Working backward – C.M.I UG -2019

Understand the problem If there exists a calculator with 12 buttons, 10 being the buttons for the digits and A and B being two buttons being processes where if n is displayed on the calculator if A is pressed it increases the displayed number by 1 and if B is...
Clocky Rotato Arithmetic

Clocky Rotato Arithmetic

Do you know that CLOCKS add numbers in a different way than we do? Do you know that ROTATIONS can also behave as numbers and they have their own arithmetic? Well, this post is about how clocks add numbers and rotations behave like numbers. Consider the clock on earth....
Circle in Circle – PRMO 2017

Circle in Circle – PRMO 2017

Understand the problem Let ( Omega_1 ) be a circle with center O and let AB be a diameter of ( Omega_1 ). Let P be a point on the segment OB different from O. Suppose another circle ( Omega_2 ) with center P lies in the interior of ( Omega_1 ). Tangents are drawn from...
Locus of vertex of an equilateral triangle

Locus of vertex of an equilateral triangle

Try this beautiful problem. We will give you hints! ABC is an equilateral triangle with vertex A fixed and B moving in a given straight line. Find the locus of C   What is the big idea ? Think about what does not change. 1. Point A is fixed. 2. The line on which...
Pappus Theorem – Story from Math Olympiad

Pappus Theorem – Story from Math Olympiad

Alexander the great founded Alexandria in Egypt. This was in the year 332 Before Christ.  Since then Alexandria became one of the most important cities of the world. It had the Light House and the Great Library. These were the wonders of ancient world. ...
A Proof from my Book

A Proof from my Book

This is proof from my book – my proof of my all-time favorite true result of nature – Pick’s Theorem. This is the simplest proof I have seen without using any high pieces of machinery like Euler number as used in The Proofs from the Book. Given a...