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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Minimum number of weights to weigh

What is the smallest number of weights needed for weighing objects with masses 1g, 2g, ..., 35g? I went this way: for 1g one needs 1g. For 2g one has to add 2g. For 3g no adding is needed. But for 4g, there are two ways: adding another 2g weight or…
user200918
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Calculating the next number in the sequence

I want to know the next number in the sequence below: 1935, 1940, 1948, 1962, 1985, 2020, … Consecutive differences are 5, 8, 14, 23, 35 They don't look like Fib-seq. Also consecutive differences of the consecutive differences increase rapidly! This…
user200918
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Time and Distance Problem : Circular Track

$A$ and $B$ start running simultaneously on a circular track from point $O$ in the same direction. If the ratio of their speeds is $6 :1$ respectively, then how many times is $A$ ahead of $B$ by a quarter of the length of the track before they meet…
Ganit
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Is there any way to prove this assumption?

This question is question $6$ on INMO $2020$: A stromino is a $3 \times 1$ rectangle. Show that a $5 \times 5$ board divided into twenty-five $1 \times 1$ squares cannot be covered by $16$ strominos such that each stromino covers exactly three unit…
Righter
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How to sort a set of number pairs so that the first number of the next one is equal to the last number of the previous one?

this is the array: [[1,0], [3,4], [2,1], [4,5], [0,2], [5,3]] Become like this: [[1,0], [0,2], [2,1]] [[3,4], [4,5], [5,3]] I want to write a program, and I want to know if there are clever ways and logic to do it. EDIT: The above example contains…
g2m.agent
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How do we find this function cardinalities?

Let $x$ and $y$ be sets and $|x|$ and $|y|$ are their respective cardinalities. It is given that there are exactly $97$ functions from $x$ to $y$.From this we can conclude that: a) $|x|=1 ,|y|= 97$ b) $|x|= 97,|y|=1$ c) $|x|=97, |y|= 97$ d) None
elina parajuli
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What does The line is reflected in the line mean?

I am doing the $2016$ CIMC (Canadian Intermediate Mathematics Contest) contest and I am kind confused with the question A6 meaning. I just wonder what does the line is reflected in the line mean? The line is reflected in the line with equation $x +…
Shawn
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If $x+y=1$ Prove that $\left(1+1/x^n\right) \left(1+1/y^n\right) \ge (1+2^n)^2$

Let $x+y=1$, where $x,y\in \mathbb R^+$ Prove that $\forall x\in \mathbb N$ $$P(n):\left(1+\frac{1}{x^n}\right)\left(1+\frac{1}{y^n}\right)\ge (1+2^n)^2$$ It's clear that the best method for proving it is induction. $P(0)$ is true, so assume that…
PNT
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Finding alternative operation given two examples

Good day, I am doing old maths questions, but I can't seem to figure out the answer to the following: Ura Wong says five times seven is 38 and six times six is 39. Using Ura's method what is the answer to six times seven? The answer key states…
Saddy
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Help in understanding the solution : Profit and Loss Problem

On buying a pen, the shopkeeper gives three refills free. On buying a pen and six refills, the shopkeeper gives additional four refills free. If the equivalent discount is the same in both cases, then how many refills will be equal in value to a…
Ganit
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Clarification on meaning of question (ISEE Test Upper Level)

QUESTION: $a$ is a factor of $10$ and $b$ is a factor of $15$. Column A Column B The smallest value that ab must be a factor of 30 Is Column A greater than/ smaller than / equal to Column B? The possible values of $a$ are $1,2,5$ (and…
PatrickT
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What is the value of certain expression?

I have got two integers, say $m$ and $n$, which I’m trying to guess. As a hint I’m getting the value of $mn+11m+11n-m^2-n^2$. After that I can unambiguously name $m$ and $n$. What was the value of the expression? In other words I need to find such…
BeesaFangirl DOTO
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How many games played in the competition? APMOPS (SMOPS)

2017 schools participated in a big inter-school chess competition. Each school sent 2 participants. The rules of the competition were: i) Participants do not compete with each other for more than 1 game; ii) Participants from the same school can not…
Oziter
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Maximize multivariable function ( from Brazilian mathematical olympiad)

Let $n$ be a positive integer bigger than one. Find the maximum value of: $x_1^3 + x_2^3 + \ldots + x_n^3$ given that $x_1 + x_2 + \ldots + x_n = 0$ and $x_1^2 + x_2^2 + \ldots + x_n^2 = 1$. This is what I have tried: Analyzing both conditions…
joao pedro menezes
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Sum of floor : $\sum_{i= 0}^{n - 1} \bigg\lfloor\frac{ai + b}{m}\bigg\rfloor$

So, I'm trying to research a formula for my programming problem which is to calculated : $$\sum_{i= 0}^{n - 1} \bigg\lfloor\frac{ai + b}{m}\bigg\rfloor$$ Because the range of $n$ is kinda big, so to calculated that sum, I have to analysis the above…
CQTshadow
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