Friday, 14 October 2011

In continuation of my earlier post on SU-DO-KU I am writing this one on Magic Squares. It is said that the Great Genius in Mathematics, Sreenivasa Ramanujam began his exploits with Magic Squares and went on to become the greatest Mathematician from India to be compared with the likes of Newton, Archimedes etc. Let us delve into it and see what it holds for us.
Magic Squares of Odd Numbers
Magic Squares can be made either for Odd number of Squares or for Even number of Squares. First let us study the Odd Number squares. For Eg: let us construct a Magic Square of 5 x 5. We will be making amazing arrangement of numbers in a way that they all add up to same total either upon each row or each column or the diagonals.The squares can be of odd number like 3,5,7,9 et all. The method creating these squares are fairly simple and follows a pattern. They can be summarised as follows: 
  1. Begin at the Top row middle square always.
  2. When at the top, drop down to the bottom row in next column.
  3. Where vacant keep ascending the diagonal to the right.
  4. When blocked at the side, go to upper row extreme left column.
  5. when blocked while ascending the diagonal. drop down to immediate lower square.
That is all folks! Keep filling those numbers following these rules and you will be amazed how easy it is to fill even the squares of 11,13,15 etc .

Magic Squares of Even Numbers
The construction of even number Magic Squares is more exciting. We can make squares of 4,8,12 etc and for now let us make 4x4 model. To begin you start from left to right and filling the numbers in natural order from 1 to 16 BUT only in the DIAGONALS. See Pic A. Then start filling again from 15 to 1 from Left to Right in the vacant squares to complete the Puzzle. Wasn't it easy! Have fun. I used to give this Puzzle to my children for creating an interest and familiarity with numbers in them. It worked and they are comfortable with Mathematics! Well even in old age this can provide the much needed exercise to the brain to keep it in shape, no kidding. it is true!

1 Comment:

  1. Krrish said...
    Interesting sir...

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