magic square generator algorithm
This Demonstration shows magic squares of any order up to 14. Writing code in comment? The elements in where is True are reversed; that is, at such a position with value , the new value is . where is a magic square of order , , , and . 1 is stored at position (n/2, n-1). Try both methods: By moving your Mouse over a Blue Arrow and waiting, you can observe the numbers in the Magic Square. The constant sum in every row, column and diagonal is 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: Don’t stop learning now. In any magic square, the first number i.e. The horizontal and vertical totals are to the right and below in green squares. Different algorithms are used to generate the magic squares, depending on whether the order is odd, singly even, or doubly even (see Details). Put numbers in the top set of squares and click on "Make Square". Move diagonally up and right, wrapping to the first column or last row if the move leads outside the grid. zeros (( N , N ), dtype = int ) n = 1 i , j = 0 , N // 2 while n <= N ** 2 : magic_square [ i , j ] = n n += 1 newi , newj = ( i - 1 ) % N , ( j + 1 ) % N if magic_square [ newi , newj ]: i += 1 else : i , j = newi , newj print ( magic_square ) N must be odd. http://demonstrations.wolfram.com/MagicSquaresForOddSinglyEvenAndDoublyEvenOrders/ 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. Shutao Tang and is attributed to GeeksforGeeks.org, Analysis of Algorithms | Set 1 (Asymptotic Analysis), Analysis of Algorithms | Set 2 (Worst, Average and Best Cases), Analysis of Algorithms | Set 3 (Asymptotic Notations), Analysis of algorithms | little o and little omega notations, Analysis of Algorithms | Set 4 (Analysis of Loops), Analysis of Algorithm | Set 4 (Solving Recurrences), Analysis of Algorithm | Set 5 (Amortized Analysis Introduction). www.mathworks.com/moler/exm. code, NOTE: This approach works only for odd values of n.References: http://en.wikipedia.org/wiki/Magic_squareThis article is compiled by Aashish Barnwal and reviewed by GeeksforGeeks team. Start in the middle of the top row, and let n = 1; Powered by WOLFRAM TECHNOLOGIES N must be odd. In the box below, enter an odd number and click the "create" button to see a magic square of the chosen dimensions. You can make your own Magic Square in two ways. 2) All numbers are then placed one column to … import numpy as np N = 5 magic_square = np . The constant sum in every row, column and diagonal are called the magic constant or magic sum, M. 1. Given n appointments, find all conflicting appointments, Check a given sentence for a given set of simple grammer rules, Find Index of 0 to be replaced with 1 to get longest continuous sequence of 1s in a binary array. Attention reader! 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I am doing it this way in JavaScript, but what is the optimal way of generating all of them? acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Check given matrix is magic square or not, Count sub-matrices having sum divisible ‘k’, Count all sub-arrays having sum divisible by k, Print array elements that are divisible by at-least one other, Find an array element such that all elements are divisible by it, Find k maximum elements of array in original order, Maximum in array which is at-least twice of other elements, Maximum difference between groups of size two, Minimum difference between groups of size two, Largest palindromic number by permuting digits, Minimum Fibonacci terms with sum equal to K, Bell Numbers (Number of ways to Partition a Set), Write a program to print all permutations of a given string, Set in C++ Standard Template Library (STL), http://en.wikipedia.org/wiki/Magic_square, Minimum cost to convert 3 X 3 matrix into magic square, Minimum changes needed to make a 3*3 matrix magic square, Count square and non-square numbers before n, Check if a number is perfect square without finding square root, Smallest N digit number whose sum of square of digits is a Perfect Square, Find smallest perfect square number A such that N + A is also a perfect square number, Check if a number is a perfect square having all its digits as a perfect square, Check if a number is magic (Recursive sum of digits is 1), Find minimum number to be divided to make a number a perfect square, Maximum size square sub-matrix with all 1s, Given an n x n square matrix, find sum of all sub-squares of size k x k, Program to find GCD or HCF of two numbers, Efficient program to print all prime factors of a given number, Program to find largest element in an array, Write Interview 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. the magic square, as an engine to generate fine-art by designing representation schemes, which will transform the inherent mathematical order of magic squares into images. This method only produces pan-magic squares. 1. 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. 2. 32 of these are "panmagic" magic squares with the additional property Try both methods: Enter your own numbers into the Red Squares and then click on "Add Rows". 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. Recently an algorithm was developed that allowed the automatic generation of any magic square of odd-numbered dimensions. If you try this method try any numbers you like. 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 . Sign-up for a FREE account today!. A magic square contains the integers from 1 to n^2.

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