Extremal Principle for Counting – AMC 10

Extremal Principle for Counting – AMC 10

Extremal Principle is used in a variety of problems in Math Olympiad. The following problem from AMC 10 is a very nice example of this idea. AMC 10 Problem 4 (2019) A box contains 28 red balls, 20 green balls, 19 yellow balls, 13 blue balls, 11 white balls, and 9...
Spiral Similarity

Spiral Similarity

Geometric Transformation is a powerful tool in Geometry. We look at one such transformation: Spiral Similarity. Watch video Try these problems. Send answers to helpdesk@cheenta.com Problem 1: Suppose O = (0, 0), A = (2, 0) and B = (0, 2). Let T be the spiral...
An interesting biquadratic from ISI Entrance 2005

An interesting biquadratic from ISI Entrance 2005

What are we learning ? Competency in Focus: Biquadratic Equations Main idea: It is usually hard to solve biquadratic equations. However, sometimes, combining tools from geometry and strategies like completing the square it is possible to do so.   Look at the knowledge...
AMC 8 2019 – Stick and Dot Method

AMC 8 2019 – Stick and Dot Method

Understand the problem Alice has 24 apples. In how many ways can she share them with Becky and Chris so that each of the three people has at least two apples? Source of the problem American Mathematical Contest 2019, AMC 8 Problem 25 Topic Combinatorics  Difficulty...