Problem 1 Let $\mathbb{N}$ be the set of all positive integers and $S=\left\{(a, b, c, d) \in \mathbb{N}^4: a^2+b^2+c^2=d^2\right\}$. Find the largest positive integer $m$ such that $m$ divides $a b c d$ for all $(a, b, c, d) \in S$. Solution Notice that $(2, 2, 1, 3)\in S\Rightarrow m$ is a divisor of $12 […]
Try this ISI BStat - BMath Entrance 2023, Problem no. 2 with hints and final solution.
In the math world, a unique challenge emerges, combining algebra and number theory. The goal: show that specific equation solutions aren't simple fractions. We reveal a key insight about b² - 4ac: it's always a distinct odd perfect square. Using "parity check," No matter the numbers, the left side remains even, while the right side stays odd. The result: these solutions differ from simple fractions, highlighting math's power in problem-solving.
In 2023, the following Cheenta students are successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 100 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 times every week. CMI B.Sc. Math Entrance I.S.I. […]
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Please use the following form to contribute problems of CMI BSc Math Entrance 2023. We will work on the solutions. Also come back to this page to see the updates on Problems and Solutions of CMI BSc Math Entrance 2023. B1. Let \( n \) be an odd positive number greater than 1. We have […]
Questions, Solutions and discussions on ISI BStat-BMath Entrance 2023.
Solutions of INMO 2023 Problem 1 Let $S$ be a finite set of positive integers. Assume that there are precisely $2023$ ordered pairs $(x, y)$ in $S \times S$ so that the product $xy$ is a perfect square. Prove that one can find at least four distinct elements in $S$ so that none of their […]
Understand how Cheenta Math Circles are critical for training students for math olympiads and other advanced mathematical competitions.
Problems and Solutions from Indian National Mathematical Olympiad (INMO) 2025, the third level of Math Olympiad in India.
Dive into the discussion of the solution to Problem 29 from the 2023 AMC (Australian Mathematics Competition), upper primary category.
Dive into the discussion of the solution to Problem 24 from the 2023 AMC (Australian Mathematics Competition), upper primary category.
Let's discuss a problem from the AMC 2021 Intermediate: Problem 26 which revolves around basic algebra and combinatorics. Problem In Australian Rules football, a team scores six points for a 'goal' and one point for a 'behind'. During a game, Vladislav likes to record his team's score with a sequence of sixes and ones. There […]
Access Australian Mathematics Competition past year paper of 2019 year 11 - 12 Senior to sharpen your problem-solving skills.
Access Australian Mathematics Competition past year paper of 2020 year 11 - 12 Senior to sharpen your problem-solving skills.
Access Australian Mathematics Competition past year paper of 2023 year 11 - 12 Senior to sharpen your problem-solving skills.
Access Australian Mathematics Competition past year paper of 2021 year 11 - 12 Senior to sharpen your problem-solving skills.
Dive into the discussion of the solution to Problem 27 from the year 2021 Australian Mathematics Competition, Intermediate category.
Dive into the discussion of the solution to the Australian Mathematics Competition(AMC), Upper Primary Problem 16 from the year 2022.