Variations
A slightly more complicated variation of this method exists in which the first number is placed in the box just above the center box. The fundamental movement for filling the boxes remains up and right (↗), one step at a time. However, if a filled box is encountered, one moves vertically up two boxes instead, then continuing as before.
| Order 5 | ||||
|---|---|---|---|---|
| 23 | 6 | 19 | 2 | 15 |
| 10 | 18 | 1 | 14 | 22 |
| 17 | 5 | 13 | 21 | 9 |
| 4 | 12 | 25 | 8 | 16 |
| 11 | 24 | 7 | 20 | 3 |
Numerous variants can be obtained by simple rotations and reflections. The next square is equivalent to the above (a simple reflexion): the first number is placed in the box just below the center box. The fundamental movement for filling the boxes then becomes diagonally down and right (↘), one step at a time. If a filled box is encountered, one moves vertically down two boxes instead, then continuing as before.
| Order 5 | ||||
|---|---|---|---|---|
| 11 | 24 | 7 | 20 | 3 |
| 4 | 12 | 25 | 8 | 16 |
| 17 | 5 | 13 | 21 | 9 |
| 10 | 18 | 1 | 14 | 22 |
| 23 | 6 | 19 | 2 | 15 |
These variations, although not quite as simple as the basic Siamese method, are equivalent to the methods developed by earlier European scholars, Johann Faulhaber (1580–1635) and Claude Gaspard Bachet de Méziriac (1581–1638), and allowed to create magic squares similar to theirs.
Read more about this topic: Siamese Method
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