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
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2answers
1k views

Particular solution to a 3rd order ode (method of undetermined coefficients not working)

I am trying to get the particular solution to the equation - $y''' + 4y'' + 5y' + 2y = e^{-t} $ We are taught the method of undetermined coefficients to solve such equations. However, one of the ...
2
votes
0answers
170 views

Sought-Given-Solution-Answers

I am a German student attending lectures delivered in English at the KTH Stockholm. There I am supposed to solve a problem sheet, using a "Sought-Given-Solution-Answer approach". I am not really into ...
1
vote
0answers
74 views

Linear Optimization Problem - Assign Objects to People

Say you have a 100x5 matrix of integers between -10 and 10, including zero. Each row represents an object; each column represents a person's ranking of the objects. Of the possible ranking values ...
2
votes
3answers
303 views

How can I find out 2 unknowns in a cubic equation?

I need to give a bit of a background first, so please bare with me. I have a set of values that represent servo motor position values. By default I end up with a large set of values and I'd like to ...
0
votes
2answers
313 views

machine learning project ideas

I am interested about playing with machine learning algorithm and time series analysis. Is there website/resource with a comprehensive list of sample projects/proposals one may be interested about?
1
vote
1answer
63 views

inequality fraction

I saw this problem in an Australian maths olympiad: $6/10 < a/b < 10/15$ The problem asked for the lowest possible value of $b\in \mathbb{Z}$. I tried manipulating but couldnt derive one of ...
5
votes
5answers
222 views

Pre-Calculus - Solving for $x^3$

In my Pre-Calculus class we were discussing $i$, and all of it's mysterious imaginary wonders, but I had a moment of confusion during the lecture. This was the problem: Solve for $x$. $$ x^3 - 1 = 0 ...
1
vote
1answer
117 views

Reverse engineer a Bayesian estimate?

My apologies if this is a basic question because I am no mathematician. Struck on my work on this, so came here to get some help.I am working on this bayesian estimate explained here.This is a ...
1
vote
2answers
363 views

Multiplying Reciprocal Exponents

This is the problem I have: $$y^{\frac{3}{2}} = 5y$$ What I tried so far was raising $y^{\frac{3}{2}}$ to the $\frac{3}{2}$, making it equal $1$, but I had trouble raising $5y$ to that power.
2
votes
2answers
1k views

An exercise from a linear algebra book (hoffman and kunze)

I am not sure how to solve this exercise: Find all solutions of $$\begin{align*}2x_1-3x_2-7x_3+5x_4+2x_5&=-2\\ x_1-2x_2-4x_3+3x_4+x_5&=-2\\ 2x_1\qquad-4x_3+2x_4+x_5&=3\\ ...
5
votes
3answers
555 views

When chessboards meet dominoes

You probably have heard about the following brainteaser : Consider a 8×8 chessboard. Remove two extreme squares (top-left and bottom-right e.g.). Can you fill the remaining chessboard with 1×2 ...
0
votes
3answers
408 views

Which is the biggest integer that divides all integers that are the product of three consecutive odd numbers?

I read this problem from a high-school-math-problems-calendar, and I'm solving them in my spare time just for the fun of it (what in math is not about the fun? =) ), but this little one it's been hard ...
1
vote
0answers
61 views

Monotonicity of Solution to $∫_0^1(x- \frac 1 g )x^{ \frac 1{gr-1} }\frac {\ln x}{(1+xgr)^2}dx = 0$

Given any parameter $g > 1$, I can show that the following equation has a unique solution $r^{*} \in (\frac 1 g, \infty) $, $$∫_0^1(x- \frac 1 g )x^{ \frac 1{gr-1} }\frac {\ln x}{(1+xgr)^2}dx = ...
0
votes
5answers
113 views

What is the algorithm for solving an equation like this one?

The solutions of the equation : $\sqrt{x+2\sqrt{x-1}} + \sqrt{x-2 \sqrt{x-1}} = 2$ are: A) $x=1$; B) $x=2$; C) $x\in [1,2]$; D) $x\in \begin{bmatrix} \frac{3}{2},2 \end{bmatrix}$; E) ...
3
votes
4answers
213 views

Are there problems that are optimally solved by guess and check?

