The math behind the Siamese method of generating magic squares. Subtraction Grids. The Yuxin Little Magic Square-1 M is a budget friendly, fully magnetic square-1 containing 28 lite magnets. A magic square consists of the distinct positive integers 1, 2, n 2, such that the sum of the n numbers in any horizontal, vertical, or main diagonal line is always the same magic constant. The sum of the integers from 1 to N is given by the well-known formula N(N+1)/2. It is known as the Chautisa Yantra since its magic sum is 34. In a traditional n by n magic square, the array is filled with the integers from 1 through N, where N is clearly equal to n 2. exe" available, which produces all reduced 5x5 magic squares; moreover, the user may prescribe fixed entries. He called his 16×16 magic square (shown below) the 'most magically magical of any magic square ever made by a magician. In a magic square the sum of the numbers in each row, each column and along the diagonals is the same. In fact the first three rows sum to 84 and the last three sum to 138. Each square contains the numbers 0 thru 15, and each row, column, and diagonal should add up to 30. This is because singly even (4n+2) order and doubly even(4n) order magic squares work differently. Add down and across. I think the same method will work in the 4-by-4 situation. Create a two-dimensional array of size n. This square became known as the One can lo-shu magic square. 21 20 19 25 10 15 14 22 17 13 9 12 11 16 18 24 23 5 by 5 Magic Square: Use each of 1,2,3,4,5,6,7,8 once, so rows, columns and diagonals have the same sum. , from all positions of the counting process, the sum has to be the same, which is 15. Returns true if and only if the square is a Magic Square. Place numbers in the grid such that every row, column and 3x3 box contain the numbers 1 to 9. In this paper a generic definition for Strongly Magic Squares is given. 6 x 6 magic square- 4 36 29 13 18 11 30 5 34 12 14 16 8 28 33 17 10 15 31 9 2 22 27 20 3 32 7 21 23 25 35 1 6 26 19 24 One can also extend the above derivation for a 6 x 6 magic square to the higher values n=12, 24, 48,. Sum = 15 One of the possible solutions A magic square of size nXn is an arrangement of numbers from 1 to n 2 such that the sum of the numbers in each row, column and diagonal is the same. Generally, we call the n×n magic square matrix as an n class magic square. Magic square. Published February 2000,July 2007,August 2007,February 2011. The sum of H and J equals D. A double even order magic square is one whose order is divisible by 4. In an order-4, regular magic (or regmagic) square, all pairs of elements that are symmetric with respect to its center sum to m / 2. Since the numbers of every row of a magic square M sum up to S M and the sum over all rows is the sum 1 + 2+ 3 + +n2 = 1 2 n2( + 1), we know that S M has to be one -th of this total. I know that the so called magic constant has to be 15, so 5 have to be placed in the middle, which reduces the combinations to 8! = 40. )” A proof is furnished for the. In order to create a Magic Square, you should use this algorithm: Create an integer value n = size of the Magic Square. The Yuxin Little Magic Square-1 M is a budget friendly, fully magnetic square-1 containing 28 lite magnets. Find 21 different ways to earn a level 2 trophy. Students are likely to use a 'Trial and Improvement' strategy to complete the magic squares. com) Interesting artwork containing a variety of Magic Squares even 6 x 6, 7 x 7, and 9. k=1 k=1 Multiplicative magic squares 3 Then clearly [m;; ] is an MMS. Lo Shu is part of the legacy of the most ancient Chinese mathematical and divinatory (Yi Jing) traditions, and is an important emblem in Feng Shui (translate as 'wind-water'), the art of geomancy concerned with the placement of objects in relation. If the Lo Shu is considered a matrix and is muliplied by itself three times, a new magic square is formed. This also means that the sum of the columns and the diagonals is also 15. hat contains each of the numbers 1, 2, 3, , n2 exactly once and has the sum of the numbers in each of its rows, columns and diagonals equal to the same thing. com) A good introduction to Dürer’s 4 x 4 Magic Square – includes video explanation of many ways to get 34, the magic sum of a 4 x 4 magic square. Magic Squares To create a “Magic Square” you must begin by choosing 9 numbers to put in your 3x3 matrix. Share Video. This is not possible since we are using the numbers 1 to 9. The strongly magic square is a magic square with a stronger property that the sum of the entries of the sub-squares taken without any gaps between the rows or columns is also the magic constant. A method for