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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What are some ways to find the minimum of an expression?

I don't get how people solve these types of questions. If you have a single variable expression then I guess you could differentiate it, but how would you find the extreme values of an expression which has more than one variable? I know this is kind…
Alraxite
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Calculate number of days to reach top of staircase

based on given input I want to calculate the number of days required to reach the top of the staircase. There are total N of stairs. He climbs X stairs upwards in a day and he came downstairs in the night by Y stairs. As I am an absolute beginner…
Jitender
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Ratio stock problem

This problem is for children and I found it while reading Ray's Intellectual Arithmetic. It is under the ratios topic. Problem : $C$ and $D$ join their stocks in trade; $C$ puts in $50\$$ for 4 months, and $D$ $60\$$ for 5 months. They gain…
Michael Munta
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How to solve this system of equations?

How to solve this system of equations? $$\begin{cases} 1+\sqrt{2 x+y+1}=4 (2 x+y)^2+\sqrt{6 x+3 y},\\ (x+1) \sqrt{2 x^2-x+4}+8 x^2+4 x y=4. \end{cases}$$
minthao_2011
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What is the solution to this algebra problem?

There is a $~10\times 11~$ grid with real numbers, the number $~N_{xy}~$ is equal to the sum of all the numbers in the column $~y~$ multiplied by the sum of all the numbers in the row $~x~$, all numbers in the grid have the same condition than…
Sartem Cacartem
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Useful techniques for mathematical competitions

I did a research about mathematical competitions and I came to a conclusion that in order to do well, one needs to master a set of particular techniques and shortcuts. I was struggling with math pretty much my entire life and I generally hated it.…
Eddie Spasov
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Minimum quadratic formula value

I have recently been researching about quadratic equations, and came across the following formula for finding the minimum $x$ and $y$ values from a "Bivariate (two equation) quadratic": $$x = -(2BC-DE)/(4AB-E^2)$$ $$y = -(2AD-CE)/(4AB-E^2)$$ Where…
Rlz
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How to express y from $\dfrac{y-2x}{y}=1$?

I need to express y from $\dfrac{y-2x}{y}=1$, I mean get the $y=...$ equation. But I'm getting 0 instead of y: $\dfrac{y-2x}{y}=1$ $y=y-2x$ $y-y=-2x$ $0=-2x$
Stdugnd4ikbd
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Honeycomb Lattice Line Passing Through

A plane is tiled with regular hexagons. This tiling is sometimes called the “honeycomb” lattice. Show that if a line passes through two points that are vertices of hexagons in the tiling, then the line passes through infinitely many such points
Bob Johnson
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How to Test Arrangements of Buyers & Products in the Most Profitable Way, Given Limitations?

There's multiple products and multiple buyers, each with their own quote for the product, and some not willing to buy the product at all. Some buyers require a minimum dollar amount for the order or they won't buy anything. I'm trying to find a…
user9028
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19 people on 8 benches with 1, 2 or 3 people. How many with only 2?

I found a math problem for 2nd graders in Norway. The article only presented drawing a table of everything and simply looking at it, instead of a mathematical approach, like a formula. I'm not sure what kind of solution is needed, so I cannot google…
Streching my competence
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How do I solve for $g$ in $12g = 12 \left(\frac{2}{3g} - 1\right) + 11$?

For this specific problem, I somehow keep coming up with the wrong answer. Can someone help me? For the problem, I need to solve for $g$. $$12g = 12 \left(\frac{2}{3g} - 1\right) + 11$$ Here is how I am trying to solve it: $$12 \cdot \frac{2}{3g} =…
Janaia Hunt
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How do you solve a simultaneous equation with 3 variables that only has two equations?

Most of the other requests for solving simultaneous equations seem to have three equations to use, which my specific problem doesn't have. I also hope to use beginner A-level mathematics, so no calculus, which I've seen in other solutions. The…
P4dfoot
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How many students like all the three subjects?

Among 64 students, 28 of them like Science, 41 like Mathematics and 20 like English. 24 of them like both Math and English. 12 students like both Science and English. 10 students like both science and math. How many students like all the three…
Peaceyou
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Finding value of an algebraic expression.

I am given $$2x = a-\frac{1}{a} \;\text{and} \; 2y=b-\frac{1}{b} .$$ I have to find the value of $ xy +\sqrt{(x²+1)(y²+1)}.$ One way to solve this is to simply putting the value of $x$ and $y$ and get the answer, but that's a very lengthy process…
user533186
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