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.
14
votes
2answers
259 views
Does every “balloon” (dragon, tadpole, canoe paddle) admit a graceful labeling?
Post-Bounty Edit: Still no answer; will gladly accept if someone can provide a reference.
Earlier Edit: It appears that the answer is "yes," either by an already existent publication or by ...
0
votes
0answers
6 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 ...
1
vote
3answers
60 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
43 views
Boats and Stream Problem
Boats and Streams:
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:
...
1
vote
2answers
43 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 ...
2
votes
2answers
53 views
0
votes
0answers
43 views
Why should problems take more time to solve than others? [on hold]
I was wondering, what is the reason exactly that some problems can be easily solved compared to others ? I read that some problems took many, many years to solve. Is it because of the tools required, ...
2
votes
2answers
51 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
23 views
math question im stumped on [on hold]
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 ...
0
votes
1answer
277 views
Distributions of $X^2$ and $X-1$ when $X$ is geometric
Let$ X$ be a discrete random variable with the probability mass function given by $p_x(x)= 2^{-x}$ for $x=1,2,3,\ldots$ and $0$ otherwise.
a) Let $Y=X^2$, find the probability mass function of ...
5
votes
2answers
169 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
51 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
47 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
21 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
57 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
8 views
Limiting Behaviour Transition Matrix
If I was given a transition matrix, and I want to know the limiting behaviour(limiting values) is there a "trick" or a quicker way instead of keep squaring my transition matrix? Also, if my only way ...
0
votes
0answers
34 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
18 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
38 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
0answers
45 views
Clasify states on a Markov chain and Compute $\mathbb{E}_{i}[\tau]$, for $0\leq i\leq n$ [closed]
In $A=(0, 1, 2,\ldots, n)$ let us have a Markov Chain with a stochastic transition matrix defined by $P=(\mathcal{p}_{i, j})_{i, j \in A}$ for $0\leq i\leq n-1$ defined as: $$\mathcal{p}_{i, ...
-1
votes
0answers
19 views
Scheduling jobs with no deadlines issue
The problem of scheduling tasks with no deadline, given n tasks and execution time of task $i$ is equal to $i$, it means that the time performance of Task 1 is 1 and execution time of task 2 is 2, and ...
0
votes
1answer
24 views
Probability “average” understanding
This is more of a problem understanding probabilities than an actual question.
In a game I am playing I can use a certain item to try to unlock different levels.
The item will unlock a new level ...
1
vote
2answers
78 views
How can I solve this problem without having to do it by hand?
I'm dealing with the following problem in computational programming. I'm trying to find a way to build an algorithm that can quickly resolve the following problem statement without forcing me to do it ...
0
votes
2answers
48 views
How many real solutions of this equation?
How many real solutions of this equation $$\sqrt{x}+\sqrt{1-x^2}=\sqrt{2-3 x-4 x^2}?$$
I posted my question at here ...
1
vote
2answers
26 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
31 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
30 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
68 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
...
15
votes
1answer
169 views
How does one cut onions in a mathematically efficient way?
Perhaps a math degree and cooking don't go hand in hand, but hopefully they do.
I have been thinking about this problem for some time when in the kitchen without making any real progress: How does ...
-1
votes
0answers
23 views
Feature of the inverse transform method of random number generation
I was asked this question...
Which of the following is a feature of the inverse transform method of random number generation?
A. the desired distribution does not need to be known
B. the generated ...
0
votes
1answer
66 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
65 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 ...
1
vote
1answer
259 views
Problem Solving ( Sequences and series)
After injection of a dose $D$ of insulin, the concentration of insulin in a patient's system decays exponentially and so it can be written as $D\exp^{-at}$ where $t$ represents time in hours and $a$ ...
0
votes
2answers
25 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 ...
14
votes
6answers
2k views
List of problem books in undergraduate and graduate mathematics
I would like to know some good problem books in various branches of undergraduate and graduate mathematics like group theory, galois theory, commutative algebra, real analysis, complex analysis, ...
0
votes
0answers
19 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 ...
1
vote
2answers
46 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
50 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
1answer
36 views
Special equation solving
I would like to get x from the following function when the y is known and which + means If ...
2
votes
2answers
26 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$ ...
3
votes
2answers
274 views
Permutation of 1…9 with no ascending or descending subsequence of length 4
Arrange the numbers $1,2,...,9$ in such an order that no four of them appear (adjacently or otherwise) in ascending or descending order.
Show that there is no arrangement of the numbers $1,2,...,10$ ...
0
votes
0answers
33 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
143 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 ...
0
votes
2answers
60 views
How to solve this quadratic form equation?
Let $Q(x,y,z)=7x^2+7y^2-2z^2-10xy+8xz+8yz$ be a quadratic form and
$A = \begin{bmatrix}
7 & -5 & 4 \\
-5 & 7 & 4 \\
4 & 4 & -2
...
3
votes
1answer
70 views
Can someone please clarify combinations vs permutations?
I see similar questions asked on here and obviously I did some research and read my book, but it seems like every explanation contradicts another in some way. There are basically infinite scenarios ...
13
votes
3answers
494 views
'Fixed Point' Irrationals
I found this interesting problem which turns out to be more difficult than it first appears:
Suppose $f: \mathbb{R} \rightarrow \mathbb{R}$ is a function such that $f(f(x))=x$ for all $x \in ...
4
votes
2answers
90 views
Egg drop problem
Suppose that you have an $N$-story building and plenty of eggs. An egg breaks if it is dropped from floor $T$ or higher and does not break otherwise. Your goal is to devise a strategy to determine ...
0
votes
1answer
33 views
How many ways are there to parenthesise an expression?
Context
I am writing a computer program to do a brute-force search for a solution to a puzzle which wanted to arrange four numbers with the four standard arithmetic operators and arrive at a given ...
0
votes
1answer
31 views
Solve equation. sum of negatie powers of two equal to one. Diaphantite.
Is the following correct?
Let $\sum_{i=1}^n \frac{1}{2^{x_i}}=1$ where $x_i \in \mathbb{N}_0$ for $i \in \{1,\ldots,n\}$ than the only solutions is
$$x_i=n-1, \quad \forall i \in \{1,\ldots,n\}.$$
...
11
votes
4answers
150 views
How do you create a nonlinear game that the player can always win?
I thought a lot about this question — and initially, I intended to ask this on gamedev.stackexchange.com — but due to its rather theoretical aspects, I think it might be more appropriate to address a ...
