Associative magic square
An associative magic square is a magic square for which every pair of numbers symmetrically opposite to the center sum up to the same value.
3 × 3
The Lo Shu Square, the unique 3 × 3 normal magic square, is associative, and as such is the only 3 × 3 associative magic square. The square is shown below in Frénicle standard form. All rows, columns and diagonals sum to 15 and all pairs symmetrically opposite the center sum to 10.
2 | 7 | 6 |
9 | 5 | 1 |
4 | 3 | 8 |
4 × 4
There are 48 order four associative magic squares. [1] Dürer's associative magic square is shown below.[2]
5 × 5There are 48,544 order 5 × 5 associative magic squares.[3]
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