For example, let's say the problem is: What is the square root of 3 (to x bits of precision)? One way to solve this is to choose a random real number less than 3 and square it. ...
1
vote
3answers
1k views

Smallest multiple whose digits are only ones and zeros [duplicate]

I have a collection of typewritten pages that formed the basis of a third year problem solving course offered about 25 years ago at U. Waterloo. I've been slowly working through the problems and have ...
1
vote
2answers
92 views

Solving Equation Difficulty (analytically or by plotting)

I found this interesting problem in a programming forum. It would be great to get some help.. Solve for $K$, $K-1 \leq 27\cdot\log_{10}(9(K-1)) $ We plotted it to find that $K\leq77$. Can you solve ...
1
vote
1answer
83 views

Squared Series Fourier [duplicate]

Possible Duplicate: Fourier 1st step? How to find fourier transform of a series of the such form: $$y_k=\left[f(x) \right]^{2},$$ but I am not sure of the step by step for going about this ...
11
votes
3answers
416 views

Penguin Brainteaser : 321-avoiding permutations

There are $k$ penguins, $k\ge 3$. They are all different heights. How many ways are there to order the penguins in a line, left to right, so that we cannot find any three that are arranged tallest to ...
5
votes
2answers
751 views

Invertible Matrices are dense

While reading about linear algebra for math olympiads in these notes, I came across the following assertion: Remark. The set of invertible matrices form a Zariski (dense) open subset, and hence to ...
23
votes
14answers
2k views

How can we produce another geek clock with a different pair of numbers?

So I found this geek clock and I think that it's pretty cool. I'm just wondering if it is possible to achieve the same but with another number. So here is the problem: We want to find a number ...
4
votes
1answer
107 views

How to represent $\max(x, y)$ in terms of absolute?

We can represent Absolute in terms of Max: $|x| = \max(x, -x)$ but how to represent $\max(x, y)$ in terms of Absolute
4
votes
2answers
648 views

Folding a rectangular paper sheet

You are given a rectangular paper sheet. The diagonal vertices of the sheet are brought together and folded so that a line (mark) is formed on the sheet. If this mark length is same as the length of ...
18
votes
1answer
1k views

What was Ramanujan's solution?

The wikipedia entry on Ramanujan contains the following passage: One of his remarkable capabilities was the rapid solution for problems. He was sharing a room with P. C. Mahalanobis who had a ...
2
votes
3answers
161 views

Solve equations using the $\max$ function

How do you solve equations that involve the $\max$ function? For example: $$\max(8-x, 0) + \max(272-x, 0) + \max(-100-x, 0) = 180$$ In this case, I can work out in my head that $x = 92.$ But what is ...
0
votes
2answers
2k views

Compound interest - how to solve this with logarithms & geometric series?

I could use some help with the following: Jacques is saving for a new car which will cost 29000 dollars. He saves by putting 400 dollars a month into a savings account which gives 0.1% interest ...
12
votes
5answers
251 views

Issues with text problems

When I tutor, I often see people who kind of know the stuff they cover in school at the moment and succeed at straight problems like: Find the derivative of $f(x) = \frac 12 x^2$ But when it ...
0
votes
1answer
135 views

How many columns in a grid of arbitrary width, with minimum and maximum allowed column widths?

In a grid of variable width, with a variable number of columns having a minimum and maximum allowed width, how can I calculate the number of columns for any given grid width so they fall within the ...
0
votes
1answer
75 views

A combinatorics problem refer to this problem?

If i define $f(m,n)=$ $$\sum_{1\leq k\leq mn}\left\{ \frac{k}{m}\right\} \left\{ \frac{k}{n}\right\} .$$ Then prove $$f(m+n,n) - f(m,n) =\frac{n^2-n}{4}$$ for all $m$ and $n$. This question came ...
17
votes
3answers
403 views

A sum of fractional parts.

I am looking to evaluate the sum $$\sum_{1\leq k\leq mn}\left\{ \frac{k}{m}\right\} \left\{ \frac{k}{n}\right\} .$$ Using matlab, and experimenting around, it seems to be $\frac{(m-1)(n-1)}{4}$ when ...
1
vote
2answers
266 views

Minimum tiles for a grid given a few conditions

Today, I came across an exercise in Problem Solving Strategies by Johnson and Herr which I was not sure was the best way to solve it. The problem given was: Below I drew up a quick sketch of a ...
10
votes
1answer
2k views

Expected Ratio of Coin Flips

If you flip a coin until you decide to stop and you want to maximize the ratio of heads to total flips, what is that expected ratio? Assuming that you want to maximize the ratio, meaning ...
1
vote
0answers
142 views

Pair of equations with any equal number of variables with unique solution?

