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
votes
4answers
87 views

Coin flipping problem

Suppose that you are flipping a coin endless times. what's the expected round where you would get the same side $3$ consecutive times? I'm guessing it would take $7$ flips to see either ...
2
votes
1answer
74 views

Let $1 + 2^m = 3^n$. What the max value of $(m+n)$?

How do I determine the maximum value of $(m+n)$ if $m$ and $n$ are natural numbers if $1 + 2^m = 3^n$ holds? I have got $\text {max} (m+n)$ to be $5$ so far, but I do not know how to determine whether ...
0
votes
2answers
42 views

Work and time problem

I came up with this problem: $150$ workers were employed to do a particular work. On first day, $150$ workers worked. On second day, $146$.. and each subsequent day, workers kept on decreasing by 4. ...
1
vote
1answer
21 views

Smallest number of groups to sniff

The question given: The sniffer dog at the airport stops beside a trolley piled high with 60 suitcases. One of the suitcases contains contraband peanuts. The dog can tell whether peanuts are hidden in ...
0
votes
0answers
33 views

$n$-couples of people in a row.

For the following problem, I feel my reasoning is something wrong, so I would like if it is in the right direction or if it needs to be rephrased/corrected. The problem reads: How many ways are ...
-1
votes
3answers
42 views

Solving two variables with one equation

I have been trying to solve the following equation, but I am still stuck after trying many different methods. I have been given this equation to solve: $$(1 + z^{-1})^4 (a + bz^{-1} + az^{-2}) - (1 ...
0
votes
1answer
25 views

How does one establish a path of least resistance when solving equations?

For certain systems of equations, it is obvious what the easiest way to organize and manipulate the equations should be. For instance, $$y = 10x + 5$$ $$2x + y = 125$$ So you take the first ...
0
votes
1answer
36 views

solving an equation $x^x= c$ [duplicate]

I would like to find a solution $x$ for $x^x = c$ where $c$ is a positive constant. Firstly I'm looking for an approximative solution when $c$ tends to infinity. Thank you in advance
8
votes
2answers
78 views

Find a succinct problem whose solution requires methods from many sub-branches of mathematics

Some mathematical problems require solution techniques from a single branch (sub-discipline) of mathematics. For instance, most problems in formal logic can be addressed by the methods of formal ...
1
vote
1answer
77 views

What is the optimal strategy when playing `head or tail` per team

Introduction Once a week, we are playing head or tail in my favorite bar. There are $N$ people in the room and each person is guessing whether ...
0
votes
0answers
31 views

Solving a polynomial with modular arithmetic.

$x^5+ax^4+bx^3+cx^2+dx+e=0$ Assume that $a,b,c,d,e$ are not arbitrary and that they are known. I was wondering if it were possible to reduce or 'simplify' this using some modular arithmetic. It ...
0
votes
1answer
46 views

is A an even number?

Let $a,b,c,d$ be positive integers such that $(3a+5b)(7b+11c)(13c+17d)(19d+23a)=2001^{2001}$ hence, prove that $a$ is even. I tried to approach this problem reducting it modulo 6. From which we ...
2
votes
4answers
520 views

How long would it take Mustafa to do the job alone? [closed]

Murat and Mustafa can do a job together in fifteen days. After they have worked together for five days, Mustafa leaves the job. Murat completes the job in sixteen days. How long would it take ...
2
votes
2answers
39 views

Solving for $x$ in $x + \frac{s}{s^2+4} = \frac{2x}{s^2+4}$

How would I go about solving for $x$ in this equation? $$x + \frac{s}{s^2+4} = \frac{2x}{s^2+4}$$
1
vote
1answer
16 views

Is my intuition about this statistics problem sensible?

I'm trying to improve my knowledge of statistics and develop my intuition for solving statistical problems. While doing so I've worked on the following exercise: There are 20 players in a checkers ...
0
votes
1answer
33 views

Related Rate of Cylindrical Cone (Filling + Leaking)

So, we are only told of how to solve related rates with one underlying problem. Either a cone is leaking or Being filled up at some point $x$ but I never encountered both working at the same time. ...
1
vote
4answers
60 views

Explain the thought process to a given solution for $ \frac{1+n}{2^n} =\frac{3}{16} $ please

Part of the given solution to a question leaves me baffled: "...solve the equation $$ \frac{1+n}{2^n} =\frac{3}{16} $$ We can check (simply by plugging in values of $n$) that if $ \leq n \leq 5$, ...
0
votes
3answers
87 views

How can I prove this equation has no solution?

