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.
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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