constructing magic squares of odd order was published by the French diplomat de la Loubère in his book A new historical relation of the kingdom of Siam (Du Royaume de Siam, 1693), under the chapter entitled The problem of the magical square according to the Indians. Odd Magic Square: 5 x 5 It's Magic Sum is: 65 17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9 Odd Magic Square: 7 x 7 It's Magic Sum is: 175 30 39 48 1 10 19 28 38 47 7 9 18 27 29 46 6 8 17 26 35 37 5 14 16 25 34 36 45 13 15 24 33 42 44 4 21 23 32 41 43 3 12 22 31 40 49 2 11 20. I don't know whether you got the value for the common sum in your magic square, but for the 3 by 3 square the sum is 15. Finally, the result can be written in …. Backtracking Algorithm A backtracking. 4 Sum = 12 There are 6 distinct magic square for this case (with a total of 25 if reﬂected squares are counted as diﬀerent): 174 741 417 255 741 336 264 642 426 345 642 345 354 543 435 444 444 444 (7) 2. The three rows, the three columns and the two diagonals of the magic square sum to 15. A magic square is a square array of numbers with the property that the sum of the numbers in each row, column and diagonal is the same, known as the “magic sum”. 3 by 3 = 45, 5 by 5 = 325, 7 by 7 = 1225, And then divide sum by the total number of squares in the Magic Square. We hope that you find exactly what you need for your home or classroom!. Magic Sum Formula If a magic square of order n has entries then the magic sum MS is given by the formula MS n n2 1 2. ; All pairs of integers distant n/2 along any diagonal (major or broken) are complementary (i. He is renowned for his works on subjects such as Multiplication Tables and the theorem bearing his name, Pythagoras' theorem, which still forms part of the foundations of today's Mathematical Sciences. This gives us perfect square sum magic squares. Any half-row or half-column in this square totals 130, and the four corners plus the middle total 260. Also includes Benjamin Franklin magic square for kids. 4 15 14 1 n 4 magic sum 34 The magic sum of an n-th order magic square is 1 n is a magic square of order mn and magic sum n2 mn2 m. The sum of the numbers in each row, column and both diagonals total 15. Thanks Hi, I'll show you a method to construct a 3x3 magic square that should work for 4x4 and 5x5 squares. The ‘order’ is the number of rows and columns, so a magic square of order 4 means it has 4 rows and 4 columns. In the magic square shown, the sums of the numbers in each row, column, and diagonal are the same. An n×n magic square with line sum r is an n×n matrix of nonnegative integers for which every row and column sums to r. Each cell in a nXn grid has a different number and the numbers range from 1 to n 2. Magical Magic Squares of Some Advanced Age (longstreet. Create a 3-by-3 magic square such that, the sum of the most cell combinations equals 15. It is true so far from 3-by-3 to 253-by-253 magic squares. It’s a Magic Square. Find 14 different ways of making 34 will earn you a level 1 trophy. Number Puzzle with Digits 1-9 in a 3 by 3 Grid Date: 10/09/2006 at 19:50:55 From: Mike Subject: Math Puzzle In a 3 cell by 3 cell grid, use the digits 1 through 9 to fill in the cells so each horizontal, vertical, and diagonal row of three has a sum of 15. Magic Squares are great and can be used in applications for every grade level. The sum of H and J equals D. In a magic square the sum of the numbers in each row, each column and along the diagonals is the same. Since the constant-sum squares constructed in this paper are all normal, the factorizaton method is applicable for any order n > 2. 5x5 magic square with sum 65 of planet mars. Example 1:. e, square) matrix of numbers containing all numbers from 1 to n2 such that all the numbers in any given row, column, or main diagonal sum to the same number. A domino magic square is deﬁned using a set of dominoes to form a magic square, each domino supplying two numbers. ) In a general magic square of order n, the magic sum S to which the numbers in any. The goal of this game is to find the missing number so that the square is magic. