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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Simplify $\log_23\ \log_34\ \log_4 5\ \log_5 6\ \log_6 7\ \log_7 8$

How do I evaluate the product: $$\log_23\ \log_34\ \log_4 5\ \log_5 6\ \log_6 7\ \log_7 8$$ I know that $$\log_ba=\frac{\log\ a}{\log\ b}$$ How can I apply it? Thanks!
Emily K
  • 99
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6 answers

Repeating Decimals

I'm just wondering how do we simplify repeating decimals into a fraction in general? Like, for example, $$0.5656\dots$$ $$0.12424\dots$$ $$4.23777\dots$$ Thanks!
lobster
  • 51
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Partition the integers into three subsets such that for any $n$, the three integers $n, n+p$ and $n+q$ belong to different subsets

Question from Engel's book problem solving strategies. Let $p$ and $q$ be fixed integers. The set of integers are to be partitioned into three subsets $A,B,C$ such that for any $n \in \mathbb{Z}$, the three integers $n, n+p$ and $n+q$ belong to…
eatfood
  • 2,414
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How to solve this inequality with another way?

I want to solve this inequality $$x^3-3 x^2+2 \sqrt{(x+2)^3}-6 x\geqslant 0.$$ I tried. Put $t = \sqrt{x + 2}$. Then, we get $$t^6+2t^3-9t^4+18t^2-8\geqslant 0.$$ Equavalent to $$(-2 + t)^2 (1 + t)^2 (-2 + 2 t + t^2)\geqslant 0.$$ From this…
minthao_2011
  • 1,885
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3 answers

Solving a cubic system of equations

I have the following equation system: $A_1 x + B_1 y + C_1 z + D_1 xy + E_1 xz + F_1 yz + G_1 xyz = M_1$ $A_2 x + B_2 y + C_2 z + D_2 xy + E_2 xz + F_2 yz + G_2 xyz = M_2$ $A_3 x + B_3 y + C_3 z + D_3 xy + E_3 xz + F_3 yz + G_3 xyz = M_3$ $A_1$,…
Tamás Pap
  • 253
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How to solve a problem with chessboard

I am beginning math student and encountered following task which I do not know how to solve: There is chessboard, ie 8x8 tiles. In the top left corner there is pawn. He cannot go diagonally and he can only move down and right. 1)How many steps will…
user8695
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1 answer

Chess tournament problem

$12$ chess players took part in a tournament. Each played against each other exactly once. After the tournament every chess player did $12$ lists of names. On the first list, the player only wrote his own name. On the second list, they wrote…
algebra1
  • 377
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1 answer

How to find a list of summands and factors adding up to a total?

I am neither a mathematician nor do I have an idea on how to write down my problem in accurate mathematic formulas. Please feel free to edit my question into shape and remove this paragraph. Also I am unsure about that tags that apply to this…
Spontifixus
  • 151
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4 answers

Solving a quintic function for zero

I got this question on my homework and I cannot for the life of me figure out how to solve for $0$. $$x^5+2x-10=0$$ I have tried this every which way and this is my last resort. Thanks in advanced.
CoffeePoweredComputers
  • 67
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How many ways are there to parenthesise an expression?

Context I am writing a computer program to do a brute-force search for a solution to a puzzle which wanted to arrange four numbers with the four standard arithmetic operators and arrive at a given answer. While I have a solution to the original…
ClickRick
  • 224
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3 answers

Where is the lost dollar?

Somebody explained me this problem, but I am not sure to understand what is wrong. Three people go to a bar to have a drink. To pay the bill everyone gives $10. The barman gives back $5 coins. Every people take $1 back and leave the $2 other dollar…
Natim
  • 155
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Find $\frac{a+b+c}{x+y+z}$ given $a^2+b^2+c^2$, $x^2+y^2+z^2$ and $ax+by+cz$.

We are given $a^2+b^2+c^2=m$, $x^2+y^2+z^2=n$ and $ax+by+cz=p$ where $m,n$ and $p$ are known constants. Also, $a,b,c,x,y,z$ are non-negative numbers. The question asks to find the value of $\dfrac{a+b+c}{x+y+z}$. I have thought a lot about this…
Alraxite
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What is a logical solution to this problem?

Monkey beans. An urn contains 23 white beans and 34 black beans. A monkey takes out two beans; if they are the same, he puts a black bean into the urn, and if they are different, he puts in a white bean from a large heap he has next to him. The…
83457
  • 304
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Solving Math Problems in your head

Recently, I have read about chess players who can not only visualize some moves, but actually "see" a chess board that is not there and play moves (e.g. Nakamura, Carlsen etc.). Now I wonder whether the same is possible to achieve for mathematics. I…
Edward Teach
  • 475
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4 answers

Serious applications of Colouring proofs

Are there any research-level applications of proofs by colouring? This is the kind of proof you use to show that you can't cover a mutilated chessboard with 31 dominoes. Afaik, this technique chiefly finds a market in IMO preparation classes; see …
Ganesh
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