Friday 10 February 2012

Magic Square with numbers from 6 to 14/Strange property.

In an earlier blog I had asked readers to verify how the strange property found in the square formed with numbers from 1 to 9 could be found in other squares like that formed from numbers 6 to 14.
The rows in the square with numbers from 1 to 9 will have digits...4,9,2...3,5,7...8,1,6.The number in the first row 492 is actually  4*100+9*10+2.So the numbers in the first row of the square from digits 6 to 14 namely 9,14 and 7 can be joined using a similar method to get 9*100+14*10+7=1047.Just like 294 formed using 4,9 and 2 in the reverse direction,we can get the second  number 7*100+14*10+9=849...Similarly the numbers in the second and third rows will give us 8*100+10*10+12=912,     12*100+10*10+8=1308.....13*100+6*10+11=1371 and 11*100+6*10+13=1173.
The squares of 1047,912 and 1371 will add up to the total 3807594 ,the same relating to the squares of 849,1308 and1173.
The numbers similarly formed using the columns are 993,1506 and 831  giving the total of squares 3944646 the same like the second set of numbers formed in the reverse direction viz 1389,714 and 1227.
Only a little imagination was required to find how the same property could be found in other magic squares.


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