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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2
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1answer
53 views

Stair flight problem

A stair flight has 10 steps. A kid can move in jumps of 1, 2 or 3 steps. Assume the kid starts on the floor (step 0), and always has to end in step 10 because there is a door that needs to be open. In ...
6
votes
2answers
426 views

Find the probability of winning at this lottery.

So, the problem I found goes like this: You have $n$ different numbers, numbered from $ 1 $ to $n$. You can randomly choose $m$ (different) of them. The computer also randomly selects $m$ ...
0
votes
1answer
17 views

Solving an equation

I have the following equation: $x_1^3 = \hat{x}_1^3 + e_1\delta(x_1,e_1)$ I have to find the function $\delta(\cdot)$ for which this equation holds. By definition: $e_1 = \hat{x}_1 - x_1$ So I am ...
2
votes
1answer
29 views

Find some probabilities given the probability tree

i've been practicing probability since it's not my strength, but i am doing that without a tutor or an official course, just books and videos. I was reading a problem, and i was capable of draw the ...
52
votes
8answers
2k views

Problems that become easier in a more general form.

When solving a problem, we often look at some special cases first, and then try to work our way up to the general case. It would be interesting to see some counterexamples to this mental process, ...
0
votes
0answers
32 views

Is this polynomial equation solvable? $ \alpha x^{n+2} + \beta x^{n+1} + \gamma x^3 + \delta x^2 + \epsilon x + \zeta = 0 $

I have an equation I wish to solve. I was going to solve it numerically but maybe there is a way to handle it analytically? $ \alpha x^{n+2} + \beta x^{n+1} + \gamma x^3 + \delta x^2 + \epsilon x + ...
1
vote
2answers
53 views

Problem solving: Counting and probability

i am a little bad at probability, i'm studying to overcome this lack. Since i'm not with a tutor i need some help on the correct way to approach a basic probability problem. I would appreciate your ...
2
votes
3answers
32 views

Simplifying nested/complex fractions with variables

I have the equation $$x = \frac{y+y}{\frac{y}{70} + \frac{y}{90}} $$ and I need to solve for x. My calculator has already shown me that it's not necessary to know y to solve this equation, but I ...
0
votes
1answer
70 views

I'm not understanding this puzzle [closed]

At first, I was thinking, mininmum amount of sticks it takes to create the figure, and then how many draw strokes it takes to create the boxes without crossing paths...but I can't figure out what's ...
0
votes
1answer
22 views

Problem Solving - Project Crashing Time

My working out: (EST,EFT) times for the activities: A: (0,0) B: (0,8) C: (3,3) D: (10,38) E: (10,18) F: (18,18) G: (25,33) H: (58,58) I: (25,33) J: (45,53) K: (118,118) Finish: (133,133) ...
0
votes
0answers
5 views

Dominance Network Worded Problems

What are some methods to solve this? Normally for dominance I do as such: Write a matrix for one step dominance, then find total dominance by = D+D^2 - then sum each row of the matrix. Using this ...
1
vote
1answer
28 views

How do i solve this to find PMT?

I know this may seem like a stupid question but i've been up late working on this math assignment and this question just isn't working when i transpose it. So this is the formula to find Present ...
3
votes
2answers
32 views

first order linear PDE solving

$$\dfrac{\partial{\phi}}{\partial{i}}=0$$ $$\dfrac{\partial{\phi}}{\partial{v}}=E-v-i R_0$$ Where E,$R_0$ are constants. How do I solve these kind of PDE's.
0
votes
0answers
19 views

The use of Weighted arithmetic mean to determine the extent to which the data correspond

I don't know when I can ask such question, because it is not a completely mathematic question. I have a text and a topic (single word). I want to check how much this text corresponds to the topic. ...
2
votes
1answer
55 views

How to solve $\int \frac{\tan^{-1}x}{(1+x)^2}dx$?

I know how to solve the following integral $$\int \frac{\tan^{-1}x}{(1+x^2)}dx$$ . We have to substitute $\tan^{-1}x$ as $t$ and we will be done. After this one, I tried to find out $$\int ...
1
vote
2answers
48 views

Solving for $\theta$ in a circle

Let's say you have a pendulum hanging straight down and touching the ground at the lowest point. The pendulum has length $l$. If you pull the pendulum back so that the end is height $h$ above the ...
0
votes
0answers
30 views

Series representation for $L=\frac{3}{2} \sqrt{4 \pi ^2 A^2+W^2}-\frac{\sqrt{5 W \sqrt{4 \pi ^2 A^2+W^2}+6 \pi ^2 A^2+3 W^2}}{\sqrt{2}}$

My question is, is there a series representation or other function of $L$ and $A$ I can use when I solve the following equation for $W$? $L=\frac{3}{2} \sqrt{4 \pi ^2 A^2+W^2}-\frac{\sqrt{5 W \sqrt{4 ...
14
votes
2answers
286 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. ...
4
votes
0answers
100 views

How far away is that cloud?

