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
147 views

Partitioning positive divisors of 100!

Is it possible to partition all positive divisors of 100! (including 1 and 100!) into 2 subsets so that each subset has the same number of integers and the product of all the divisors making up the ...
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0answers
45 views

Is it possible to find out how many results were unexpected?

During a school year Andrew was given 40 mathematical problems as part of his assessment, one problem per week. As a result of marking he could receive 2,3,4 or 5 marks for each problem. Andrew called ...
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1answer
66 views

Perimeter problem involving different sized sticks?

Could you please help me find the answer to this question. I think it has something to do with grouping or pairing some numbers.I would appreciate easy-to-understand solutions. Thank you. There are ...
0
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3answers
53 views

How to solve $h(i) = \frac{i^2}{(n-i)^2+i^2}h(i-1) + \frac{(n-i)^2}{(n-i)^2+i^2}h(i+1)$

$h(i) = $P(reach n eventually| the initial state = i) $h(0) = 0$ $h(n) = 1$ 0 and n are stopping time. For $ 0 < i < n$, $$h(i) = \frac{i^2}{(n-i)^2+i^2}h(i-1) + \frac{(n-i)^2}{(n-i)^2+i^2}...
1
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1answer
90 views

Two rows or two columns with the same number of plusses

I have tried drawn numerous tables in attempt to explain this and understand that the number of cells must be even however, I am not sure how to create this proof. I appreciate your support. Each ...
1
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1answer
203 views

Solve All Sequence (Rubik's Cube)

Can you prove/disprove that there is a solve-all sequence of moves to complete the Rubik's Cube from any solvable-position? If so, can you explain how long it is? If not, explain why not. Just to be ...
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1answer
61 views

Prove that $a_i\leq 0$ for $i=1,2,…,N-1$?

Let $a_0,a_1,...,a_N$ be real number satisfying $a_0=a_N=0$ and $$a_{i+1}-2a_i +a_{i-1}=a_{i}^{2}$$ for all $i=1,2,...,N-1$. Prove that $a_i\leq 0$ for $i=1,2,...,N-1$. I saw the problem in "...
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2answers
123 views

How should a programmer store and solve simultaneous algebraic equations?

I need to store and solve simultaneous algebraic equations (no trig, no calc, no logs) as part of a larger program. I am not yet committed to a particular language, so long as it's a free one. For ...
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1answer
54 views

Can problem solving be axiomatized? [closed]

Is it possible to develop a set of axioms for solving any problem, that are certain to work? Similar to problem solving strategies or proof strategies, though a set of steps that work indefinitely if ...
0
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1answer
417 views

How to find the minimum value of this integral?

I am struggling to find the solution to this problem. If anyone could help to explain how to solve this problem to me, it would be really appreciated. Let $$ f(x)=-\sqrt{3}x+(1+\sqrt{3}) $$ $$ g(x)=...
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1answer
23 views

For probabilities in sets, why multiply together for the complement but not for the normal probability?

For the birthday problem, the probability that a set of n birthdays (where n=1) contains your birthday is 1/365. The complement is that there is a 364/365 chance that it does not contain your birthday....
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1answer
14 views

Find caluclation to equal this value?

How can I find the calculation needed to reach the given value? This is related to programming but I don't see how I can do this myself. ...
0
votes
1answer
37 views

Problem Analysis - Answer but no procedure - Differential Eq.

I stumbled with this problem in a notebook that has been bothering me...The answer is written but there's no explanation nor a steb-by-step procedure or anything. If you know how to analyse the ...
0
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1answer
28 views

What is the name for an ODE with an integral as a side condition?

My question: I have to find a function $y: \mathbb R \rightarrow \mathbb R$ fulfilling $$y^\prime(t) = f(t, y(t)),\ \int_{-\infty}^\infty y(t) dt = c$$ with a given $c \in \mathbb R$. What is the ...
0
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3answers
63 views

If |G|>1 is not prime, there exists a subgroup of G which is not G or {e}

Question: Prove the following: if|G|>1 is not prime, then $G$ has a subgroup other than $G$ and {e} We know that $\langle g \rangle$ is a subgroup of $G$ by previous part of the question and $G$ is ...
3
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2answers
56 views

Property of the solution for a specific system of non-linear equations.

We are stuck on a proof, and would appreciate any help: Let $\gamma >1$ be a known scalar and let $g,h=1,...,G$ and $s=1,...,S$. Let $\pi _{gs}$, $\beta _{s}$ and $y_{g}$ be known variables with $...
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1answer
82 views

Problem Analysis - Answer but no procedure - Finding Trajectories.

