# 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.

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### Bagging a random sample with duplicate

this is a question posed by an engineer friend who had this probability problem arise at work. It goes like this, Say we have 5000 marbles. Of them, we know that 50 are duplicates. They are not ...
1 vote
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### Determine the mapping matrix $A=M_B^B$ with the base $B=(1,t,t^2,t^3)$

Hey I have some problems with this problem Consider all polynomials with $\leq \deg 3$ and the following map: $f: \mathbb{R}[t] \rightarrow \mathbb{R}[t]$ $f(t) \rightarrow f(t+1)-f(t)$ a) Determine ...
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### When should you give up on a specific approach while working on a hard problem? [closed]

Over the past three days, I have been spending an unreasonable amount of time on a relatively simple problem. I listed my failed attempts in the post and it turns out that my first attempt was the one ...
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1 vote
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### How to determine which non-right angle to use when determining components of a vector

I'm learning electrostatics right now and just had a quick problem that involved calculating the electric field at a test point z units above the $x$ axis due to $2$ equal charges separated by equal ...
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### Two subsets $A$ and $B$ of the $(x,y)$ plane are said to be $equivalent$ if there exists a function $f:A\to B$ which is both one-to-one and onto.

Two subsets $A$ and $B$ of the $(x,y)$ plane are said to be equivalent if there exists a function $f:A\to B$ which is both one-to-one and onto. $(i)$ Show that two line segments in the plane are ...
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1 vote
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### Is there an algorithm to solve number manipulation problems?

There are this kind of problems where, given a certain amount of the same numbers, it's needed to manipulate them with functions or operators in a way to get a certain result. It's allowed to glue ...
• 546
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### Finding the hypotenuse on a triangle with a circle inscribed. [closed]

The problem is a right-angled triangle with a inscribed circle, see figure, where you want to solve the distance CB (the hypotenuse). The only known values are two lines which are linked to the circle ...
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### Lagrangian of a spherical pendulum

I am working on a problem that's asking me to express the lagrangian of a mass $m$ suspended from a rigid massless rod of length $L$, but free to rotate otherwise (a spherical pendulum). The problem ...
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### Calculating Expected Increase In Prize Line Count

Hello and thanks in advance. I'm trying to solve a problem I'm having with a pattern matching game. The game's board consists of a 5x5 grid of numbers where column 1 (on the far left) contains 5 ...
1 vote
29 views

### Hamiltonian for a free particle in $2$D in Polar coordinates

I am working through a problem that's asking me to calculate the Hamiltonian of a free particle in polar coordinates moving in two dimensions. I believe I have the correct form of the equation, ...
1 vote
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### Fomin et al., Mathematical Circles Chapter 4- Pigeon Hole Principle Problem 12. Max. no. of kings that can be placed so no two put each other in check

I found this problem in Mathematical Circles in the Pigeon Hole Principle chapter: What is the largest number of kings which can be placed on a chessboard so that no two of them put each other in ...
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### Problem solving strategy to determine who wins a game?

Consider a game on a chess board with a single counter in the top right corner. You can only move this counter to a square that is adjacent. There are two competitors and the aim of the game is to get ...
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### Average commute time

Roads in town looks like this: Where $t=45$ means the path takes 45 minutes, and $t=\frac{N}{100}$ means the path takes as many minutes as the number of drivers who chose that path divided by $100$. ...
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### How do I determine whether our idea is novel?

Mathematics talent runs in my family, but although I enjoy learning about things in mathematics and biostatistics, I am a biochemist by training. So I read a blog post by a mathematician, and started ...
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### Randomly pressing buttons of a calculator [closed]

There's a normal scientific calculator with only $12$ buttons: from $0$ to $9$ and $+-$ Randomly press these buttons $n$ times. What will be the math expectation of the result? (Imagine that the ...
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### Solving Linear Non-Homogeneous Recurrence - where F(n) contains an exponential (2^n) and a polynomial (n+3)

. . . What is the reason as to why we are allowed to "solve it one by one" (highlighted in red) ? - where we go on to consider 2^n (green) and n+3 (pink) of F(n) seperately and then find ...
1 vote
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### Invariants principle Sikinia (Engel problem-solving strategies E4)

I'm studying Engel book and the invariant principle, but the solution of problem E4 blocks me. E4. In the Parliament of Sikinia, each member has at most three enemies. Prove that the house can be ...
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### How to express the area of a right triangle in terms of altitude and bisector of its right angle?

In a right triangle $ABC$ with the right angle $C$, the altitude $CH$ is equal to $h$, and the angle bisector $CL$ is equal to $l$. Find the area of triangle $ABC$. My attempt: Let $AC=a$, $BC=b$, ...
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1 vote
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### How to solve a trinomial with a rational exponent $x^{q}-x-c=0$

I require solutions to equations of the following form: $x^{q}-x-c = 0$ where $q$ is a rational number very close to 1 with $q$ such that: $$q=\frac{p^k+1}{p^k}$$ $$q=\frac{p^k}{p^k-1}$$ $p$ prime, ...
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