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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0answers
27 views

How to solve even/odd divide-and-conquer problems?

I am looking into something called the Josephus problem, which seems to be popular, so I am sure there are lots of explanations online, but I want to do the work myself, but I do need a small push to ...
2
votes
1answer
44 views

Sum of squares using generating functions

I tried using generating functions to solve the sum of squares formula based on the recurrence $a_n = a_{n-1} + n^2$ with $a_0 = 0$. $$G(x) = \sum_{n=0}^{\infty} a_n x^n \\ G(x) - 0 = ...
0
votes
1answer
30 views

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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votes
2answers
38 views

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 $29$
2
votes
2answers
87 views

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 ...
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1answer
31 views

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 ...
9
votes
4answers
533 views

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 ...
3
votes
0answers
33 views

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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3answers
41 views

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 ...
2
votes
0answers
31 views

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 ...
0
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1answer
30 views

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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3answers
85 views

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?
0
votes
1answer
30 views

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 ...
2
votes
3answers
105 views

How to solve an irrational equation?

I want to solve this equation $$2 (x-2) \sqrt{5-x^2}+(x+1)\sqrt{5+x^2} = 7 x-5.$$ I tried The given equation equavalent to $$2 (x-2) (\sqrt{5-x^2}-2)+(x+1)(\sqrt{5+x^2}- 3)=0$$ or $$(x-2)(x+1)\left ...
2
votes
1answer
22 views

Find all sets of N addends equal to a given total W

How many distinct combinations of N natural numbers sum to a given natural number W? For example; for $W=16, N=4$ two of the combinations are $(4,4,4,4)$ and $(5,4,4,3)$ Note: Combination not ...
1
vote
1answer
35 views

Sum of $n$ positive real numbers is 1. Estimate subsums of k elements.

Sum of $n$ positive real numbers $a_1, ...,a_n$ is $1$. Let $S_k$ be maximal sum of k distinct elements of $a_n$. (they can be equal but must have different indexes). What is $\sup S_k$ and $\inf S_k$ ...
2
votes
3answers
75 views

Applying trigonometry in solving quintic polynomials?

So I came across the unsolvable quintic polynomial noticing that solutions can be found by connections with ellipses and such here. But more importantly, I was considering methods we use (or at least ...
0
votes
1answer
54 views

Clock Problem, Number of Chimes

An old fashioned clock chimes as many times as the number of hours it is when it hits a new hour. For example, the clock ticks two times when the clock reads two or the clock ticks 12 times when the ...
8
votes
2answers
90 views

Solution to $e^{e^x}=x$ and other applications of iterated functions?

While trying to solve $e^{e^x}=x$, I ran into the simple solution $x=-W(-1)$. I found it by using the equation $$e^x=x$$Then powering both sides with a base $e$.$$e^{e^x}=e^x$$Now note that the left ...
0
votes
1answer
39 views

Problem solving rolling dice

You are rolling two fair dice, and you are blindfolded, after a certain roll, your partner tells you that you have rolled at least 9. What is the probability that you have rolled at least 11? ...
2
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2answers
19 views

Problem involving counting about marbles

Five red cards and four blue cards are blaced in a bag, five cards are selected blind from the bag, what is the probablity that they are all red?
4
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2answers
56 views

The chart-problem; problem solving

In how many ways can we construct a $6\times 6$ chart with only $1$ and $-1$ such that in every row and column, the product is always positive?
0
votes
1answer
19 views

Showing properties of the kernal and range of a linear transformation.

Let $T:\mathbb{R}^3\to V$. Show directly that the Ker($T$) is a subspace of $\mathbb{R}^3$ and that dim(Ker($T$)) $\leq 3$. Show that $R(T)$ is a subspace of $V$ and that dim$(R(T)) ...
2
votes
1answer
28 views

Finding the formula for a linear transformation given the transformation of the basis vectors.

Consider the basis $\{\vec{p},\vec{q}\}$ where $\vec{p}=(1,1)$ and $\vec{q}=(-1,0)$. Let $T:\mathbb{R}^2\to\mathbb{R}^2$ be the linear operator such that $T(\vec{p})=(1,-2)$ and ...
2
votes
3answers
60 views

Finding roots of Equation involving trig. functions.

In a problem of classical mechanics, I encounter the following equation: $$\mu \sin^4 \theta + \cos \theta = 0 \qquad \mu > 0 \qquad \frac{\pi}{2} < \theta < \pi,$$ where $\mu$ is some ...
2
votes
2answers
36 views

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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1answer
32 views

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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votes
5answers
61 views

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 ...
3
votes
0answers
65 views

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 ...
0
votes
2answers
73 views

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 ...
1
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1answer
85 views

Prove that 012345678910111213 etc is not a periodic sequence.

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 ...
3
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0answers
28 views

Green's Theorem with respect to a given polar region.

