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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1answer
61 views

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 ...
0
votes
2answers
26 views

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 ...
0
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0answers
30 views

How to invert a transformation

I've come across a recursive equation involving vectors. You basically have one starting point $P = (x, y)$ and you transform it to another point $P'=(x', y')$ with the following equations $$ x' = x ...
2
votes
3answers
61 views

Where did two dollars go?? [duplicate]

One of my school friends gave me this sum.Its basically a story formated into a sum STORY There were 3 friends. They each gave 20 dollars to buy a radio. They bought the radio for 60 dollar. Later ...
1
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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 $py$ ...
-3
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 ...
1
vote
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 ...
1
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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
votes
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 $c, d \in \mathbb C$?
-4
votes
3answers
86 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
votes
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
37 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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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
vote
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
votes
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
vote
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
votes
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
vote
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
vote
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.
1
vote
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?
4
votes
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
vote
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 ...