complex numbers

complex

13th Friday

Prove that in each year, the 13th day of some month occurs on a Friday.

START 2012, KVPY 2012

A sequence is called tworri c if its first term is 1 and the sum of every pair of
consecutive terms is a positive power of 2. One example of a tworri c sequence is 1, 7, -5,7, 57. (a) Find the shortest possible length of a tworri c sequence that contains the term 2011.
(b) Find the number of tworri c sequences that contain the term 2011 and have this
shortest possible length.
PRACTICE PROBLEMS FOR "KVPY & START 2012"

PASCAL'S Triangle

In Pascal’s triangle the number 1 appears infinitely many times. All other numbers will appear a finite amount of times*.

The number 2 appears just once.
The number 3 appears twice.

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TRIVIA FOR ABR & VEDANSI ON AUSPICIOUS NAVAMI

TRIVIA FOR ABR & VEDANSI ON AUSPICIOUS NAVAMI: Imagine a circular billiard table of unit radius, with centre at (x,y ) coordinates (0,0). It has two billiard balls on it. Ball A is at coordinates (-0.8, -0.1); ball B at (0.6, 0.4). What are the coordinates of the point(s) on the cushion to which one must hit ball A so that it bounces off the cushion once and then hits ball B?

 

Integers