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
51
votes
5 answers

Finding the value of $\sqrt{1+2\sqrt{2+3\sqrt{3+4\sqrt{4+5\sqrt{5+\dots}}}}}$

Is it possible to find the value of $$\sqrt{1+2\sqrt{2+3\sqrt{3+4\sqrt{4+5\sqrt{5+\dots}}}}}$$ Does it help if I set it equal to $x$? Or I mean what can I possibly…
user84940
  • 421
33
votes
1 answer

Is it possible to construct a sequence that ends in 1000000000?

Starting from the number $1$ we write down a sequence of numbers where the next number in the sequence is obtained from the previous one either by doubling it or rearranging its digits (not allowing the first digit of the rearranged number to be…
0327
  • 337
18
votes
3 answers

Decipher the greeting card $( X^2 +Y^2 -1 ) ^3 - X^2 Y^3 = 0$

A friend of mine just got a rather weird congratulations card through the door They have zero idea what it means, I have tried graphing it and nothing spectacular comes out. Is there a standard name for this equation or does it signify…
nyxthulhu
  • 283
9
votes
3 answers

Egg drop problem

Suppose that you have an $N$-story building and plenty of eggs. An egg breaks if it is dropped from floor $T$ or higher and does not break otherwise. Your goal is to devise a strategy to determine the value of $T$ given the following limitations on…
1110101001
  • 4,188
8
votes
3 answers

How to solve this irrational equation?

How to solve this equation in the set real numbers $$\sqrt{8x + 1} - \sqrt{6x - 2} - 2x^2 + 8x - 7 = 0.$$ Using Mathematica, I know, this equation has two solutions $x = 1$ and $x = 3.$
minthao_2011
  • 1,885
8
votes
4 answers

Optimization-like question

Let's say I have a formula like $ax + by + cz = N$. $a, b, c$, and $N$ are known and cannot be changed. $x, y$, and $z$ are known and can be changed. The problem is that the equation is not true! My problem (for a program I'm writing) is: how can…
D. Bruce
  • 81
7
votes
0 answers

Given that $f(x) :=x^6-6x^5+ax^4+bx^3+cx^2+dx+1$ has its roots as all positive, find $a,b,c,d$

From Larson's "Problem Solving Through Problems" 7.2.10: Given that $f(x) :=x^6-6x^5+ax^4+bx^3+cx^2+dx+1$ has its roots as all positive, find $a,b,c,d$ Thus chapter is about (generalized) Arithmetic-geometric mean inequality so I would have to use…
Squirrel-Power
  • 3,638
7
votes
2 answers

Find a succinct problem whose solution requires methods from many sub-branches of mathematics

I've edited and reposted a version of this question on mathOverflow (for professional mathematicians) here, which may prove interesting to others. Some mathematical problems require solution techniques from a single branch (sub-discipline) of…
David G. Stork
  • 29,774
6
votes
4 answers

Complicated but easy problem solving?

I'm going to be in the UKMT Team Challenge in a few days and revising some questions used in the previous year. The questions are really bugging my mind. I know it may seem like a lot and quite easy but thanks if you help out, I will be grateful.…
itshanks
  • 532
6
votes
3 answers

What should I do if I don't know where to start?

Sometimes getting started on a problem seems to be the hardest part. Once you find something to sink your teeth into, everything goes smoothly. What are some good things to try when you're staring at the problem with no ideas, and all the MSE…
dfeuer
  • 9,069
6
votes
0 answers

A system of equations of Vietnamese Mathematical Olympiad 2013

This is a system of equation of Vietnamese Mathematical Olympiad 2013, the first day. Solve the system of equations $$\begin{cases} \sqrt{\sin^2 x + \dfrac{1}{\sin^2 x}} + \sqrt{\cos^2 y + \dfrac{1}{\cos^2 y}} =…
minthao_2011
  • 1,885
6
votes
1 answer

Ways to Score 18 Points in Football Excluding 2-point conversion

The Chicago Bears score 18 points in a football game. In how many different ways can the Bears score these points? Points are scored as follows: a safety is 2 points, a field goal is 3 points, a touchdown is 6 points, and a point after touchdown…
Joe
  • 4,757
  • 5
  • 35
  • 55
5
votes
3 answers

Secret Number Problem

Ten students are seated around a (circular) table. Each student selects his or her own secret number and tells the person on his or her right side the number and the person his or her left side the number (without disclosing it to anyone else). Each…
Aeon
  • 253
5
votes
2 answers

Basic combinatorics question

In a tennis tournament there are $2n$ participants. In the first round of the tournament, each player plays exactly once, so there are $n$ games. Show that the pairings for the first round can be arranged in exactly $(2n -1)!/2n^{n-1}(n-1)!$…
Akash
  • 91
5
votes
4 answers

Number of people having shaken hands an odd number of times

This is from a book called USSR Olympiad Problem book: Every living person has shaken hands with a certain number of other persons. Prove that a count of the number of people who have shaken hands an odd number of times must yield an even…
Evgeny Danilenko
  • 51
1
2 3
…
28 29