Latin Squares?

I know Times Square, Tinanmen Square...But, Latin Square? Where is it? Or Should I say what is it? Well, it doesn't happen to be a place or an object, but an interesting thing that the jobless mathematicians conjured up to keep their left brains busy.

In simple terms, it happens to be a 2-dimensional square matrix (like the crossword squares) into which you fill numbers from 1 to n (or n distinct letters / symbols) , n being the size of your matrix, based on these two rules

• Each row should contain a number (from 1 to n) only once
  
• Each column should contain a number (from 1 to n) only once
  

Here is a simple example (of a 3 x 3 latin square)
1 2 3
2 3 1
3 1 2

and a 4 x 4 latin square

@ # $ %
# @ % $
% $ # @
$ % @ #

So much for what is a latin square..It isn't all that complex as it sounds, right? Right!

If you didn't notice already, it resembles those sudoku puzzles that you see everywhere these days..Isn't it?

Yes, that's true. Sudoku puzzles are but special cases of latin squares. They are

• 9 x 9
• In addition to the above two rules of normal latin squares, Sudokus satisfy an additional rule. If you divide the 9x9 matrix, into nine 3 x 3 blocks, each of these blocks should contain a number (from 1 to 9) only once

Now, that makes our latin squares little more interesting, doesn't it ?

Is this blog going to be all about latin squares? The answer is a big NO. For the simple reason that, I dont know much about latin squares myself. You may ask, Why did you name it as 'Latin Squares' then ? The answer is simple again, because it was available & not used by anyone yet!