On the construction of even order magic squares abdullahi umar, sultan qaboos university, alkhod, p. The program should determines if the matrix is a magic square. This is a generalization of the above two transforms. Be sure to close the file stream object, in the main function, that you create to write to the file. Magic square vat, ug, shp vat ugh ship notice that 1 each side has an energy, 2 each energy is flanked by its two most important natural variables, 3 conjugate variables occupy opposite ends of each diagonal, 4 crossed arrows point upward toward v and t and away from s and p. For example, if the chosen numbers are 3, 11, and in the squares. So, in any closed knight tour magic square all the black cells, for example, contain odd numbers and all the white cells contain even numbers. An algorithm for constructing magic squares sciencedirect. A magic square is an nxn square matrix whose numbers usually integers consist of consecutive numbers arranged so that the sum of each row and column, and both long main diagonals are equal to the same sum. Also the sum of the elements in each row, column, and diagonal have the same. A magic square is a simple mathematical game developed during the 1500 square is divided into equal number of rows and columns.
A symmetric magic square is also called an associative magic square 11, p. Proofs of some properties of magic squares, as well as some descriptions of methods of constructing magic squares, depend on the use of latin squares. You have just created a magic square where the sum of the numbers in each horizontal line, each vertical line, and each main diagonal has the value of s. A magic square is an arrangement of the numbers from 1 to. The client takes the rank of the matrix as an argument on the command line. Magic square routines, puzzles and presentations, including one novel contribution by the author which combines origami the crossed box pleat with a magic square, the origami magic square eddie dawes, m. I asked this over on stack overflow and it was recommended i post it here. In this paper a generic definition for strongly magic squares is given. Some of my published papers on magic squares these papers are posted here with permission from. A magic square a of a set of magic squares g is a generator of gif. Magic squares first appeared in recorded history in ancient china.
A magic square is a square matrix of numbers with the. In 1770 leonhard euler found a magic square of order 4 filled of squares. A magic square is an nxn square matrix whose numbers usually integers consist of consecutive numbers arranged so that the sum of each row and column, and both long main diagonals are equal to the same sum which is called the magic number or magic constant. Nov 02, 2016 there are so many solutions to this problem so please dont ever think that this is the right way. A magic square is an nxn square matrix whose numbers consist of consecutive numbers arranged so that the sum of each row and column, and both diagonals are equal to the same sum which is called the magic number or magic constant a magic square of singly even order has a size that is a multiple of 4, plus 2 e. A magic square of size n is a matrix composed of distinct integers between 1 and n2 set such as the sum of any line or column are equal. These magic squares are square grids of numbers 3x3, 4x4, etc. For example, this matrix that has all four properties. Magic squares with a given total mathematics and statistics. A very curious question that has taxed the brains of many inspired me to undertake the following research that has seemed to open a new path in analysis and in particular in the area of combinatorics.
The magic square is an expandable pattern that can be built to any size, all in one round. Like the sudoku puzzle, the magic square involves recreational. Show that you can not make a 3x3 magic square using the first nine prime. We characterize the scattering data for this class and.
The only extra consideration is to include leading diagonals of each 4 x 4 subsquare. Xantcha stanleys theory of magic squares theorem 1 hilbert. Typically, an audience member is asked for a number say between 30 and 100 and the magician quickly creates a magic square and shows off the many ways that their total is obtained. A magic square is a two dimensional array n x n which contains a numerical value between the values 1 and n2 in each location. For example, a 3x3 magic square has nine cells and a normal 3x3 magic square will only contain the numbers 19 in it. One of the most notable magic squares in western civiliza. The counting is wrapped around, so that falling off the top returns on the bottom. A spectator names any two digit number between 2299 and after you fill in the 16 boxes there will be 28 possible combinations where the boxes will add up to. Pdf present paper is an important study for formulation of generalized method to construct magic squares. A double even order magic square is one whose order is divisible by 4.
The order of a transformation group t of gdenoted as tg is the cardinality of the set, i. The method we use to construct a magic square of order 8 is the same as the method used for the 4 x 4. Apr 15, 2012 the mathemagic of magic squares steven klee outline what is a magic square. This method is useful for calculating magic squares with odd order. Jan 29, 2015 a magic square is an arrangement of unrepeated integer numbers in a square grid, where the sum of numbers in each row, column, and the main and secondary diagonals, all add up to the same number. Basically, you have a matrix a square 2 dimensional array, which you have to fill in the numbers in each cell of the matrix starting from 1 so that the sum of all the numbers in each column equals. In fact, this solution isnt efficient because a lot of the calculations can be done in one go. Magic squares lia malato leite victoria jacquemin noemie boillot experimental mathematics university of luxembourg faculty of sciences, tecnology and communication. Start filling each square with the number from 1 to num where num no of rows x no of columns you can only use a number once. November 2, 20 magic square, recreational math, recreational mathematics, tutorial tutorial adminjollymathsblog. Similarly, a 4x4 magic square with 16 cells contains only the values 1 through 16, and a 5x5 magic square only contians.
Start with figure 10 and give the magic square obtained by each rotation described. Magic square is a group of cells arranged in a grid based on the given dimensions. The mathemagic of magic squares university of washington. This example demonstrates the use of a multidimensional dynamic array to hold the magic square implemented by a matrix class. The mathemagic of magic squares steven klee outline what is a magic square. To sum up, we conclude that c is a magic square of order. Given a magic square, other magic squares may be obtained by rotating the given one. C program to generate magic square c programming tutorial. The reason being called a magic square is the sum of any row or column or diagona. In this paper an example of universal hixohoxi magic square of the same order with numbers of four digits and. Clearly any magic square in that set will be again be a magic square in the set if any of the former transformations are applied. One way to generate a magic square when n is odd is to assign the integers 1 to n2 in ascending. Magic squares of odd order you are encouraged to solve this task according to the task description, using any language you may know.