Using Green's Theorem, compute the counterclockwise circulation $I$ of $\vec{F}=\langle-\sqrt{x^2+y^2},\sqrt{x^2+y^2}\rangle$ around the region defined by the polar coordinate inequalities $7 ...
2
votes
1answer
61 views

Solve matrix vector equation

Let $A$ be a real $n\times n$ matrix and $w,x$ real $n\times 1$ vectors. For fixed $A$ and $w$ solve the following for $x$: $(x^\top A x)w - (x^\top w) (A+A^\top) x = 0$ Any hints? I do not really ...
1
vote
1answer
63 views

Optimal strategy for unlocking Cho'gall (probability intuition question)

Right now there is an event occurring in Heroes of the Storm where a special hero (Cho'gall) is unlocked if you play with another player currently playing that hero. I ran into a bit of an intuition ...
1
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1answer
46 views

How do we integrate $xe^{x^2}$ in this differential equation?

Yeah I did try searching how to integrate $e^{x^2}$ and mostly I stumbled upon how a similar but not this function called Gaussian function $e^{-x^2}$ is un-integrable , now I was given to solve a ...
0
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0answers
36 views

Solutions of diophantine equation: $s^2 = (ad)^2+ (bc-ad+4ac)^2$

Given diophantine equation: $$s^2 = (ad)^2 + (bc-ad+4ac)^2$$ $s,a,b,c,d$ are all variables. They are all odd. a and b are coprime. c and d are coprime. How do you parametrize all the solutions? ...
1
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1answer
65 views

Quartic diophantine equation: $16r^4+112r^3+200r^2-112r+16=s^2$

Given this diophantine equation: $$16r^4+112r^3+200r^2-112r+16=s^2$$ Wolfram alpha says the only solutions are $(r,s)=(0,\pm4)$ How would one prove these are the only solutions? Thanks.
1
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0answers
31 views

Proof for a periodic function

I have to solve the following exercise: The function $f : \mathbb{R} \rightarrow \mathbb{R}$ is a periodic function with $P = 2\pi$ so that $f(x) = f(x + 2\pi)$ is true for all $x \in \mathbb{R}$. ...
0
votes
0answers
10 views

Point set in affine euclidian planes

Let $\cal{P}$ be an affine euclidian plane, $F_1$ and $F_2$ two points of $\cal{P}$. We consider the following set: $\cal{H}$ = $\{M \in \mathcal{P} \ |\ |MF_1 - MF_2| = F_1F_2\}$ I need to ...
0
votes
1answer
43 views

How to solve the quadratic form

I am a physicist and I have a problem solving this \begin{equation} Q(x)=\frac{1}{2}(x,Ax)+(b,x)+c \end{equation} In a book it says that: "The minimum of Q lies at $\bar{x}=-A^{-1}b$ and ...
0
votes
1answer
27 views

How can I use the solve() function inside of itself?

I'm trying to use the solve function recursively on my TI-89 calculator. Minimal example to demonstrate the concept: ...
0
votes
1answer
14 views

Mandelbrot set, inequality proof

If I have the relation $z_{n+1} = z_{n}^2 + c$. How can I show that $|z_{n+1}| > k |z_n|$ for some $k>1$, if $|z_n| > |c| > 2$? I have no idea how to proof this, any help will be good.
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2answers
28 views

There exist fractal with similarity dimension between 0 an 1?

How to prove that there exist a fractal with similarity dimension D = x, where x is between 0 and 1?
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0answers
92 views

Winning Strategy with Addition to X=0

Problem: Two players play the following game. Initially, X=0. The players take turns adding any number between 1 and 10 (inclusive) to X. The game ends when X reaches 100. The player who reaches 100 ...
1
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1answer
25 views

Game Dealing with Multiplication and Winning Strategy

Two players play the following game. Initially X=1. The players take turns multiplying X by any whole number from 2 to 9 (inclusive). The player who first names a number greater than 1000 wins. Which, ...
1
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2answers
180 views

Determine if a 4-tuple exists

Starting with 2,0,0,3, we construct the sequence 2,0,0,3,5,8,6,..., where each new digit is the mod10 sum of the preceding four terms. Will the 4-tuple 0,4,0,7 ever occur? Any help is greatly ...
1
vote
1answer
34 views

Working Backwards to Determine Winning Strategy

There are two piles of candy. One pile contains 20 pieces, and the other 21. Two players take turns eating all the candy in one pile and separating the remaining candy into two (not necessarily equal) ...
1
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1answer
13 views

Approaching concepts involving graphs in analysis

At least in undergraduate algebra, we can discuss the properties of algebraic structures and their elements without losing generality with notation such as let $G$ be a group and $g\in G$. In using ...
0
votes
1answer
22 views

Proper mathematical description for outer perfect shuffling

I was given the following problem: Consider a pack of $2 n$ cards, numbered from 0 to $2 n − 1$. An outer perfect shuffle is a shuffle of the cards, in which one first splits the pack in two ...
0
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1answer
97 views

Clarification on the intended meaning of a probability problem [closed]

I am just wondering if anyone can help with this question: A radio station held a competition where contestants were invited to pick a number from $1$ to $50$. If a contestant picked the ‘winning’ ...