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. […]
The leaders in the IOQM, ISI Entrance, American Math Competitions and Math Kangaroo mock contests in Cheenta
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.
Problem 1 Andy and Betsy both live in Mathville. Andy leaves Mathville on his bicycle at $1: 30$, traveling due north at a steady 8 miles per hour. Betsy leaves on her bicycle from the same point at $2: 30$, traveling due east at a steady 12 miles per hour. At what time will they […]
Problem 1 What is the ones digit of $$222,222-22,222-2,222-222-22-2 ?$$ (A) 0(B) 2(C) 4(D) 6(E) 8 Answer: (B) 2 Problem 2 What is the value of this expression in decimal form? $$\frac{44}{11}+\frac{110}{44}+\frac{44}{1100}$$ (A) 6.4(B) 6.504(C) 6.54(D) 6.9(E) 6.94 Answer: (C) 6.54 Problem 3 Four squares of side length $4,7,9$, and 10 units are arranged in […]
AMC 8 2004 is a classic middle-school math contest featuring 25 engaging problems in algebra, geometry, counting, probability, and logical reasoning. It tests speed, accuracy, and smart problem-solving strategies in a fun competitive format.
Problem 1Theresa's parents have agreed to buy her tickets to see her favorite band if she spends an average of 10 hours per week helping around the house for 6 weeks. For the first 5 weeks, she helps around the house for $8,11,7,12$ and 10 hours. How many hours must she work during the final […]
Get the official AMC 8 - 2003 paper with all questions. This exam from the Mathematical Association of America helps young students practice analytical thinking and prepare effectively for upcoming competitions.
The AMC 8 - 2002 paper is a middle-school level mathematics contest featuring engaging problems that test logical reasoning, number sense, and problem-solving skills. This paper is ideal for students preparing for Math Oympiads and competitive exams.
Problem 1 At Euclid High School, the mathematics teachers are Mrs. Germain, Mr. Newton, and Mrs. Young. There are 11 students in Mrs. Germain's class, 8 in Mr. Newton, and 9 in Mrs. Young's class are taking the AMC 8 this year. How many mathematics students at Euclid High School are taking the contest?(A) 26(B) […]
Problem 1 Mindy made three purchases for $\$ 1.98, \$ 5.04$ and $\$ 9.89$. What was her total, to the nearest dollar?(A) $\$ 10$(B) $\$ 15$(C) $\$ 16$(D) $\$ 17$(E) $\$ 18$ Answer: (D) $\$ 17$ Problem 2 On the AMC 8 contest Billy answers 13 questions correctly, answers 7 questions incorrectly and doesn't answer […]
Practise the AMC 8 2005 paper to sharpen your core math skills and contest thinking. This set of problems covers key topics like arithmetic, algebra, geometry, counting, and logical reasoning — perfect for Grades 6–8 students aiming for AMC 8 and other olympiad-style exams.
The 2015 American Mathematics Contest 8 (AMC 8) was a 25-question, 40-minute multiple-choice exam for students in Grade 8 and below, conducted by the MAA.
It focused on strong middle-school problem solving—covering algebra basics, geometry, number theory, and counting/probability—with an emphasis on logic and speed (no calculators).