Each square is divided into cells, and the rules require that the sum of any row, column or. C program to create magic number square i am a beginner programmer trying to create a program that creates a magic square where all of the rows add up to the same number depending on the number specified by the user. A, in addition to being magic, has the property that the sum of the twosymmetric magic square numbers in any two cells symmetrically placed with respect to the center cell is the same 12, p. A magic squares is an nbyn matrix of the integers 1 to n2, such that all row, column, and diagonal sums are equal. Magic squares example this example shows you how to create a client for the magic square server. There are certain types of latin squares of interest in dealing with magic. Square is divided into equal number of rows and columns. This video will show you how to make a 3x3 magic square using the basic up. Magic squares have been the subject of interest among mathematicians for several centuries because of its magical properties. In a magic square, the numbers in each row, column, and diagonal have the same sumthe magic sum. Magic square lexicon 1 to 174 references 175 the authors 1 81 magic square bibliography a11 to a115. This socalled loshuis an early example of a magic square.
Then fmplq gplq p1 lqd for some integral polynomial gplq. C program to check whether entered matrix is magic square or not. In the example each cell is identified by the letter c and a. The rst player to choose 3 numbers that add up to 15 wins.
If d 0, then a c, and the assertion is true, for fcplq 1. Judging by the given general definition of magic squares, there is no difficulty in. This particular type of magic square is called the gnomon magic square. Abstractin recreational mathematics, a normal magic square is an n. A magic square is any n x n array of numbers where each of the n2 elements appears only once. Franklin squares a chapter in the scientific studies of magical. Actually pretty excited i go this problem solved in under 2 hours. The numbers are usually but not always the first n 2 positive integers. For example, starting with the magic square in figure 10, a 90 rotation in a clockwise direction gives the magic square shown here.
In a true magic square, the diagonals also have that same. The constant sum in every row, column and diagonal is called the magic constant or magic sum, m. The magic square is then generated and displayed in tabular format on the screen and written to the ouput file. The mathematician may be pleased to learn that the truncated rhombohedron in the background has come to be known as durers solid, and its graph of vertices and edges as the durer graph. Magic squares are one of the simplest forms of logic puzzles, and a great introduction to problem solving techniques beyond traditional arithmetic algorithms. Investigations on a new type of magic square leonhard euler translation by andie ho and dominic klyve1 1. A magic square is a simple mathematical game developed during the 1500. A magic square is any n x n array of numbers where each of the n2 elements appears only. I have changed my presentation of algorithms to construct magic squares,because its really hard to show all aspects as html pages. One such example is a method of constructing a pandiagonal magic square of order 8 given later in this chapter. A magic square is a square matrix of numbers with the property that the sums along rows, columns, and main diagonals are all equal to s which is called the magic sum.
An nbyn magic square is an array containing the integers from 1 to n2. B we note that if a and b are magic squares, then each c i j in is also a magic square. One such example of magic in numbers is the concept of a magic square. But its absolutely clear that all existing pages, especially all interactive pages, remain. This means that the subsquares have an odd size, which plays a. In the present talk, the history of magic squares will be discussed in. A latin square is a matrix of numbers or letters or different colors with the. For a 3x3, 4x4, 5x5, 6x6, 7x7, 8x8, 9 x 9, and 10 x 10 magic squares the sum of the.
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. Magic squares what you see here is a magic square, much like the addition and subtraction squares you may have used as a child. Magic squares with a given total many magicians, including the authors of this paper, create magic squares as parts of their shows. It begins by placing a 1 in any location in the center square of the top row in the above example, then incrementally placing subsequent numbers in the square one unit above and to the right. This video will show you how to make a 3x3 magic square using the basic upone, rightone method. My solution works but it feels incredibly convoluted. Im still teaching myself c out of kn kings c programming. A magic square is an arrangement of the numbers from 1 to in. A magic square is an arrangement of the integers from 1 to m 2 in an mxm matrix, with. History of magic squares mathematics and magic squares constructing magic squares magic circles warmup the 15 game players take turns choosing numbers between 1 and 9, without repeats.
A magic square is an arrangement of unrepeated integer numbers in a square grid, where the sum of numbers in each row, column, and the main and secondary diagonals, all add up to the same number. I need help debugging and finishing a program that would. Interesting, because most of the 3x3 squares with 7 correct sums come from the lucas family, in which the magic sum is a square. Suppose now that a is generated by d elements of degree 1, among which is a. On the construction of even order magic squares arxiv. The strongly magic square is a magic square with a stronger property that the sum of the entries of the subsquares taken without any gaps between the rows or columns is also the magic constant. Magic squares and modular arithmetic jim carlson november 7, 2001 1 introduction recall that a magic square is a square array of consecutive distinct numbers such that all row and column sums and are the same. Let a be generated by d elements of degree 1, and let m be a module. C programming tutorial, learn c programming, c aptitude question answers, c interview questions with answers, c programs, find all basic as well as complex c programs with output and proper explanation making c language easy and interesting for you to learn. So i will publish these algorithms as pdf documents. A magic square is considered normal if the square contains numbers that are the smallest possible values.
375 662 18 1342 515 1442 713 4 577 885 766 182 1591 529 1120 1319 1229 72 1486 14 698 1457 599 42 699 1359 1224 693 1359 1433 1612 626 99 782 64 613 651 92 1430 345