Category Archives: Trick

2003 AMC 12 a Problem 23 on Perfect Squares

Posted on July 30, 2021 by Sumant Sumant
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Interesting Limit Calculation using Fundamental Theorem of Calculus and L’hopital rule

Posted on January 27, 2021 by Sumant Sumant
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Mamikon Mnatsakanian’s Idea of Sectors on Polygon

Posted on August 16, 2020 by Sumant Sumant

I came across this on Starbird’s Lecture on Visual Geometry. What Mnatsakanian idea does is to draw sectors of same radius on the extended side of the polygon (It need not be regular). The benefit of this is we get … Continue reading →

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Fun Warm Up Problem

Posted on August 2, 2020 by Sumant Sumant

There is a forest and among the many trees there is an apple tree. Then there happened a hurricane. Before the hurricane there were apples on the tree, after the hurricane there were no apples on the tree and no … Continue reading →

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Trisection of Angle using Ruler

Posted on July 13, 2020 by Sumant Sumant

One of the three problems of antiquity. While one cannot use an unmarked ruler and compass to trisect a given angle. Archimedes found a method to trisect using a marked ruler. Here is his brilliant proof. I learned this from … Continue reading →

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Chicken Nugget Problem

Posted on July 12, 2020 by Sumant Sumant

This is a very famous problem that I first read in Mathematical Journeys and later in Paul Zeitz’s book. The analysis based on lattice method is due to Paul Zeitz. The problem is about two chicken boxes. One has a … Continue reading →

Posted in Combinatorics, Graph Theory, Proof, Trick | Tagged , | 3 Comments

9 dots problem

Posted on July 8, 2020 by Sumant Sumant

A classic problem one can find it any lateral thinking book. From Edward De Bono to Paul Zeitz’s book on problem solving. The idea is to connect 9 dots using only 4 straight lines without lifting the pencil and making … Continue reading →

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An interesting problem on Divisibility and Gauss Pairing

Posted on June 30, 2020 by Sumant Sumant
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AM GM Proof by Induction (clever bifurcation)

Posted on December 16, 2019 by Sumant Sumant
Posted in Inequalities, Mathematical Induction, Proof, Trick | Leave a comment

G Ehlers AM GM Proof

Posted on December 14, 2019 by Sumant Sumant
Posted in Inequalities, Mathematical Induction, Proof, Trick | Tagged | 1 Comment