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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3
votes
1answer
94 views

Last 7 digits of 7th powers

Alice and Bob play the following game. They alternately select distinct nonzero digits from $1$ to $9$, until they have chosen seven such digits. Consider the resulting seven-digit number by joining ...
2
votes
1answer
84 views

How to see 4th dimension? [closed]

Anyone has tricks or methods? Great help, thank you. P.S.: Abstractly of course, not actually seeing 4D, which I don't think is possible.
3
votes
1answer
55 views

Re professional mathematicians working on several problems at once. Source needed.

Recently I read a quote from a working mathematician where he pointed out that professionals have to get used to carrying around several unsolved problems at once. Can anyone help me with the source ...
4
votes
4answers
180 views

Inequalities, when does the sign change here?

I have encountered a problem with inequalities. I have been looking at examples provided by two websites which 'solve' inequalities, however when I try using my own method, the extremely simple ...
6
votes
2answers
182 views

The best balance in studying Mathematics?

I'm a student studying Mathematics at a university level. I've completed Single Variable Calculus, Differential Equations, Multivariable Caculus, Real/Complex Analysis, and Linear Algebra and I've ...
6
votes
1answer
119 views

Coming up with short “magical” proofs

I was reading the solution to this problem: Prove that $f(n) = 2n$ is the only non-constant solution to $2f (m^2 + n^2 ) = (f (m))^2 + (f (n))^2 .$ The solution used these identities, pulled out of ...
12
votes
3answers
214 views

How could I improve this approximation?

In a computer application, I need to solve trillions of times an equation which can be reduced to $$f(x)=\sin(x)-a x=0$$ Newton methods (quadratic and higher orders) are used for the solution. ...
1
vote
1answer
77 views

Books in mathematics based on problem solving

Hi I'm looking for mathematical books that try to teach mathematical concepts by motivating and solving real life problems. For example a book in topology that is motivated by problems of planetary ...
0
votes
3answers
19 views

How to find 2 data point in Bezier satisfy the condition the Chord Length Method?

Suppose bezier curve have 4 control point $P0$, $P1$, $P2$, $P3$. How to find 2 data point $D1$, $D2$ satisfy the condition the Chord Length Method? The Chord Length Method : ...
2
votes
3answers
108 views

Trouble with inequalities

I'm a 9th grade student, going into 10th grade. Math has always been a subject I enjoyed and excelled in. I'm writing a schoolboard-wide math contest next year in mid-February I believe. To prepare ...
40
votes
15answers
13k views

Interview riddle

On the Mathematics chat we were recently talking about the following problem @Chris'ssis had to solve during an interview : $$3\times 4=8$$ $$4\times 5=50$$ $$5\times 6=30$$ $$6\times 7=49$$ ...
5
votes
2answers
55 views

Putting objects in a line.

I'm working on a project outside of school, and I've run into a bit a problem. I thought, maybe there are some problem solvers on the internet who would enjoy this. I have 8 balls, 3 red cubes, and ...
1
vote
2answers
84 views

How to solve for $x$ in the function $y=x\ln(x)$?

I have $y=x\ln(x)$ and I need to solve for x. How am I supposed to do that? Because I get $y=x\ln(x)$ $y=\ln(x^x)$ $e^y=x^x$ and I am stack here... Can somebody help me? EDIT In my case the ...
0
votes
1answer
198 views

Finding the range from standard deviation and Gaussian Curve

The figure above shows a normal distribution with mean m and standard deviation d, including approximate percents of the distribution corresponding to the six regions shown. Suppose the heights of a ...
1
vote
3answers
29 views

Iterative Equation Problem with Constraints

I was given a programming riddle recently. It was eluded to that there is an equation, but I was told that finding the equation was not the goal, and that writing a simple program was the goal. I ...
3
votes
2answers
90 views

Sum of square roots of integers

Let $x, y$ be integers and consider the equation $$\sqrt{x}+\sqrt{y}= 8 \sqrt{31}.$$ It is claimed that this implies $\sqrt{x}= a\sqrt{31}$ and $\sqrt{y}=b \sqrt{31}$ for $a,b$ integers. While this ...
0
votes
0answers
33 views

Can I solve this problem with matrices?

So I have some two dimensional data sets thats I want to analyse. They can be viewed in 2D form as below: $M1$: $$\begin{matrix}00 & 00 & 00 & 00 & 00 & 00 & 00 & 00 ...
0
votes
1answer
25 views

LASSO Problem - A matrix structure!