A few weeks ago I was on an airplane and to pass the time started thinking about this problem. Using the following information, I wanted to know how far away a cloud I could see was. Under some ...
0
votes
3answers
51 views

Derivation of the “Combined Work Formula”

Before I get to my question, some background: Person $A$ can paint a fence at the rate $9 \frac{hour}{fence}$ (or equivalently $\frac{1}{9} \frac{fence}{hour}$) Person $B$ can paint a fence at the ...
-1
votes
0answers
51 views

Represent math problems as Markov chains [closed]

The step by step that takes to solve a math problem (algebra, calculus, etc.) could be seen as a Markov chain? When solving a problem, the next math rule that you are going to apply only depends of ...
2
votes
1answer
77 views

Exponential Diophantine: $2^{3x}+17=y^2$

Is there a way of solving the following equation, in integers $(x,y)$, by hand? : $2^{3x}+17=y^2$. You can also try: $2^{2x}+17=y^2$ or more generally $2^x+17=y^2$; each of these has at least 1 ...
0
votes
1answer
31 views

Finding distance using rates of change — best approach?

The question: A man drives from state $A$ to state $B$ going $60 \frac{miles}{hour}$. Then he returns from state $B$ to state $A$, driving $45 \frac{miles}{hour}$. His total driving time is $2.5 ...
9
votes
2answers
192 views

Computing $\int {\dfrac{\csc^{2014}x-2014}{\cos^{2014}x} dx}$

I don't know how to compute: $$\int {\dfrac{\csc^{2014}x-2014}{\cos^{2014}x} dx}$$ I have tried substituting $t=\tan ^{2} x$ but got nothing out of it. I know there's some trick involved, but ...
2
votes
1answer
66 views

Russian Old Merchant Problems

Anybody know where I can find more of these old merchant problems: Lui: Please tell us a little bit about your early education. Were you already interested in math- ematics as a child? ...
1
vote
3answers
43 views

Consider the following system of linear equations..

Story cut short, I have an exam in a weeks time and this is a question off a previous exam paper - I'm unsure as to how I should go about it as there are 4 variables with only three linear equations.. ...
4
votes
2answers
190 views

Solving awkward quadratic equation to obtain “nice” solution.

I would like to solve the following quadratic equation to get a "nice" analytic solution for $\rho$. $\rho^2(r\sin\theta-2nr^2)+\rho(2nr^3-2r^2\sin\theta-2\sin\theta+2nr)-2nr^2+3r\sin\theta=0$ where ...
7
votes
3answers
373 views

How to find natural solutions of an equation?

When I'm solving problems, I'm often confronted to solving equations, and when I'm solving equations, I'm often confronted to find the natural solutions of these equations. My actual personal ...
1
vote
0answers
25 views

Slicing through a cuboid containing spheres, how many are exposed to the surface and what is their combined volume

So I place spheres of radius chosen at random from a normal distribution of known mean and standard deviation in a cub or cuboid at random (not overlapping) until a known density of the entire cube is ...
10
votes
3answers
267 views

Calculate $\frac{1}{5^1}+\frac{3}{5^3}+\frac{5}{5^5}+\frac{7}{5^7}+\frac{9}{5^9}+\cdots$

I'm an eight-grader and I need help to answer this math problem. Problem: Calculate $$\frac{1}{5^1}+\frac{3}{5^3}+\frac{5}{5^5}+\frac{7}{5^7}+\frac{9}{5^9}+\cdots$$ This one is very hard for me. It ...
4
votes
2answers
110 views

Prove that $\sqrt{n} \le \sum_{k=1}^n \frac{1}{\sqrt{k}} \le 2 \sqrt{n} - 1$ is true for $n \in \mathbb{N}^{\ge 1}$

I'm trying to solve these induction exercises proposed by the department of mathematics of Oxford University. I don't know how to give a valid proof for the third one which says the following: ...
1
vote
1answer
20 views

Problem involving pseudomonotone mappings on Banach space

I have the following question regarding mappings on a Banach space $X$. If anyone has an idea or hint as to how to resolve this question it would appreciated. Let $X$ be a Banach space, $X^{*}$ its ...
2
votes
3answers
936 views

