Difference between revisions of "Magic squares"
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== Definition == | == Definition == | ||
| − | A magic square is a <math>n \times n</math> grid filled in with numbers where the sum of the rows are the same, and the sum of the columns are the same. | + | A magic square is a <math>n \times n</math> grid filled in with numbers where the sum of the rows are the same, and the sum of the columns are the same. <math>n</math> is the order of the square. |
| − | A magic square can be rotated, you can add or subtract a same number to all the numbers, and it can be flipped to produce another valid magic square, | + | A magic square can be rotated, you can add or subtract a same number to all the numbers, and it can be flipped to produce another valid magic square. |
| + | |||
| + | == Number of Magic Squares == | ||
| + | |||
| + | {| class="latextable" | ||
| + | !Order !! Number of Different Magic Squares | ||
| + | |- | ||
| + | |1 || 1 | ||
| + | |- | ||
| + | |2 || 0 | ||
| + | |- | ||
| + | |3 || 1 | ||
| + | |- | ||
| + | |4 || 880 | ||
| + | |- | ||
| + | |5 || 275, 305, 224 | ||
| + | |} | ||
== Resources == | == Resources == | ||
Revision as of 09:47, 19 August 2011
Definition
A magic square is a 
grid filled in with numbers where the sum of the rows are the same, and the sum of the columns are the same. 
is the order of the square.
A magic square can be rotated, you can add or subtract a same number to all the numbers, and it can be flipped to produce another valid magic square.
Number of Magic Squares
| Order | Number of Different Magic Squares |
|---|---|
| 1 | 1 |
| 2 | 0 |
| 3 | 1 |
| 4 | 880 |
| 5 | 275, 305, 224 |
Resources
The Zen of Magic Squares, Circles, and Stars by Clifford A. Pickover
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