Different algorithms are used to generate the magic squares, depending on whether the order is odd, singly even, or doubly even (see Details). Magic numbers in this sense are bad style. © Wolfram Demonstrations Project & Contributors | Terms of Use | Privacy Policy | RSS 2. I am doing it this way in JavaScript, but what is the optimal way of generating all of them? Writing code in comment?

Sign-up for a FREE account today!. Based on the above approach, the following is the working code: edit The numbers in the Red Squares form the 3x3 magic Square. 3.

Try both methods: By moving your Mouse over a Blue Arrow and waiting, you can observe the numbers in the Magic Square.

they wrap around. In this post, we will discuss how programmatically we can generate a magic square of size n. Before we go further, consider the below examples: Did you find any pattern in which the numbers are stored? Please use ide.geeksforgeeks.org, generate link and share the link here. Contributed by: Shutao Tang (May 2015) (Northwestern Polytechnical University, Xi'an City, China) Experience. N must be odd. 1.

Take advantage of the Wolfram Notebook Emebedder for the recommended user experience. Enter your own numbers into the Red Squares and then click on "Add Rows". The position of next number is calculated by decrementing row number of the previous number by 1, and incrementing the column number of the previous number by 1. A magic square contains the integers from 1 to n^2. This Demonstration shows magic squares of any order up to 14. By using our site, you Rotation, reflection, and translocation provides 128 variations for each of these fundamenstal squares for a grand total of 384. Swap the values of at with the corresponding values of . # Create an N x N magic square. Mathematica Stack Exchange. Similarly, if the calculated column position becomes n, it will wrap around to 0.2. A magic square is a square array of the numbers 1, 2, …, arranged so that the sum of the numbers in a row, column, or either main diagonal is constant. Wolfram Demonstrations Project The algorithm is simple, powerful, and at your fingertips. This reveals the underlying structure of a 4x4 Pan-Magic Square - one in which all of the diagonals are magic. is divisible by 2 but not by 4). If is singly even, then is odd, and a magic square of order can be constructed from four copies of the magic square of order . Let this position be (i,j). brightness_4 Tool to generate magic squares size N, kind of matrices composed of distinct integers set such as the sum of any line or column are equal. You can experiment with any numbers using any strategy. Attention reader! At any time, if the calculated row position becomes -1, it will wrap around to n-1. The constant sum in every row, column and diagonal are called the magic constant or magic sum, M. The magic constant of a normal magic square depends only on n and has the following value: M = n(n2+1)/2. A Magic square is an n-by-n two-dimensional matrix of numbers from 1 to n^2 such that the sum of the values in each row, column, and long diagonals are the same. I am following these steps: 1) The number '1' goes in the middle of the top row. If the magic square already contains a number at the calculated position, calculated column position will be decremented by 2, and calculated row position will be incremented by 1.3. N must be odd. Define to be a matrix of the integers from 1 to , stored sequentially in rows. close, link If this cell is already filled, move vertically down one space instead; The following program creates and displays a magic square.

If you try putting in your own numbers you may succeed in making a magic square which is magic but where only main diagonals are magic. A magic square contains the integers from 1 to n^2. A magic square of size 6 x 6 is to be constructed, (with additional properties: nine of the 2x2 subsquares have equal sums and the inner 4x4 subsquare is pandiagonal). A magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. (Apr 23, 2015) mathematica.stackexchange.com/questions/80674/better-method-to-swap-the-values-of-two-2-d-arrays/80680#80680. Contributed by: Shutao Tang (May 2015) (Northwestern Polytechnical University, Xi'an City, China) Open content licensed under CC BY-NC-SA How to check if two given sets are disjoint? Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products. A Magic Square is a grid of numbers (N by N) in which the rows, columns, and diagonals add up to the same number. This Demonstration shows magic squares of any order up to 14. M = n(n^2+1)/2.

Start in the middle of the top row, and let $n=1$; Step 2. A magic square of order n is an arrangement of n^2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. Flood fill Algorithm – how to implement fill() in paint?

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