Crossword puzzle- Crossnumber puzzle

The puzzle below is a cross number puzzle, similar to a crossword puzzle except that the entries are numbers. Enter one digit per square. The thick heavy line is a separator. ACROSS: a. A prime ...
0
votes
2answers
24 views

Die Probability Question + Basics of Conditional Probability

A die is rolled twice. What is the probability of observing: a) a four and a three P (obtaining a four and a three) or P(obtaining a three and a four) therefore P(obtaining a four)* P(obtaining a ...
2
votes
2answers
549 views

Missing dollar problem

This sounds silly but I saw this and I couldn't figure it out so I thought you could help. The below is what I saw. You see a top you want to buy for $\$97$, but you don't have any money so you ...
0
votes
0answers
46 views

A simple repartition problem

Suppose the following conditions exist: A and B together own two values, X and Y; X > Y; A buys X for a value of X1; B buys Y for a value of Y1; X1 > Y1; X > X1; Y > Y1. We need to calculate how ...
0
votes
1answer
286 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 ...
3
votes
2answers
529 views

Proving Holder's inequality using Jensen's inequality

Let $p$ and $q$ be positive reals such that $\frac{1}{p}+\frac{1}{q} = 1$, so that $p,q$ in $(1,\infty)$. For $\vec a$ and $\vec b \in \mathbb{R}^2$ prove that $|\vec a \cdot \vec b | \leq ||\vec ...
17
votes
5answers
4k views

How to Improve Mathematical Thinking and General Problem Solving Skills?

I'm a sophomore in university and seriously feel that I'm bad at solving mathematical and algorithmic problems (be it discrete math, calculus or just puzzles). I noticed that I'm only good at solving ...
-1
votes
1answer
54 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 ...
0
votes
0answers
36 views

$\sum$ of binomial coefficients inequality

Let $m,n$ be positive integers with $m>n$. When is it true that $$m\cdot 5^{m-1}\cdot 3+\binom{m}{3}\cdot 5^{m-3}\cdot 3^3\cdot 2+\cdots +\binom{m}{2k+1}\cdot m^{m-2k-1}\cdot 3^{2k+1}\cdot ...
1
vote
2answers
23 views

Problem of bodies in motion in circles.

Consider two circles of radii $4\;cm$ and $8\;cm$, respectively, both circles have the same center $C$ and is two bodies $A$ and $B$, so that $A$ is smaller circumference of the trajectory at a ...
1
vote
1answer
136 views

Comparing $\pi^e$ and $e^\pi$

Comparing $\pi^{e}$ and $e^{\pi}$ I read the answer there but I didn't understand one thing. How I should know to put $\dfrac{π}e-1$ instead of $x$? If I had this question on a test, I had no idea ...
3
votes
0answers
59 views

How to find $f$ and $g$ if $f\circ g$ and $g\circ f$ are given?

The question is: Let $f:\mathbb R\rightarrow \mathbb R$ and $g:\mathbb R\rightarrow \mathbb R$ be two functions such that $(f\circ g)(x)=4x^2+4x+1$ and $(g\circ f)(X)=x^2+2x+2$. Find $f(x)$ and ...
2
votes
0answers
30 views

Fermat pseudo primes

Is it possible for a number of the form $2^p-1$ with $p\in \mathbb{P}$ (the primes) to satisfy $3^{2^p-2}\equiv 1\pmod {2^p-1}$ and not be a prime? In other words, can a Mersenne number be a Fermat ...
0
votes
3answers
15 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 : ...
1
vote
1answer
96 views

If one plays $132$ games in $77$ days, there is a span of consecutive days with exactly $21$ games

This is a high school contest question. Simple answers are required A chess player has $77$ days to prepare for a tournament. During this time he wants to have a match everyday and to have $132$ ...
4
votes
2answers
111 views

Difficult generating function

Define a beautiful number to be an integer of the form $a^n$, where $a\in\{3,4,5,6\}$ and $n$ is a positive integer. Prove that each integer greater than $2$ can be expressed as the sum of pairwise ...
1
vote
2answers
226 views

Can't solve this trignometric equation, why am I wrong?

There is this trig equation: $$ 5\tan x - 2\tan 2x = 0 \text{ for 0 < 0 < 360 } $$ So far I've gotten $$\tan x = \text{0, 180}$$ and all I have to solve now is $$\tan ^2x = 0.2$$ which gives ...
0
votes
1answer
43 views

Best approach or algorithm to solve equation with multiple variables?

I have an equation : $A^6x_1 + A^5x_2 + A^4x_3 + A^3x_4 + A^2x_5 + A^1x_6 + x_7 = B$ What can be the best algorithm/approach I can use to crack this? $A$ and $B$ are constants. $x_1,x_2...x_7$ are ...