Solve the equation $$-x^3 + x + 2 =\sqrt{3x^2 + 4x + 5.}$$ I tried. The equation equavalent to $$\sqrt{3x^2 + 4x + 5} - 2 + x^3 - x=0.$$ $$\dfrac{3x^2+4x+1}{\sqrt{3x^2 + 4x + 5} + 2}+x^3 - x=0.$$ ...
0
votes
1answer
37 views

How this type of equation is solved? [closed]

I'm solving a relative and ends when the function (x²+y²)²-4x² derive out this equation, but not that I have to do to get resolve it $$f'x = 4x³+4y²x-8x$$ $$f'y = (4x²+4y⁴)y$$ How solve this ...
1
vote
0answers
28 views

Simple exercise in differential geometry

Problem: Prove the identity $V=\sum V[x_i]U_i$, where $x_1, x_2, x_3$ are the natural coordinate functions. (Hint: evaluate $V=\sum v_i U_i $ on $x_j$) Elementary differential geometry written by ...
1
vote
4answers
79 views

How would one solve the following equation?

This equation is giving me a hard time. $$e^x(x^2+2x+1)=2$$ Can you show me how to solve this problem algebraically or exactly? I managed to solve it using my calculator with one of its graph ...
0
votes
1answer
33 views

There exist three consecutive vertices A, B, C in every convex n-gon with n≥3, such that the circumcircle of triangle ABC covers the whole n-gon

From Problem Solving Strategies by Arthur Engel: Problem to prove: There exist three consecutive vertices $A$, $B$, $C$ in every convex $n$-gon with $n \ge 3$, such that the circumcircle of triangle ...
-1
votes
2answers
38 views

$n = a^2 + b^2, \; p^3 = a^3+b^3, \; m^3+2p^3 = 3mn$ then prove that $m = a+b$

If $a$ and $b$ both are positive integers then $m = a+b, \;n = a^2 + b^2, \; p^3 = a^3+b^3$ Then show that $ m^3+2p^3 = 3mn$. This is a easy problem to solve. Just substitute those values and ...
0
votes
1answer
14 views

Mixture & Alligation problem

In what ratio must a person mix three kinds of wheat costing him 1.20,1.44 and 1.74 dollars per kg., so that the mixture formed is worth 1.41 dollars per kg? a)11:77:7 b)12:7:7 c)ratio other than a ...
0
votes
0answers
18 views

Simple ratio problem

I am currently working through some tests for graduate schemes and I am finding the maths tests relatively okay despite the time restrictions. However, I have come across one basic ratio question that ...
4
votes
5answers
125 views

Explanations for why someone cannot divide by $x-4$ for $x(x-4)=x(x-4)(x-5)$

A student divides both sides by $x-4$ and lost a solution $x=4$. How could you explain to the student that they are not allowed to divide by $x-4$ Here is the problem: $x(x-4)=x(x-4)(x-5)$ I am ...
3
votes
2answers
38 views

What is the speed of the car given the time taken to receive an echo?

I am trying to solve this question- The driver of an engine produced a whistle sound from a distance $800m$ away a hill to which the engine was approaching.The driver heard the echo after ...
1
vote
1answer
44 views

Is there another way to solve this equation?

My problem is Solve the equation $$2 \left(\sqrt{x^3-7 x^2+17x-14}+\sqrt{x^4-7 x^3+23x^2-37 x+28}\right)=4x^2-17 x+25.$$ And my solve. We have $$\sqrt{x^3-7 x^2+17x-14}= \sqrt{(x-2) \left(x^2-5 ...
0
votes
1answer
51 views

Resources for solving Euclidean geometry problems using symmetries

I know a number of books that treat geometry from the viewpoint of transformations/symmetries. However, very few of them actually teach someone to solve Euclidean geometry problems using said ...
0
votes
1answer
22 views

Does this System of Complex Variables Has Solutions?

Find all the complex vectors $\mathbf{x}=[x_1,\ldots,x_n]^\top$ and $\mathbf{y}=[y_1,\ldots,y_n]^\top$ in $\mathbb{C}^n$ such that $$ \sum_{i\in S}x_i\bar{y_i}=1,\text{ for all } ...
2
votes
1answer
55 views

Solving diophantine equations

So the equation I am trying to solve is $x^2=y^4-77$ So far I have rearranged and factorised the equation to get: $$(y^2-x)(y^2+x)=77$$ But I am really unsure of how to solve it from here. Thanks in ...
0
votes
0answers
27 views

Understanding foundational terms: notions, objects and meta-objects

I am trying to take my problem solving skill to next level. It looks like It takes a lot of mathematical discipline. Here, This post buys me to get better at proof writing. So, I think is useful to ...
0
votes
0answers
14 views

How to split out tax components

I am working on a problem where I want to split out different tax rate components. Example: Income $= \$1,230,903.00$ Dividends $= -\$2,456.00$ $1231 -\$5,116.00$ Credits $-\$2,161.00$ Long ...
0
votes
1answer
46 views

Transformation of $\log(X)+\log(1-X)$, where $X$ is uniform.

