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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2answers
264 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
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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 ...
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0answers
141 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 ...
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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
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1answer
111 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 | ...
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4answers
378 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
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1answer
426 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
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1answer
155 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 ...
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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 ...
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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
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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 ...
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1answer
553 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 ...
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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
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1answer
116 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 ...
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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
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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 ...
0
votes
3answers
1k views

200 ft race (with turnaround) where two people have different jump lengths but jump the same distance in equal time - who wins and by how much?

This problem is from Problem Solving Strategies - Crossing the River with Dogs and Other Mathematical Adventures by Ken Johnson and Ted Herr. I decided to draw a picture from the segment of $90$ ft ...
2
votes
1answer
73 views

Determining probability that blue is part of an outfit based on five shirts and four ties along with a constraint for the possibilities

This problem is from Problem Solving Strategies - Crossing the River with Dogs and Other Mathematical Adventures by Ken Johnson and Ted Herr. I first let capital letters denote shirts, and ...
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vote
2answers
362 views

Reverse Cuthill McKee Ordering and Solution of systems of Linear Equations

I just learned about the RCM. I am trying to solve a problem that is a result of fluid dynamics and chemistry so I have a very large sparse matrix. I also learned reducing the bandwidth would ...
2
votes
1answer
209 views

Methods of solving a problem regarding withdrawing and depositing from a bank account.

I have an imaginary bank account with an initial balance $x$. I can only withdraw $0\% < w\% < 100\%$ (of the current balance) or deposit $0\% < d\% < 100\%$ (of the current balance) at a ...
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1answer
573 views

Problem Solving - Ways to add 6 even, positive, non-zero integers to get 26

I believe I have gotten all of the ways now - thanks for the hints below Yun, Andre Nicolas, and Gerry Myerson. If anyone could confirm my answer (I feel there should be more possibilities, but ...
0
votes
1answer
552 views

Problem Solving Question - Can't eliminate possibilities based on clues given

The Problem: Ed, the eldest child of the Family family, met a new girl named Candy at the beginning of his senior year in high school. He really liked here, so he wanted her phone number. He knew the ...
8
votes
2answers
173 views

Neat problems using roots of polynomials

On a recent test in a course I'm TAing, students were asked to prove that sin(x) is not a rational function by using the fact that polynomials only have finitely many zeroes. During my tutorial, I'd ...
6
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0answers
1k views

Ways to Score 18 Points in Football Excluding 2-point conversion

The Chicago Bears score 18 points in a football game. In how many different ways can the Bears score these points? Points are scored as follows: a safety is 2 points, a field goal is 3 points, a ...
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vote
1answer
1k views

Problem Solving Question - A sidewalk being built around a garden

We have a garden that measures 17 feet by 20 feet. We want to pour cement for a 3-foot-wide sidewalk around the garden. To make the forms for the cement, we will need to buy some 2-by-4-inch lumber. ...
2
votes
2answers
576 views

Problem Solving Question Relating to Directions and finding Burger Jack

I stopped at a street corner and asked for directions to Burger Jack. Unfortunately, the person I wasked was Larry Longway, whose directions are guaranteed to be too complicated. He said,"You are now ...
4
votes
2answers
182 views

A game of numbers: When can we have 2011?

Two friends are playing a game. In every turn, after one of them says a number $k$, the other one has to say a number in form $a\cdot b$ where $a,b\in \mathbb{N}$ such that $a+b=k$ holds. The game ...
3
votes
2answers
577 views

Strategy / calculus riddle [duplicate]

Possible Duplicate: A lady and a monster Here is another rather famous riddle - I've seen it several times, but only once in its full form that I quote here: A duck is located in the ...
6
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1answer
211 views

Vectors inside the unit hypercube.

The following problem has been bothering me for a while, and I finally gave up to solve it on my own. However, I still would like to see a solution: For an arbitrary integer $n$ consider a set of all ...
1
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2answers
167 views

Constrained optimization problem

I'm having problems with this assignment: $$\begin{array}{rl} \min & x^3 + 2xyz - z^2 \\ \text{subject to} & x^2 + y^2 + z^2 \leq 1 \\ \end{array}$$ Disregarding the constraint, find all ...
2
votes
1answer
298 views

Word problems - Sum of squares & a strange function

These were two of 20 problems I had to do in a test today that I didn't manage to solve. 1) Find the least $k$ such that $1^2 + 2^2 + 3^2 + 4^2 + \dots + k^2$ is a multiple of 200. 2) ...
2
votes
1answer
59 views

A problem with polynomials.

