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:
- Begin at the Top row middle square always.
- When at the top, drop down to the bottom row in next column.
- Where vacant keep ascending the diagonal to the right.
- When blocked at the side, go to upper row extreme left column.
- 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 .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!
Magic Squares of Even Numbers
Magic Squares of Even Numbers
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.
SU-DO-KU Challenge - Preamble
When I first came across this puzzle 2 years ago I casually started solving them and slowly it began to attract me more and more with challenges to solve higher difficulty level puzzles. The solution does not require any technical expertise or any mathematical knowledge. With concentration. Logic and some quick reflexes one can solve almost all the puzzles unless of course the Author deliberately gives lesser numbers than required to make it more challenging etc. Now let us get on with the Game:
Have a look at the picture above. You can see an empty Grid with 81 squares and a Solved Sample SU-DO-KU. The Author of the puzzle fills certain squares of the grid himself and you have to complete filling the rest of the empty squares adhering to some rules of the Game. The rules are as follows:
- Each Row should contain 1 to 9 with no repeats
- Each column should contain 1 to 9 with no repeats
- There are 9 Mini Squares within the Main Square with 3 Rows&3 Colums each. They should get filled up with numbers 1 to 9 with no repeats.
Looks simple right! The challenge is the third requirement of mini squares. Ready, Go!
Our PuzzleFor starters let us take an easy one. See the Puzzle on the left. We have to solve this. You can see some squares are filled already. To identify them they are in RED. I am sure it looks difficult and has more than 1 choice for each square. Relax, let us use our logic and the facts we know. Sice no rows or columns can have duplicate numbers let us look for common numbers in rows or colums. Number 6 appears in top 2 rows and 8th row column 5. Now the top middle mini square (Row 1,2,3 Col 4,5,6) cannot have 6 in the first row, second row or 5th col in 3rd row because these rows and column already have 6 in them which leaves only 3rd row 6th column for 6.("A") Presto you got 1.
Do a similar exercise with columns 4,5,6 for number 5 and you will get row 5,col 5 as the place for number 5.("B") Another trick is take rows 4,5,6 and check for 1. 5th row col 2 has 1 so you cannot have 1 in the cols 1 and 3 above. Similarly there is 1 in Row 6,col 8 and hence you cannot have 1 in col 7,8,9 of Row 4. So 1 can fit in Row 4,Col 4 only.("C")
Just by checking for missing numbers in a Row or column with available numbers you can find the numbers you need. If you are too tired to complete or just curious see the completed Puzzle below.
For the Die-Hard SU-DO-KU fans plenty of puzzles, with solutions (lol!), are available at online websites. To see them clik HERE. We shall look at "Magic Squares" in my next article. See you Guys!!
Wednesday, 5 October 2011
My All-time favourites
Written for Reel-life Bloggers contest Wogma
1. Gandhi - English Version
Even as a school boy I was deeply attracted towards the Great Mahatma and read a lot about him. I was impressed by his unique brand of fight against the Mighty British, his enchanting charisma and his witty remarks. When the movie Gandhi, with Ben Kingsley doing the lead, was released I was very eager to watch the movie. The role of Gandhi was played so well by Ben Kingsley and his striking resemblance to the Mahatma added more fervor. The scene when Gandhi tells Om Puri to adopt a child, especially a Muslim one, and raise him as a Muslim takes the Cake!
2. Step Mom
Julia Roberts has always been my favourite actress for a long time. Her performances in "Erin Brokovic" and "Pretty Woman" were of very high standard and fetched her the coveted Oscar! In Step Mom she did the role of a professional photographer in love with a divorcee with two children and the stress of endearing herself to the kids. She carried the burden with aplomb and I still remember the scene in which she tells the mother of the kids, Susan Sarandon, about her fears that the girl might still be thinking about her mother on her wedding day to which Susan replies that she is afraid that she may not be thinking that way! An emotional and sentimental scene not usually seen in an English Movie.
3. Erin Brokovic
Playing the role of a mundane activist would deter the strongest of actors from accepting the role. Not Julia Roberts. She not only accepts the challenge but goes on to win an Oscar for her role in that movie.It was made as close to the original events as possible that it had the credibility and ready acceptance of the viewers. Alfred Finney as the Lawyer who employs Julia was brilliant too in his role. His humour and affection for her was beautifully picturised throughout. One scene, towards the end, when he goes to her office to handover her cheque for handling the case, was the icing on the cake. He remarks after surprising her with a generous bonus amount. "Do they teach the Beauty Queens how to apologise?, because you suck at it!". A movie I wouldn't mind seeing again.
Written for Reel-life Bloggers contest Wogma
Sunday, 2 October 2011
Falling in Love!
Adolescence plays such an important role in the life of a person that it could make a difference between a well planned life and a frustrated one. The ability of the person to handle this delicate period decides how successful he / she will be in the adult life. This period relates to the span of time between the time of Puberty and the Maturity. With the changes that take place in the body and the brain due to hormonal effects can really influence a person’s behaviour. Examples of such behaviour can be that of youngsters who get infatuated with their favourite Film Hero / Heroine and keep carrying their pictures with stars in their eyes! They are too immature to know the difference between “Infatuation” and “Love”. The momentary crush due to physical attraction is often misinterpreted as Love.The Role of Parent
The parents have a very important role to play in this regard. When their children attain puberty and are in their adolescence, it is vital for them to discuss about sex, relationships etc with the children in a free and frank manner. This would provide the much needed opportunity for the children to open up with their doubts and feelings without any inhibition. Unless your child feels free to discus with you about anything that is bothering him / her you are failing in your duty of creating the much needed trust.
A parent has to explain detail about the feeling of Love, what it entails and how it builds mutual bond of friendship, affection and respect. They should be advised about letting it mature into a deep bond of relationship before resorting to any physical form of committing to each other. They have to be counseled on the need for compatibility on many things besides just emotion, like education, financial stability, social and economical issues etc. Hasty decisions based on perceived Love often result in unsatisfactory marriages and lead to separation eventually.Practical Situation
I know of a friend whose daughter fell in love with a boy and wanted to marry him. When she told her parents about the same the parents were taken aback. The girl had just completed her graduation and was looking for a job and she had met this boy at the “Employment Registration” office. The parents acted in a very structured manner. They called her for a detailed discussion. They asked her whether she knows all the details about him and if he is in a position to support her and maintain an independent Family. She said that he was an Engineering Graduate looking for a job and has passed with distinction. His parents are school teachers. They asked her to invite the boy to their house for Tea. When the Boy came home they were happy to see a well mannered, handsome young man . The boy spoke of his ambitions to become a scientist in Rocket Propulsion and help the country in exploring the space. He also said that he loved the girl very much and would like to get engaged to her for eventual marriage to be done after he settles into a permanent Job of his dreams. He had also spoken to his own parents about his decision and they were keen to meet the girl’s family. Hearing this, the girl’s parents knew that the boy is very matured and well balanced man and a suitable match for their child. This is the way an adolescent should approach this issue, in my opinion.