magic square generator algorithm

magic square generator algorithm

Sign-up for a FREE account today!. close, link But, to get a conventional square use: How to check if an instance of 8 puzzle is solvable? In any magic square, the first number i.e. We use cookies to ensure you have the best browsing experience on our website. A magic square contains the integers from 1 to n 2. A Magic Square is a grid of numbers (N by N) in which the rows, columns, and diagonals add up to the same number.

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. http://en.wikipedia.org/wiki/Magic_square, This article is compiled by Aashish Barnwal and reviewed by GeeksforGeeks team. Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products. 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. This Demonstration shows magic squares of any order up to 14. When "show" or "quick" is activated, a backtracking algorithm will continue the search for a solution; interruption can be caused by … 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. This method only produces pan-magic squares. [2] kguler. where is a magic square of order , , , and . A magic square is an N × N grid of numbers in which the entries in each row, column and main diagonal sum to the same number (equal to N (N 2 + 1) / 2). Let this position be (i,j). You can experiment with any numbers using any strategy. Different algorithms are used to generate the magic squares, depending on whether the order is odd, singly even, or doubly even (see Details). 1. The algorithm is simple, powerful, and at your fingertips.

(Now the second swap is colored.). 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). 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.

2. Wolfram Demonstrations Project Contributed by: Shutao Tang (May 2015) (Northwestern Polytechnical University, Xi'an City, China) They have a long history, appearing in both ancient Chinese scriptures and Dark Ages Christian sculptures. If the calculated row position is -1 & calculated column position is n, the new position would be: (0, n-2). A magic square contains the integers from 1 to n^2.

Magic numbers in this sense are bad style. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. 3. ; here, "" is the equal operation yielding True or False component-wise, so that is a matrix of Boolean values. A magic square contains the integers from 1 to n^2. Different algorithms are used to generate the magic squares, depending on whether the order is odd, singly even, or doubly even (see Details). 129–132. The next number is stored at position (i-1, j+1) where we can consider each row & column as circular array i.e.

At any time, if the calculated row position becomes -1, it will wrap around to n-1.

Performance of loops (A caching question), Minimum adjacent swaps to move maximum and minimum to corners, Manacher’s Algorithm – Linear Time Longest Palindromic Substring – Part 1, Manacher’s Algorithm – Linear Time Longest Palindromic Substring – Part 2, Manacher’s Algorithm – Linear Time Longest Palindromic Substring – Part 3, Divide and Conquer Algorithm | Introduction, Multiply two integers without using multiplication, division and bitwise operators, and no loops, Number which has the maximum number of distinct prime factors in the range M to N, Given a number, find the next smallest palindrome, Find the largest multiple of 3 | Set 1 (Using Queue), Print all permutations in sorted (lexicographic) order, Measure one litre using two vessels and infinite water supply, Russian Peasant (Multiply two numbers using bitwise operators), Count all possible groups of size 2 or 3 that have sum as multiple of 3, Find Excel column name from a given column number, Calculate the angle between hour hand and minute hand, Find the smallest number whose digits multiply to a given number n, Draw a circle without floating point arithmetic. The constant sum in every row, column and diagonal is called the magic constant or magic sum, M. A Magic Square is a grid of numbers (N by N) in which the rows, columns, and diagonals add up to the same number. 1 is stored at position (n/2, n-1). 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

If $n=N^2$ the grid is complete so stop. http://demonstrations.wolfram.com/MagicSquaresForOddSinglyEvenAndDoublyEvenOrders/ The constant sum in every row, column and diagonal are called the magic constant or magic sum, M. Start in the middle of the top row, and let n = 1; Swap the values of at with the corresponding values of .

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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. http://en.wikipedia.org/wiki/Magic_square, This article is compiled by Aashish Barnwal and reviewed by GeeksforGeeks team. Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products. 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. This Demonstration shows magic squares of any order up to 14. When "show" or "quick" is activated, a backtracking algorithm will continue the search for a solution; interruption can be caused by … 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. This method only produces pan-magic squares. [2] kguler. where is a magic square of order , , , and . A magic square is an N × N grid of numbers in which the entries in each row, column and main diagonal sum to the same number (equal to N (N 2 + 1) / 2). Let this position be (i,j). You can experiment with any numbers using any strategy. Different algorithms are used to generate the magic squares, depending on whether the order is odd, singly even, or doubly even (see Details). 1. The algorithm is simple, powerful, and at your fingertips.

(Now the second swap is colored.). 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). 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.

2. Wolfram Demonstrations Project Contributed by: Shutao Tang (May 2015) (Northwestern Polytechnical University, Xi'an City, China) They have a long history, appearing in both ancient Chinese scriptures and Dark Ages Christian sculptures. If the calculated row position is -1 & calculated column position is n, the new position would be: (0, n-2). A magic square contains the integers from 1 to n^2.

Magic numbers in this sense are bad style. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. 3. ; here, "" is the equal operation yielding True or False component-wise, so that is a matrix of Boolean values. A magic square contains the integers from 1 to n^2. Different algorithms are used to generate the magic squares, depending on whether the order is odd, singly even, or doubly even (see Details). 129–132. The next number is stored at position (i-1, j+1) where we can consider each row & column as circular array i.e.

At any time, if the calculated row position becomes -1, it will wrap around to n-1.

Performance of loops (A caching question), Minimum adjacent swaps to move maximum and minimum to corners, Manacher’s Algorithm – Linear Time Longest Palindromic Substring – Part 1, Manacher’s Algorithm – Linear Time Longest Palindromic Substring – Part 2, Manacher’s Algorithm – Linear Time Longest Palindromic Substring – Part 3, Divide and Conquer Algorithm | Introduction, Multiply two integers without using multiplication, division and bitwise operators, and no loops, Number which has the maximum number of distinct prime factors in the range M to N, Given a number, find the next smallest palindrome, Find the largest multiple of 3 | Set 1 (Using Queue), Print all permutations in sorted (lexicographic) order, Measure one litre using two vessels and infinite water supply, Russian Peasant (Multiply two numbers using bitwise operators), Count all possible groups of size 2 or 3 that have sum as multiple of 3, Find Excel column name from a given column number, Calculate the angle between hour hand and minute hand, Find the smallest number whose digits multiply to a given number n, Draw a circle without floating point arithmetic. The constant sum in every row, column and diagonal is called the magic constant or magic sum, M. A Magic Square is a grid of numbers (N by N) in which the rows, columns, and diagonals add up to the same number. 1 is stored at position (n/2, n-1). 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

If $n=N^2$ the grid is complete so stop. http://demonstrations.wolfram.com/MagicSquaresForOddSinglyEvenAndDoublyEvenOrders/ The constant sum in every row, column and diagonal are called the magic constant or magic sum, M. Start in the middle of the top row, and let n = 1; Swap the values of at with the corresponding values of .

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