I'm wondering if anybody knows about the structure of $A^{m\times n}$ in real big data LASSO problems. I want to ask if anybody know what is the degree of sparsity and separability(number of nonzero ...
0
votes
2answers
128 views

Unsure how to solve equation

I have the problem. Solve: $x^3 - 3x^2 + 2x - 5 = 0$. I've done similar, simpler ones like this, but in this case I don't know. Can someone at least tell me what you'd even call this exact type of ...
-1
votes
1answer
55 views

Find the speed of stream from rowing speeds with and against the stream

Problem A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is: (A) 1 ...
1
vote
2answers
46 views

How to solve this simple linear equation

I have the following equation (I personally wrote) $2x + (5+3) = 46 + 3x$ Is the above equation possible at all? If yes, how to solve it? I am new to math, as a free-learner (not associated with my ...
1
vote
2answers
57 views

Elements and Unions [closed]

Need help solving this problem step by step!
2
votes
2answers
70 views

Why does the additive subgroup of $\mathbb{R}$ generated by $1$ and $\sqrt{2}$ contain arbitrary small elements? [duplicate]

Let $G\subset \mathbb{R}$ be the additive subgroup of $(\mathbb{R},+)$ defined by $G=\mathbb{Z}+\sqrt{2}\mathbb{Z}$. I want to prove that for every $\epsilon>0$ there exists an element ...
-2
votes
1answer
40 views

math question im stumped on [closed]

Two race cars are speeding around the racetrack at different speeds. One goes around the track in 2 minutes; the other goes around the track in 1 1/2 minutes. How often does the faster car pass the ...
5
votes
2answers
194 views

How many diamonds did they steal?

There are $7$ thieves. They steal diamonds from a diamond merchant and run away into the jungle. Whilst they're running, night falls and they decided to rest in the jungle. When everybody is ...
1
vote
1answer
56 views

what is wrong in my answer and what will be the correct solution for this probability question ?

A and B play a game where each is asked to select a number from 1 to 5. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is - ...
0
votes
2answers
51 views

X and Y are independent random variables and their distributions are..

X and Y are independent random variables and their distributions are.. $P(X=1) = 0.1 $ $P(X=2) = 0.2$ $P(X=3) = 0.3 $ $P(X=4) = 0.4 $ $P(Y=4) = 0.4 $ $P(Y=2) = 0.3$ $P(Y=3) = 0.2 $ $P(Y=4) = 0.1$ I ...
0
votes
1answer
26 views

$X $ and $Y$ are continuous $RVs$, such that$ f(x,y) = 2, 0\leq x\leq 1, 0\leq y\leq 1, 0\leq x+y\leq 1$

X and Y are continuous RVs, such that $f(x,y) = 2, 0\leq x\leq 1, 0\leq y\leq 1, 0\leq x+y\leq 1$ I'm trying to find $P(x<1/2,y>1/2)$. So i'm integrating from $\dfrac{1}{2}$ to $1$ for $y$ ...
1
vote
3answers
70 views

Let $U$ be $~U [0,1] $and let $Y = U^{\frac{1}{2}}$

Let $U$ be $\sim \mathcal{U}[0,1]$ and let $Y = U^{1/2}$. I'm having trouble finding the $E(Y)$. How do I go about doing this?
0
votes
0answers
48 views

Strategy in solving linear equations with 3 unknown variables

I have an equation with this form: $ A x + B y + C z = N$ $A$, $B$, $C$, and $N$ are known. $A$, $B$, $C$, $N$, $x$, $y$, and $z$ are positive integers $>= 0$. I need to find out values of ...
0
votes
1answer
50 views

P(X>Y) Probability Double Integral

$f(x,y) = \frac{12}{7(x^2 + xy)}$ $ 0 \le x \le 1$ and $0 \le y \le 1 $ I want to know the $P(X>Y)$. I believe the correct solution to this is integrating from 0 to 1 for dy and y to 1 for dx ...
0
votes
1answer
21 views

Uniform Spinner is spun twice..

A fair uniform spinner is spun twice, and the results V and W are noted. V and W are uniform RVs ∼U[0,1]. I'm trying to answer the question what is the joint pdf for V and W. I know that I have to ...
0
votes
1answer
24 views

Probability “average” understanding

This is more of a problem understanding probabilities than an actual question. In a game I am playing I can use a certain item to try to unlock different levels. The item will unlock a new level ...
0
votes
2answers
50 views

How many real solutions of this equation?

