|
|
|
Revision difference : magic square |
| Version current |
Version 1 |
| A magic square of order $n$ is an $n\times n$ array using each one of the numbers $1,2,3,\ldots,n^2$ once and such that the sum of the numbers in each row, column or main diagonal is the same. |
A magic square of order $n$ is an $n\times n$ array using each one of the numbers $1,2,3,\ldots,n^2$ once and such that the sum of the numbers in each row, column or main diagonal is the same. |
|
|
| Example: |
Example: |
| \begin{equation*} |
\begin{equation*} |
| \begin{pmatrix} |
\begin{pmatrix} |
| 8 & 1 & 6\\ |
8 & 1 & 6\\ |
| 3 & 5 & 7\\ |
3 & 5 & 7\\ |
| 4 & 9 & 2 |
4 & 9 & 2 |
| \end{pmatrix} |
\end{pmatrix} |
| \end{equation*} |
\end{equation*} |
|
|
| It's easy to prove that the sum is always $\frac{1}{2}n(n^2+1)$. So in the example with $n=3$ the sum is always $\frac{1}{2}(3\times 10)=15$. |
It's easy to prove that the sum is always $\frac{1}{2}n(n^2+1)$. So in the example with $n=3$ the sum is always $\frac{1}{2}(3\times 10)=15$. |
|
|
| One way to generalize this concept is to allow any numbers in the entries, instead of $1,2,\ldots,n$. |
|
|
|
|
|
