The magic constant of a magic square is the sum of numbers in any row, column, and diagonal of the magic square. For example, the magic square shown below has a magic constant of 15.
If a magic square of order n is normal (i.e. it contains the numbers 1 to n²), then any such sum is known as a magic series, and its magic constant depends only on n having the value
.
The magic constants of normal magic squares of order n = 3, 4, 5, … are (sequence A006003 in OEIS):
- 15, 34, 65, 111, 175, 260, 369, 505, 671, 870
The term magic constant is similarly applied to other "magic" figures such as magic stars and magic cubes.
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