How many real solutions of this equation $$\sqrt{x}+\sqrt{1-x^2}=\sqrt{2-3 x-4 x^2}?$$ I posted my question at here ...
14
votes
2answers
302 views

Does every “balloon” (dragon, tadpole, canoe paddle) admit a graceful labeling?

8/18/14 Edit: If anyone has a copy of a related reference, then I would be happy to see it. For now, I am accepting the answer below and considering the question answered in the affirmative: Yes. ...
1
vote
1answer
53 views

How is this card/paper plate magic trick done?

There are 3 paper plates, in which A is written on one, B on the 2nd, and C on the third. Now the person performing the trick knows the initial order of the paper plates. He then asks an audience ...
1
vote
1answer
32 views

Ehrenfest's urns have been loaded with a total of 6 balls…

Ehrenfest's urns (two of them) have been loaded with a total of 6 balls. If the first urn now contains 1 ball, what is the probability that it will contain 2 balls after the next transition? My ...
1
vote
1answer
33 views

Probability - A trial consists of tossing a fair coin twice and noting H = number of heads observed…

A trial consists of tossing a fair coin twice and noting H = number of heads observed. What is the probability that if 5 trials are performed, we will note H=0 two times, H=1 one time, and H=2 two ...
6
votes
2answers
130 views

Advice for self-studying Inequalities and Calculus

I'm interested in self-studying the following books over the next year or so: Spivak's Calculus (I'm already in Ch. 5 and it is very slow going) The Cauchy-Schwarz Master Class by J. Michael Steele ...
1
vote
2answers
89 views

How can I solve this problem without having to do it by hand?

I'm dealing with the following problem in computational programming. I'm trying to find a way to build an algorithm that can quickly resolve the following problem statement without forcing me to do it ...
0
votes
1answer
72 views

How can I solve this problem without doing it by hand? [duplicate]

I'm dealing with the following problem in computational programming. I'm trying to find a way to build an algorithm that can quickly resolve the following problem statement without forcing me to do it ...
1
vote
2answers
73 views

Is there any way to solve this problem without having to do it by hand? [duplicate]

I'm dealing with the following problem in computational programming. I'm trying to find a way to build an algorithm that can quickly resolve the following problem statement. Is there any way to group ...
0
votes
2answers
29 views

Guess the right permutation game

Consider the following game (somewhat similar to Bulls and Cows): player A selects a permutation of $n$ different numbers, say $1$ to $n$. Player B then has to guess the permutation: he suggests some ...
1
vote
2answers
61 views

Concept of Probability in math first level

I am trying to teach myself the concepts of probability and I was wondering if this is correct. I am only 13 years old and did not learn this yet. I am just reading parts of a probability book to get ...
-1
votes
1answer
72 views

Mean and Standard Deviation self thought problem

I am 13 years old trying to teach myself about standard deviation and was wondering how this problem would look like. I know I am young to be learning this but I was reading about this and got ...
0
votes
0answers
21 views

Difficult Integral in functional basis

Let $$g(x)=\int f\prime(x)\left[\frac{4}{3}x^2+4x^3+(2x^2+4x^3)f(x)+6x^2f^2(x)+xf^3(x)\right]dx$$ express $g(x)$ in terms of $\{1,x,x^2,x^3,....\}$ and $\{f(x),f^2(x),f^3(x),...\}$. Is there a clever ...
2
votes
2answers
32 views

Divisibility of sum of squares

I'm currently working through an olympiad problem book that uses the following fact: $3 \mid a^2 + b^2 \implies 3 \mid a$ and $3 \mid b$. I don't see how to show this. I know for that a prime $p$ ...
0
votes
1answer
40 views

Special equation solving

I would like to get x from the following function when the y is known and which + means If ...
0
votes
0answers
51 views

Finding minimum of a distance function using matlab

I have a function for that I want to find the minimum. The function calculates the distance between two sets where a set is defined as matix of row vectors $ D = [ d_1, d_2, ..., d_n]$, $d_n$ is a $m ...
5
votes
1answer
147 views

Solving the equation $a ^ b + b ^ a = 200$

Find $a$ and $b$, $a ^ b + b ^ a = 200$ One of the answers is $a = 1$ and $b = 199$. Lets say $a, b$ belongs to $\mathbb{R}$ then there will be many solutions, for each $a$ there exist $b$, in ...