$(a+b+c\cdots)\neq(a^{2}+b^{2}+c^{2}\cdots)$ given all distinct values for the variables? When I came across this topic, it made me curious as to explore other possibilities, as here, what other two ...
0
votes
2answers
160 views

$(a+b+c\cdots)\neq(a^{2}+b^{2}+c^{2}\cdots)$ given all distinct values for the variables?

Please note that the solution must not require more equations to solve as do the variables increase. Apparently, $(a+b+c\cdots)\neq(a^{2}+b^{2}+c^{2}\cdots)$ seems pretty obviously to be true given ...
2
votes
1answer
112 views

Conditional probability: Why can't I make this assumption?

Here is the question :If we are told that among the 10 coins, at least three have landed on heads. What is the probability that there are at most five heads? In other words, P( at most five head | ...
0
votes
4answers
406 views

How to get from: $a^2 - a + 1 = 0$ to $a = \frac{1}{2}(1\pm\sqrt{1+4})$

Given that $a^2 - a + 1 = 0$, my book says: Therefor $a = \frac{1}{2}(1\pm\sqrt{1+4}).$ I have forgotten all the theory behind this.
0
votes
1answer
435 views

Equations and Pattern formulas problem solving

I have this question to answer and I need help with finding or creating a equation. You own a license plate manufacturing company. Write a formula or equation that takes a population and ...
0
votes
1answer
157 views

packing boxes inside boxes

given 2 boxes (in 3-space) determine if one of the boxes resides within the other, or if a third box must be constructed that holds them both? given that a box is defined by its center($x,y,z$), and ...
0
votes
3answers
3k views

How to calculate perimeter using the area and the perimeter of a smaller area

I have having trouble understanding how to break this problem apart. I have an $ L$ shape with a rectangle in it. The smaller rectangle has a side of $5 m$ and a side of $7 m$, the $L$ shape has an ...
0
votes
1answer
91 views

What's the size of K in this figure?

What's the size of K in this figure? A and a are parallel B and b are parallel
3
votes
4answers
1k views

Variation of a “Who is Lying” Question

While reading Problem Solving Strategies - Crossing the River with Dogs and Other Mathematical Adventures by Ken Johnson and Ted Herr, I came across a problem I was not sure how to solve. One of ...
1
vote
1answer
80 views

Number Reasoning problem

PersonA bought a Camera at an electronics show with the intention of reselling it at a 30% profit. However, he misjudged the value of the Camera and could only sell it at a 35% loss. If PersonA ...
1
vote
1answer
561 views

Problem involving drawing a diagram with belts and elevators and specific directions on a given floor/belt

Today, while reading A Practical Guide to Problem Solving in Mathematics by Carol Meyer and Tom Sallee, I came across a problem I was unsure of how to solve except by brute forcing possibilities and ...
0
votes
1answer
200 views

Is it possible to derive the CDF of $Z$?

Assume that $X_i$, $Y_k$, $i=0,\ldots,N$, $k=1,\ldots,K$ are non-negative independent non-identically distributed random variables. Let us define the random variable $Z$ as \begin{align} ...
4
votes
2answers
157 views

Which polynomial equations of higher degree will have a solution formula?

A polynomial equation of degree greater than four will in general have no solution formula. But what are some typical cases one should be aware of as a practical person in which there are solutions?
2
votes
1answer
117 views

Geometrical combinatorics

This question was inspired by Rush Hour game: You have a 6x6 grid, 12 pieces of size 2, and 4 pieces of size 3. A piece can be placed on the grid either horizontally or vertically. The pieces can't ...
2
votes
1answer
1k views

Permutations and Combinations - How many different ways to do certain things before having to repeat?

Recently, while reading, I came across a problem in Problem Solving Strategies: Crossing the River with Dogs by Ken Johnson and Ted Herr that I was not entirely sure how to solve. Alas, I have come ...
0
votes
0answers
60 views

Help solving for $x$, $y = c_1 + 640a + 16x$ OR $y = c_2 + 648b + 16x$ with consistent result.

I'm writing a program. Part of the program fetches a cryptic memory value from another program (which stores information on a value i'm looking for) and reverse engineers it. I need help figuring out ...
0
votes
1answer
91 views

Solving a one line matrix, constraining the coefficients

I will give a simple example of my question then the full one. Let's say I am trying to reconcile my bank account, and have no statement. I opened it with $0 exactly, and a small number of ...
1
vote
1answer
40 views

Four golfers in a square in two teams of two - who tees off second given that one person is diagonal from another?

I am not sure if I am interpreting the question correctly per se. I drew a picture in which Clark was diagonal from Diana. So, that means Chris could either face Clark OR Diana. If Chris is facing ...