the Christmas market, a man was selling nuts in a market stall. The first person bought one nut, the next customer bought two nuts, the next bought four, and so on. That is, every new ...
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### Chess tournament problem

$12$ chess players took part in a tournament. Each played against each other exactly once. After the tournament every chess player did $12$ lists of names. On the first list, the player only wrote ...
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### A coin is tossed if a dice is rolled

I was given this question yesterday. A dice is rolled. If the number is even, a coin is tossed. If it is odd, the dice is rolled exactly once again and results are recorded. Find the probability ...
Prove that the sequence $012345678910111213...$ (all non-negative integers written one by one in natural order) is not periodic. I want to know the shortest and most elegant way to prove it. Can you ...