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 10:47, 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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