Maverick Tastes

On a certain day of a certain month in a certain year, my best friend said to me, " You know, I have a test tomorrow, and guess what the topic is ? Sigmund Freud and his Psychoanalytic theory! what a pervert! always linking everything to sex!! If you ask him why the grass is green and why water is wet you'd probably end up with him deducing that either you have repressed sexual desires which make you think about the "wetness" or there is something inherently sexual about mother nature..A freak of nature is what i call him!". I replied, "Well, I don't really know much about him and his theories, except for that book he wrote..though i haven't read it" and then she says, "Yeah! well lucky you! ".  Today, she is no more. It's a depressing thought, she was the finest friend i ever had. The most wonderful girl of them all. The smartest, cutest and most beautiful girl ; she passed away in January 2009 at the age of 18. There is no equa...

I begin my blogging career by writing this cute little post on Chessboards and Combinatorics. It is not a great deal but it's a fun way to begin and it also has quite a bit of recall value I must admit for I am constantly besieged by people who often forget the solution to this very trivial problem. And lest my conscience prick me with the proverbial "needle", I admit that I too am of the ilk! :p .Anyhow, the question that concerns us now is to find the number of squares and rectangles in an ordinary 8x8 chessboard. I don't wish to use the vertical line and horizontal line method for this which "en effet" reduces the problem to the simplistic 9C2*9C2=1296 for the rectangles. Oh! the answers by the way are 204 squares and 1296 rectangles(including squares) or 1296-204= 1092 pure rectangles!! The method i propose goes somewhat like this.. 1>. The number of squares in a chessboard-               The various sizes of the squares can range on...