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
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How many possible different arrangements?

There are $1000$ numbers $1,2,3,...999,1000$ to be arranged in a line so that every number other than the rightmost differs by 1 from one or more of the numbers to its right. How many different arrangements are possible? If $1$ is the rightmost…
jinha0001
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Trying to simplify the expression

Can anybody simplify it? Show me the way of simplification. The expression is as follows: $$F(x) = 1 *(1!+x)+2*(2!+x)+ ..+x*(x!+x)$$ for a positive integer $x$ I've tried but nothing got.
Frustrated
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how can you solve this pipe question?

Two pipes, A and B can fill a tank in 24 and 35 minutes respectively. If both the pipes are opened simultaneously, after what time should A be closed so that the tank is filled in 18 minutes? Can you solve this?
the quizzer
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1 answer

A problem regarding table decorations

My one friend Alex has r red, g green and b blue balloons. To decorate a single table for the banquet he needs exactly three balloons. Three balloons attached to some table shouldn't have the same color. What maximum number t of tables can be…
Shahed Al Mamun
  • 71
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2 answers

"A secretary had to call all the clients in her company" probably an easy problem that I am really struggling for some reason.

"A secretary had to call all the clients of her company. By the morning she made 1/3 of the calls; in the afternoon she made 3/5 of the calls that were left and at night called the last 64 clients. With how many clients did she talk in the…
Itami
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Minimum value of $(\frac{1}{a}-1)(\frac{1}{b}-1)(\frac{1}{c}-1)$

If $a,b$ and $c$ are positive real numbers such that $a+b+c=1$, what is the minimum value of $(\frac{1}{a}-1)(\frac{1}{b}-1)(\frac{1}{c}-1)$ ? How can we solve this? I tried to simplify the expression but still can't figure a way to solve this. My…
Ganit
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1 answer

A logic question based on code language

Source: Today I gave the NCO(National Cyber Olympiad) exam and this question was there in the logical reasoning section. The question is as follows: 'In a certain code language, if 'VOLCANO' is written as 'QPCENQX', then how will 'RAINBOW' be…
Coder
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Solutions to $(m-n)²=4mn/(m+n-1)$

Find all solutions in integers $m,n$ for the equation $(m-n)²=4mn/(m+n-1)$ I tried solving this but got stuck at one point , after simplification this equation reduces to, $(m-n)²=m+n$, after this how do we conclude that $m=k(k+1)/2$,$n=k(k-1)/2$,…
Dhruva
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1 answer

If 3^1993 =100k + n, where n < 100 is a nonnegative integer, what is n?

If 3^1993 =100k + n, where n < 100 is a non-negative integer, what is n? Is there a simple solution for this?
VS Puzzler
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1 answer

Geometric Inequality problem

Within a problem I was solving I came across Prove $xy+yz+xz \geq 2xyz$ for all non-negative real numbers $x,y,z$. I have attempted to prove this for some time now, but cannot find a solution that works. The closest I came was trying the AM GM…
Smartsav10
  • 177
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There are 9 blocks whats the length and width of one block. the pic has the rest of the info for the question

The rest of the questions information is here I'm really confused. Please help me with this question.
Wolfie01
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1 answer

How is this notation read?

How is this notation read $$a_{0}^{2^{i}}??$$ Here is also an image of the full reference:
devdev_dev
  • 117
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2 answers

Manhattan Distance

The Manhattan Distance between two points (a, b) and (c, d) is given by |a−c|+|b−d|, where |u−v| refers to the absolute value of (u−v). Given an integer S, your task is to find the number of points (x, y), where both x and y are integers, such…
Patrick Schick
  • 441
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1 answer

Mental Math Speed Test Computation Help

I appreciate this may not be the correct forum to askt this on but wasn't sure where else to ask this. Does anyone have any reccommendations for how to begin working on such questions under time constraints: 786.3 * 1.03 684.9 * 1.07 78.2 *…
InvestingScientist
  • 433
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Waterloo Fermat contest 2020

last Question: (not verbatim) if x, y, z is between [0, 1], what is the probability that $|x-y| >z$ and $|x-z| >y$ In the contest, I had a very hard time trying to visualize and graph the graph of a cube which represents the x, y, z value and the…
SuperMage1
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