Friday, 14 October 2011

Games of Puzzle and 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:

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:
  1. Each Row should contain 1 to 9 with no repeats
  2. Each column should contain 1 to 9 with no repeats
  3. 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 Puzzle

For 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!!

1 Comment:

  1. KParthasarathi said...
    Thank you.I am a sudoku addict trying to solve atleast 3 diabolical level game daily.Thanks for the site.Do you have the online tips for solving very intricate problems?

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