It is straightforward to compute the magic constant
M of a standard n × n magic square. Adding the entries
in each row produces the magic constant M and, as
there are n rows, the quantity nM must equal the sum
of all the entries in the table. Thus, as the SUMS OF
POWERS formulae show:
yielding:
For n = 1, 2, 3, 4, 5, … this gives the sequence of values 1,5,15,34,65,…
M
nn
=
+
1
2
1
2
(
)
nM
n
n n
= + + + +
=
+
1 2 3
1
2
2
2 2
L
(
)
27 29 2
4 13 36
9 11 20 22 31 18
32 25 7
3 21 23
14 16 34 30 12 5
28 6 15 17 26 19
1 24 33 35 8 10
326 magic square
Taken from an 18th-century blockbook version of the Book of Changes, or the I Ching, the left diagram depicts the Lho shu magic square.
(Photo courtesy of C. Walker/Topham/The Image Works)
M of a standard n × n magic square. Adding the entries
in each row produces the magic constant M and, as
there are n rows, the quantity nM must equal the sum
of all the entries in the table. Thus, as the SUMS OF
POWERS formulae show:
yielding:
For n = 1, 2, 3, 4, 5, … this gives the sequence of values 1,5,15,34,65,…
M
nn
=
+
1
2
1
2
(
)
nM
n
n n
= + + + +
=
+
1 2 3
1
2
2
2 2
L
(
)
27 29 2
4 13 36
9 11 20 22 31 18
32 25 7
3 21 23
14 16 34 30 12 5
28 6 15 17 26 19
1 24 33 35 8 10
326 magic square
Taken from an 18th-century blockbook version of the Book of Changes, or the I Ching, the left diagram depicts the Lho shu magic square.
(Photo courtesy of C. Walker/Topham/The Image Works)