I stumbled with this problem in a notebook that has been bothering for the whole day(actually 3)...The answer is written but there's no explanation nor a steb-by-step procedure or anything. If you ...
0
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3answers
48 views

Problem Analysis - Answer but no procedure

I stumbled with this problem in a notebook that has been bothering for the whole day(actually 3)...The answer is written but there's no explanation nor a steb-by-step procedure or anything. If you ...
0
votes
2answers
32 views

The additive inverse for negative values only (otherwise zero)

I want to create a formula that only applies the additive inverse for negative values because I am trying to come up with a simple formula whereby two numbers are entered and if the second is larger ...
0
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1answer
178 views

What is a Single Objective Optimization problem?

I can't find any definition of this problem on the Internet. Could you help me by providing some definition?
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2answers
22 views

The Monthly Cost of the Third House Given the Total Rent Receipts of 186,390 in a Year.

This is how I solved this problem but I have some reservations regarding my answer. 1st house = x ; 2nd house = 3x ; 3rd house = [3x + x] - 2610 12(x) + 12(3x) + 12(4x - 2610) = 186,390 96x = 155,...
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1answer
327 views

Age Word Problem with 4 Variables

Simon is nine years older than Jairus. Simon is four times as old as Joter was three years ago. Joter is eighteen years younger than Marshall. How old is Jairus? The choices are as follow: 10 / ...
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2answers
64 views

Determining the Number of Adult Tickets from a Ratio of 4 is to 5

The ratio of adult tickets to student tickets for the play was 4:5. If the sum of the adult tickets and one half of the student tickets is 260, how many adult tickets were sold? The choices are as ...
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2answers
52 views

Show if $0 \le a <b$ implies $0 \le a^{\frac{1}{n}}<b^{\frac{1}{n}}$

Given that $0\le a<b$ show that $0\leq a^{1/n}<b^{1/n}$ Is this proof by induction? Show it's correct for $n=1$ Assume true for $n=k$, then $0\leq a^{1/k}<b^{1/k}$ holds for some $k$, ...
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2answers
176 views

How do you calculate P(A/B), when event B occurred after event A?

There's really only one question I can't begin to handle when it comes to probability, literally. It's not the only type of question I struggle with, though it's the type of question where I can't ...
1
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1answer
38 views

Isolate points of a metric space with some properties?

Suppose that all dense subspace of a metric space $(X,d)$ is open. Prove that the set of the isolate points of $X$ is dense in $X$. My Idea: all isolate points of $X$ are in any dense subspace, ...
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2answers
125 views

Is there a method or algorithm to solve “in what base is the equation true” questions?

I have been given some exercises in which I'm given some equation that doesn't hold in base ten, and I need to figure out in which base the equation does hold. For example: $\sqrt{41} = 5$ which I ...
1
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1answer
189 views

Does there exist continuously differentiable function $f:\mathbb{R}\longrightarrow\mathbb{R}$?

Does there exist continuously differentiable function $f:\mathbb{R}\longrightarrow\mathbb{R}$ such that for all $x\in \mathbb{R},\,\,f(x)>0$ and, $f'(x)=(f\circ f)(x)$? I see this question in ...
2
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1answer
252 views

What is the answer of this problem solving question?

You need to order 4 plastic cups for each of the 800 runners. Plastic cups are sold in 2 different pack sizes and you must choose one type of pack only. A pack of 500 costs £12.50 or a pack of 800 ...
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1answer
193 views

Wrong ILP solution with LPSolve (simple example)

I added the following example into LPSolve and found a strange issue. I don't want S1 and S2 to overlap within certain margins. ...
0
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1answer
154 views

Math Exercises, Highschool Student

I really want to improve my problem solving skills.. However I have found that most of the exercise books (lots of problems) are above my curent level (e.g. Olympiad and College) I am currently in ...
0
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1answer
60 views

Finding subgroups of a group from specific order

Given the following group: $$ \left<\left\{ \begin{bmatrix}a & b \\0 & c \end{bmatrix} \mid a,b,c\in \Bbb Z_{5},a,c \neq 0 \right\} ,\:\: * \right> $$ where ∗ is multiplication. ...
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2answers
78 views

List of N items, randomly putting them in order, showing the procedure ends.

