Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [problem-solving]

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.

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.

4495 questions
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Strategies for a game where players alternate placing $2\times 2$ squares and three-square "L" shapes on a $100\times100$ board

This is a question for a homework assignment that I need to solve: please only provide advice, I need to understand it. I also want to solve it on my own. The question is as follows: On a $100\times100$ board, two people, Art and Bart take turns…
Manfred Söderby
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Equations Proof Solvers

Can Someone solve $$x(x+1)(x+2)...(x+2020)=1$$ analitically rather than numerically and show me all steps. Also maybe with some preconditions, like only natural solutions, so that it‘s adaptable to diophantine equations, etc. Thank you all in…
user688736
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Creating simultaneous non-linear equations

Suppose, for each given $w_1 \in \mathbb{R}$, there exists unique $x_1,y_1,z_1 \in \mathbb{R}$ that satisfy the following system of equations: $F_1(w_1,x_1,y_1,z_1)=0\\ F_2(x_1,y_1,z_1)=0\\ F_3(x_1,y_1,z_1)=0$ Note that $F_2$ and $F_3$ do not…
Amatya
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How far can you get in math by doing random problems and generalizing them in as many possible ways as you can imagine?

Off course 1) the notion of 'far' would have to be defined. As well as 2) what counts as a 'random problem'. And of course 3) different people can think of different generalizations and can do the problems at different rates. Let's say 1) An…
delivosa
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Solving equation with natural numbers

I have the following question: In a store I want to pay with exactly 50 coins. There are 2€, 1€, 0,5€ 0,2€ and 0,1€ coins. So I'd have 2a + 1b + 0,5c + 0,2d + 0,1*e = amount I have to pay And a+b+c+d+e=50 (number of coins) Since there are no half…
8t3ph
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What would be the answer to this question? We were instructed to use Polya’s Four Steps in Problem Solving

Vacation Money Last January 2018, my family went on vacation to Cagwait White Beach Park at Cagwait, Surigao del Sur. We also celebrated the 70th birthday of our grandmother. We saved money for the said vacation. We spent 10,000 on the catering…
Viole
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Shortest possible string of functions to give $4x+22$ and $4x+3$

I want to check if my solution to a) iii) and b) iii) are correct. For a) iii) I got AAMAMA and for b) iii) I got MAMMSD or MMAMAD I'm not sure if they are the shortest; I just suspect they are because I haven't found any smaller ones.
user1488
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Prove that $F(x,y)=(x-4y,2x+3y)$ is bijective

I saw the solution of this similar exercise Prove that $F(x,y) =(2x+y, x+4y)$ is bijective, But we didn't study ker Yet, I want an elementary solution, please I need to prove that :$F(x,y)=(x-4y,2x+3y)$ is injective and surjective.
user835019
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If I were a child interested on becoming a mathematician, when should I start learning proofs?

I've been trying to start with mathematics from "scratch", but I do not rely on my foundations. I want to be a mathematician, so I picked this book "Basic mathematics" by Serge Lang and I picked up on that fact I requires proof-knowledge. So, if…
NewSelfTaughtMathematician
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IMO problems, can someone help me to learn problem solving skills?

I am a student and I want to enhance my problem-solving abilities of maths-problems. I am Italian and I try to resolve the national problems (of course of my country) and I have some difficulty in solving them but I bought a maths-puzzles-book…
MathLover
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Determine how many integer ordered pairs $(x, y)$ satisfy the equation $\mid x + 2020\mid + \mid y + 505\mid = 4$.

I do not see how this is possible if all of it equals to a number higher than $4$. If $x$ or $y$ is negative would it make a difference? How can $x$ and $y$ adding two big numbers equal $4$. Is there a faster way to figure out the amount of pairs?
user799255
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What is the largest number k < 100,000 such that k has an odd number of factors?

so i do not know how to solve this problem and is confused on a method to find odd number of factors. How can I find the odd number of factors for a number that high?
user799255
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frac{a}{b}+\frac{b}{a} \notin \mathbb{Z}$

I know that $a \neq b$, then $\frac{a}{b}+\frac{b}{a}$ would not equal to $m$ (an integer) so I set them into one that wasn't a fraction by squaring. So I got $\frac{a^2+b^2}{ab}$. How can I show that $a^2+b^2$ is not divisible by $ab$?
user799255
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How to solve this equation? $t-ln|t+1|+1 = 0$

How do I solve this equation? $$t-ln|t+1|+1 = 0$$ I know it has solution (saw graph).
naruto25
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Problems that are very difficult, but can be solved efficiently?

Are there any equations that look very hard to solve at first (e.g. many involved parameters etc), but can be solved/reduced efficiently solved with a certain algorithm? I'd like to create some programming problems/puzzles - hence the question. I…
n00b.exe
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