This is a problem from a test in my course in analytic functions. I didn't manage to solve it. Could you please give me a hint? The problem is: Calculate the third root of the sum of the coefficients ...
0
votes
1answer
60 views

Problem with an equation.

I have this equation: v*t-(u*g*t^2)/2 = d And I'm having trouble solving it for t. Mathematica gave me two results, ...
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1answer
731 views

Solving modular inequalities/constraint solving

A few of my current programming problems boil down to solving inequalities over modular domains and possibility could benifit from knowledge of efficient maths/algorithms rather than brute force ...
3
votes
1answer
144 views

Linear Algebra problem: intersection of a subspace with a cone.

In $\mathbb{R}^n$, consider the closed cone $$C^+ = \{ (x_1, \ldots, x_n) : x_i \geq 0,~~i= 1, \ldots, n\}.$$ Let $S \subseteq \mathbb{R}^n$ be a subspace (of any dimension) such that $S \cap C^+ = ...
6
votes
3answers
240 views

Is there an efficient algorithm to find a length maximizing combination?

The problem is the following Given $v_1, \, v_2, \, \ldots, \, v_n \in \mathbb R^m$; find $\epsilon_1, \, \epsilon_2, \, \ldots, \, \epsilon_n \in \{0,1\}$ such that $$\left\vert \sum_{i=1}^n ...
5
votes
3answers
701 views

Secret Number Problem

Ten students are seated around a (circular) table. Each student selects his or her own secret number and tells the person on his or her right side the number and the person his or her left side the ...
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votes
5answers
793 views

How many rationals of the form $\large \frac{2^n+1}{n^2}$ are integers?

This was Problem 3 (first day) of the 1990 IMO. A full solution can be found here. How many rationals of the form $\large \frac{2^n+1}{n^2},$ $(n \in \mathbb{N} )$ are integers? The possible ...
13
votes
1answer
307 views

How many $N$ of the form $2^n$ are there such that no digit is a power of $2$?

How many $N$ of the form $2^n,\text{ with } n \in \mathbb{N}$ are there such that no digit is a power of $2$? For this one the answer given is the $2^{16}$, but how could we prove that that this ...
1
vote
4answers
273 views

solve complex equation

$x^8 = \frac{1+i}{\sqrt{3} - i} = \frac{\sqrt[8]{\frac{2}{\sqrt{2}}}(\cos \frac{\pi}{4} + i \sin{\frac{\pi}{4}})}{2 \cos \frac{\pi}{6} + i \sin \frac{3\pi}{2}}$ What's the way to solve this kind of ...
3
votes
3answers
292 views

What is the answer to this hard problem for 4th graders?

Here is the problem. Peter's password for his mail is a 6 digit number. The first two digits are his house number. Next to them is the sum of the digits of his phone number. Next to them is the sum of ...
3
votes
4answers
8k views

Probability of winning a prize in a raffle

My work is having it's annual Christmas raffle today. 1600 tickets have been sold, and there are 40 prizes to win. I have bought ten tickets. What are the odds I will win a prize? While an initial ...
0
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2answers
597 views

What is the difference between Centroid of area and Bisector of area?

We got this fuzzy course in the university, there was a problem which it's result led to multiple overlapping fuzzy values. in order to conclude a value out of that there was different approaches ...
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1answer
173 views

How to answer to this algebra problem?

Thanks for your attention to this question, here is the problem: Compute the number of positive integers $x$ less than or equal to $1000$ that satisfy the following condition: $$x! \text{ is ...
1
vote
2answers
195 views

Pack box inside “smaller” box

Now, there is a puzzle that is quite well known as far as I know, concerning the packing of rectangular boxes in 3-dimensional space. You also have a measurement of a box as the sum of the hight, ...
5
votes
2answers
85 views

Help with a geometry problem

The problem says: A triangle has its lengths in an arithmetic progression, with difference d. The area of the triangle is t. Find the dimensions. the solution says: the notation can be even better if ...