On a bookshelf, there are N tomes of the encyclopedia in random order. Every hour, a librarian takes a tome which is not in place and puts it in its place, and we must show this process will stop ...
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5answers
657 views

Examples of open problems solved through short proof

Are there good examples of reasonable open problems in mathematics that had an 'obvious' solution via application of a theorem already known/not yet found in mathematics but could have been found with ...
1
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0answers
48 views

Techniques for approximating a partial sum formula for any function.

There are several ways of computing the partial sum formulas of many summations, but is there a technique that can approximate a closed form for any summation? So far I found for $\sum_{x=0}^{n} \...
3
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4answers
50 views

Prove $F^2_{n+1} - F_nF_{n+2} = (-1)^n$

This is a question about Fibonacci sequences, a sequence in which the previous terms build up upon the current term (e.g. $F_1 + F_2 = F_3$ where $F_1 = F_2 = 1$). How would I go about proving $F^2_{n+...
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1answer
202 views

Finding the Compound Interest on 7500 Dollars at 4% per annum for 2 Years

Find compound interest on $\$7500$ at $4\%$ per annum for $2$ years, compounded annually. The choices are as follow: $\$512$, $\$552$, $\$612$, $\$622$. I tried to solve this problem by: C.I. $= ...
1
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1answer
53 views

Experiments with random selection: when to respect order?

I have a hard time imagining experiments of this nature without noting the arrangements (I draw that ball with my left hand, the other with my right. I draw that ball first, the other second) so I'm ...
0
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1answer
93 views

Help establishing restrictions for consistency on a linear system.

I'm having trouble wrapping my head around this problems, and others similar to it. I can typically solve systems of linear equations, but some give me trouble, especially dealing with unknown ...
0
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1answer
174 views

The Profit Gained by a Shopkeeper who Uses an 800gm Weight Rather than a Kilogram weight

A shopkeeper professes to sell his goods at $200 but uses a weight of 800gm instead of kilogram weight. Thus, he makes a profit of The choices are as follow: 20% 22% 25% None of these The ...
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2answers
84 views

For which $n, k$ is $S_{n,k}$ a basis? Fun algebra problem

Here it is a nice algebra problem I had some fun with Let $V$ be a vector space over $\mathbb R$ of finite dimension $\dim V = n$. Let $v = \{ v_1, \dots, v_n\}$ be a basis for $V$. Let $$S_{n,k} = \{...
1
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1answer
322 views

What's the Total Number of Candidates who Applied for the Exam?

In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how ...
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1answer
59 views

Solving equation with exponentials

How to solve $ {z = x^y, x = y^z, y = z^x }$ for $ x, y $ and $ z? $ Is some sort of triple Lambert W to be introduced? Done so far: Taking logs, $$ \log z = y \log x , \log x = z \log y , \log ...
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1answer
59 views

How to best approach a problem of this kind (problem solving and simple linear equations)

This is a common type of problem that appear on algebra tests to test problem solving abilities (this is not from a real test or homework). I am curious on how to best approach these kind of problems ...
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3answers
265 views

Trouble with Vakil's FOAG exercise 11.3.C

I'm having trouble with the exercise in the title, even with part (a), which asks to prove that if $X$ is a closed subset of $\mathbb{P}^n_k$ of dimension at least 1 and $H$ is a non-empty ...
1
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1answer
55 views

One hundred indistinguishable ants are dropped on a hoop of diameter 1

I have this question which I am not sure how to solve: One hundred indistinguishable ants are dropped on a hoop of diameter 1. Each ant is traveling either clockwise or counterclockwise with a ...
2
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1answer
50 views

Finding the best fit of 3 categories ( restaurants/meal/person analogy problem )

I have this problem that sounds tedious and long and I'm not sure if there exist an intuitive way to solve it. The problem is related to image recognition but I will try to give an analogy to it You ...
1
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1answer
107 views

Time & Distance : Pokemon Hunter and the Rogue Brook

I was working my way through some Puzzles in Discrete Maths by Rosen, when I came across the following question: A Pokemon Hunter is rowing upstream a brook As he passes under the 'bridge-of-...
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23answers
10k views

An example of a problem which is difficult but is made easier when a diagram is drawn

I am writing a blog post related to problem solving and one of the main techniques used in problem solving is drawing a diagram. Essentially, I want to illustrate that some hard problems (for example, ...
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0answers
53 views

problem solving on work rate

please tell me this problem has insufficient data.. 5 men and 2 boys working together can do four times as much work as a man and a boy. working capacities of a woman and a boy are in the ratio ... ...