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Thursday, 2 February 2012

Magic Squares-3/3 cells-Hints

I had asked readers in one of my earlier blogs to frame magic squares in compliance with certain conditions.
I am giving below some hints-
It is merely necessary to replace the digits with new numbers/digits to comply with the conditions as indicated below-(The first row shows the digits 1 to 9 while the subsequent rows show the replacement values.The last column shows the totals in the case of each square formed with the replacement values)
1         2         3         4         5         6        7         8         9         15
4         5         6         7         8         9       10        11       12       24
0         2         4         6         8        10      12        14       16       24
-4      -1         2         5         8        11      14        17       20       24
20      17       14       11        8         5        2         -1       -4        24
6        6.5       7        7.5       8        8.5      9         9.5      10       24
8        9         10       11       12       13      14        15       16        36
8        7          6         5         4         3        2          1         0         12
8        6          4         2         0        -2      -4         -6       -8         0
8       10        12       14       16       18      20        22       24        48
The first 5 of the replacement values indicate that the central cell will have the number 8 giving the totals 24 in all those cases.The subsequent replacement values indicate that the digit 1 should be replaced by  8 leading to different totals based on the number/digit replacing 5.
You can similarly form different magic squares adopting some other number/digit instead of 8 adopted  in the above examples.

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