I am trying to calculate the variance of: $$\log(X)+\log(1-X)$$ where $X \sim \mathrm{Unif}(0,1)$. So far, I have tried to use a random variable transformation, i.e. define $Y=\log(X)+\log(1-X)$, ...
0
votes
0answers
28 views

Weird behaviour of CLT's application to binomial.

I am carrying out the simulations of the following experiment for all $n$ in the set $\{1,2,3,...,100\}$. (0) Set $k=0$. (1) Generate $n$ $Bernoulli(0.9)$ trials. (2) Construct estimate ...
1
vote
1answer
42 views

Solving $x^e =c$ in $\mathbb{F}_{p}$

Find all solutions to the equation $x^3=7$ in $\mathbb{F}_{13},\mathbb{F}_{19}$ and $\mathbb{F}_{35}$. In An Introduction to Mathematical Cryptography (Hoffstein et al), we have that proposition ...
0
votes
1answer
60 views

Show that one equation equals another (trigonometry)

I'm studying for a test and when going through old exams I find this one which I'm not able to solve. Show that $$a^2 = (b−c)^2 + 4bc \sin^2 \left(\frac A2\right)$$ equals $$a^2 = b^2 + c^2 ...
0
votes
2answers
81 views

Complex proof - Not sure where to go from here. (homework)

Knowing $2\pi r =\dfrac{h}{m \left(\sqrt{\frac{e^2}{mr}}\right)}$, How do I prove $r = \dfrac{h^2}{((2\pi)^2m e^2)}$? I started by dividing both sides by $2\pi$ to get $r = ...
0
votes
1answer
14 views

Given an integer $i\in\{1,\ldots,NM\}$, find its place in a matrix of size $N\times M$?

The integers $N$ and $M$ are positive. Given the matrix $\mathbf{A}=\left[\mathrm{a}_{nm}\right]$ defined as follows: $\mathrm{a}_{nm}=m+(n-1)M$ for all $m\in\{1,\ldots,M\}$ and $n\in\{1,\ldots,N\}$. ...
0
votes
2answers
37 views

How can I solve this nature log equation?

$ln(x+2)=e^{(x-4)}$ Is there any way to solve this equation without graphing or using GDC ? Thank you
0
votes
1answer
23 views

Recover Marginal Distribution subject to a Constraint

I want to identify the marginal of a normal distribution subject to a restriction. Take two normally distributed random variables $x,y$. Their pdfs are denoted by$\phi(x)$ and $\phi(y)$. The moments ...
0
votes
0answers
44 views

In a sweepstakes giveaway scenario, how does having 2 chances to win the same prize affect the overall odds?

In a sweepstakes giveaway scenario where total entries are expected to result in final odds of 1:93,150.685 for/against a single entrant (after adjusting for multiple entries) and can be won by either ...
0
votes
1answer
28 views

Finding the number of multiples [closed]

I have recently been doing problem solving in math, and I came across this problem: Determine the number of positive multiples of $6$ or $9$ or both, less than $1000$. I appreciate any help. Thanks! ...
4
votes
1answer
76 views

Finding the Determinant of a particular Matrix

I've come across the question of finding the determinant of the $(n\times n)$ matrix, given by $$A:= \begin{pmatrix} x & 1 & 1 & \dots & 1 \\ 1 & x & 1 & \dots & 1 \\ ...
4
votes
2answers
42 views

Example of inverse semigroup with at least two idempotent elements

We say that the semigroup $S$ is inverse semigroup if for any $s\in S$ there is a unique $t\in S$ such that $sts=s,\ tst=t$. Suppose that $E(S)=\{e:\ e\in S,\ e^2=e\}$ and define $$s\sim ...
-3
votes
1answer
61 views

Counting and Abstract Problem Solving [closed]

Suppose that you have a bucket holds fiv-sev c, and one holds tw-one c. How could you use them to measure out thre c of water?
1
vote
2answers
58 views

Solve equation of inverse functions

I have two different functions $y_1=f_1(x)$ and $y_2=f_2(x)$, both invertible but quite complex. I am able to find their inverse functions numerically, i.e. $f^{-1}_1(x)$ and $f^{-1}_2(x)$, by ...
0
votes
0answers
47 views

How do I derive the cubic formula? (without substitutions)

I've heard of a number of ways that people have derived a cubic formula (I've even heard of a number of different ways to show the formula itself too). What I want to know is how to derive it without ...
1
vote
2answers
21 views

Survival bias and probability

Imagine the following situation: A new virus is discovered that is believed to have infected 20% of the population. Anyone infected with the virus has a chance of 50% of dying in their sleep every ...
0
votes
1answer
26 views

How can we solve this system of linear inequalities?

Let $c_i$ be a given non-negative integer for all $i\in\{1,\ldots,n\}$. I would like to find the non-negative integers $a_i$ and $b_i$ for all $i\in\{1,\ldots,n\}$ such that: \begin{align} ...