Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [contest-math]

For questions about mathematics competitions or the questions that typically appear in math competitions. Provide enough information about the source to confirm the question doesn't come from a live contest.

This tag is intended for

  1. Questions from mathematics competitions.
  2. Inquiries about alternative proofs for problems that are from math contests.
  3. Questions that have been inspired by a contest problem, including practice problems.
  4. Questions requesting advice on competing in contests.

See this list of mathematics competitions to get an idea of the types of questions this tag is for.

Mathematics StackExchange has a policy on questions from current competitions. Questions from ongoing competitions will be locked and temporarily deleted until the end of the contest. It is a good idea to include information about a contest, such as a link to the contest webpage.

9758 questions
0
votes
2 answers

Textual problem from a competition. I believe the use of proportions is needed, but I can't seem to find the answer.

3 fathers footsteps are as long as 5 daughters footsteps. While the father makes 6 footsteps, the daughter makes 7. The daughter has already made 30 footsteps when the father went after her, after how many footsteps will the father reach the…
zermelovac
  • 941
0
votes
2 answers

Painting cells in a table

There is a 4*4 cells table. We paint cells by the following rule: any unpainted cell has an adjacent side with a painted cell, and any painted cell has an adjacent side with an unpainted cell. For example, for n = 12 (1 - painted, 0- not painted) 1…
student28
  • 385
0
votes
2 answers

A task about two moving trains

Two trains are heading towards each other. The first train has a speed of 60 km/h, the 2nd one has the speed of 50 km/h. The length of the first train is 0.35 km, the length of the second train is 0.42 km. What is the distance between the point…
student28
  • 385
0
votes
3 answers

Hcf and Lcm pairs

The $HCF$ and $LCM$ of two numbers are $12$ and $720$. lets try to find how many pairs are possible and what may be those number. Cant get to the answer given help please $Answer :$ $4$ $pairs$ $(12,720) , (36,240) , (48,180) ,(60,144).$
Pallab
  • 101
0
votes
3 answers

Split the cookies between people

The problem from a math magazine that I am struggling to solve. Little Red Riding Hood has 60 cookies and 5 guests. She needs to split the cookies on the plates in a way that everyone has the equal amount of pies. But she does not know how many…
student28
  • 385
0
votes
1 answer

Find max f(a,b)

$f(a,b)=min(a,b,\frac1a+\frac1b)$, where $a$ and $b$ are positive real numbers. Basically what I would do is simply find when are these 3 terms equal($a=b=\sqrt 2$), and then manually check what happens when I up/down both values and that should…
Dovla
  • 205
0
votes
3 answers

Time and Work Problem 5

If A, B,C,D can do 150 sums in 6 days. Let us find in how many days will A and D finish 250 sums if each of them does equal number of sums everyday. this much is given in the question, i dont knw how to solve with this much data.
Pallab
  • 101
0
votes
2 answers

Math Olympiad Question- Proof

I can think of examples but I cannot generalize the proof Suppose you have a currency that has coins to represent 1 cent, 2 cents, 5 cents, 10 cents, 20 cents, 50 cents and 1 dollar. Also suppose you can pay A cents with B coins. Prove that you can…
J. Don
  • 13
0
votes
2 answers

Does referring a friend for an extra contest entry actually increase your odds of winning?

I've entered sweepstakes and contests, and recently they all have the option to refer a friend. If your friend enters the contest, you get an extra entry for yourself, "increasing your odds of winning", as the contest likes to proclaim. Is this…
Stephen S
  • 193
0
votes
3 answers

$f(x) = x^2 + 4$, $f(y) = x^2 + 23$, $f(x-y) = ?$

$\text{integer number }x,y >0\\f(x) = x^2 + 4\\ f(y) = x^2 + 23\\ f(x-y) = ?$ My Work: This doesn't make any scene to me.. The second equation is telling that $f(y)=x^2 + 23$ for any positive integer $y$. If we set $y=x$ then $f(x) = x^2 +…
Rezwan Arefin
  • 3,106
  • 1
  • 14
  • 39
0
votes
2 answers

Speed and Time Problem

A boy is climbing up a flight of $35$ steps from Level $1$ to Level $2$ of a building. If he climbs at his fastest speed for $15$ steps and slowest speed for $15$ steps, he will take $40$ seconds to climb $30$ steps. If he climbs at his fastest…
space
  • 4,561
0
votes
2 answers

Solve $\left(\frac{1}{25\cdot26}+\frac{1}{26\cdot27}+\frac{1}{27\cdot28}+\frac{1}{28\cdot29}+\frac{1}{29\cdot30}\right)\cdot150+\frac{1}{x-1}=11$

Solve for $x$: $$\left(\frac{1}{25\cdot26}+\frac{1}{26\cdot27}+\frac{1}{27\cdot28}+\frac{1}{28\cdot29}+\frac{1}{29\cdot30}\right)\cdot150+\frac{1}{x-1}=11$$ I have tried alot of things, but nothing seems to work. I imagine there is a really…
DDomjosa
  • 447
0
votes
0 answers

A problem from ITYM - Centro-Symmetric

I am searching for the problems of ITYM as you can see here: https://docs.google.com/viewer?a=v&pid=sites&srcid=aXR5bS5vcmd8d3d3fGd4OjdkODJiYTNhYWM0ZDNjNDU International Tournament of Young Mathematicians (ITYM)! CentreSymmetric I am so interested…
Igor Titara
  • 9
0
votes
2 answers

Finding the maximum without using calculus

Find integers $x, y, z > 0$ where: $xy - xz - 10z$ is maximal, and $2x + y + z = 110$ How would one solve something like this using just algebra? It would be trivial to solve with calculus, but that shouldn't be necessary here.
user341554
  • 113
0
votes
0 answers

Candidates Tournament

Five players $A$, $B$, $C$, $D$, $E$ participated in a chess tournament. It is known that all of the participants ended with a different amount of points, and that when ordered by them, they end up $ABCDE$. However, when ordered by the number of…
Roman83
  • 17,884
  • 3
  • 26
  • 70
1 2 3
…
31 32