Friday 9 March 2012

Magic squares-4/4 cells

I have so far dealt with 3/3 cells.
Let me now deal with 4/4 cells formed with numbers 1 to 16-
I will first show how the magic square can be formed by way of steps-
Step 1-You write down the 16 numbers in 4 rows/4 columns,starting with 16 first,and going down upto 1.
Step 2-The numbers in the 2nd and 3rd columns are now changed to read from bottom to top-viz the 2nd column will now read as 3,7,11,15 instead of 15,11,7,3.same step in 3rd column.
Step3-The numbers in the 2nd and 3rd columns are now interchanged.
Step 4-The numbers in the 2nd and 3rd rows are now altered by reading from right to left,viz for example the 2nd row will now read as 9,7,6,12 instead of 12,6,7,9 .same process 3rd row.
Step 5-The numbers in the 2nd and 3rd rows are now interchanged.
You will now find the magic square  as follows-shown in groups of each row-
(16,2,3,13)...(5,11,10,8)...(9,7,6,12)..(4,14,15,1)....The totals of each row,column and both diagonals will be 34..This is a total which is double the sum of the first and last number viz twice (1+16).
Same procedure can be followed for forming squares with any consecutive 16 numbers.
Also by taking the first 16 even numbers  or 16 odd numbers,or starting with  any even or odd number. 

No comments:

Post a Comment