Types and Construction
There are many ways to construct magic squares, but the standard (and most simple) way is to follow certain configurations/formulas which generate regular patterns. Magic squares exist for all values of n, with only one exception: it is impossible to construct a magic square of order 2. Magic squares can be classified into three types: odd, doubly even (n divisible by four) and singly even (n even, but not divisible by four). Odd and doubly even magic squares are easy to generate; the construction of singly even magic squares is more difficult but several methods exist, including the LUX method for magic squares (due to John Horton Conway) and the Strachey method for magic squares.
Group theory was also used for constructing new magic squares of a given order from one of them, please see.
| How many n×n magic squares for n>5? |
The number of different n×n magic squares for n from 1 to 5, not counting rotations and reflections:
- 1, 0, 1, 880, 275305224 (sequence A006052 in OEIS).
The number for n = 6 has been estimated to 1.7745×1019.
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