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1. In this magic square, the sum of the rows, sum of the columns, and sum of the diagonals have to equal 15, and each number 1-9 can only occur once in the square. The numbers of the central 3x3 grid in the above 21x21 magic square can be reduced to their Pythagorean root numbers to generate the classic 3x3 Luo Shu magic square. The Magic Square, Level 5 shows why three times the centre number is equal to the sum of the magic square. It is named "magic square" and they are very well investigated. Magic square python I’m coding a program that reads a line in a file and determines whether or not the line makes a Lo Shu Magic square. All columns and rows add up to 15. If we use this formula for that example output which is below, for [5x5] matrix; 5 [ ( 52 + 1 ) / 2 ] = 65. The sum across should equal the sum down. In magic square theory, all of these are generally deemed equivalent and the eight such squares are said to make up a single equivalence class. The resulting magic square (Fig. Maths Game: 6-11 year olds. Magic Squares: Decimals Materials: Magic Squares: Decimals cards _____ 1. public boolean isMagic {boolean isMagic = false; /** Add up each column, add up each row, and the diagonals. NET examples used for Magic Square - Iterative Algorithm. If the numbers from 1 to 16 are used then the sum for each row, column and diagonal should be 34. Given, semifilled 5 x 5 - Magic square is Here is the solution to the given magic square… But, unfortunately I got semi magic square of the same. 2 7 6 9 5 1 4 3 8 There are three types of magic squares: 1) M is an odd number (1, 3, 5, 7, etc. 320 a lot better. Whether you're seeking an introduction to magic squares, an in-depth study, some historical information, or just some enjoyable magic figure problems, tricks, properties, or novelties. You can also achieve 15, if you add the middle number 5 three times. The constant sum in every row, column and diagonal is called the magic constant and has the value ! M= n(n2+1) 2. Already by order six they have become uncountable, and as a result only statistical estimates are then possible. Question : Rearrange the numbers 13 to 21 such that the sum of. These pages attempt to show the complete list of 4x4 magic squares. Choose a matrix size (i. 7040/8=880. 5x5 Magic Square Help!? I have to do a work sheet and it has clues to complete this magic square. If empty fill next number. sum(M) ans = 1×3 15 15 15 sum(M,2) ans = 3×1 15 15 15 Magic Square Visualization. I have tried brute force algorithm but it is consuming too much time. Another fact is the smallest order of a bimagic square is 8. Magic Squares date back over 4,000 years to ancient China and have existed throughout history and in many different parts of the world. complete); Doubly-even pandiagonal normal magic squares (i. The sum of numbers in any row Vector glowing magic square frame black friday sale. About this resource. SWB introduced to the ideas of using variables and thinking algebraically. In other words, the winning solution would be the one that provides the highest count of unique cell combinations, the sum of the cells within each combination equals 15. A magic square is a square array of numbers with the property that the sum of the numbers in each row, column and diagonal is the same, known as the "magic sum". Generally a 3 x 3 Magic square is filled with numbers 1 to 9 ( 9 = 3 x 3), a 4 x 4 magic square with 1 to 16 ( 16 = 4 x 4 ) and a 5 x 5 magic square with 1 to 25 etc. sum(diag(X)) is the trace of X. 21 20 19 25 10 15 14 22 17 13 9 12 11 16 18 24 23 5 by 5 Magic Square: Use each of 1,2,3,4,5,6,7,8 once, so rows, columns and diagonals have the same sum. simply ensure that all rows, columns and diagonals sum to 15. Here, the sum of the numbers in each row = sum of the numbers in each column = the sum of the numbers in each diagonal = 15. 5x5 Magic Square Help!? I have to do a work sheet and it has clues to complete this magic square. Magic squares of order 3 through 8 are shown above. Our proof in Section 2 depends in part on RC-magic squares that are also transversal. how to fill a square of 5x5 cells using numbers 1 to 25 at once so that sum of each row and column and diagonal being equal. And the sum of the elements in each row, obtained by transposing twice, is the same. In the magic square shown, the sums of the numbers in each row, column, and diagonal are the same. A magic square is a square grid of numbers, in which each number appears once and the numbers in each row, column, and the two main diagonals sum to the same value. For m=6 and S=18, we have the following magic square in which A is minimum 2 9 7 11 6 1 5 3 10; As S=3*m, the average value of the terms of the square is always equal to m. Tes Classic Free Licence. A magic square is a quadratic scheme of numbers which adds up vertically, horizontally and diagonally to the same sum. The following VB. n (n) 3 15 4 34 5 65 6 111 7 175 8 260 You can compute (n. Macau's magic square stamps just made philately even more nerdy they sum to 15 also. Choose a matrix size (i. A magic square of singly even order has a size that is a multiple of 4, plus 2 (e. These 4 puzzle pieces can also be formed into a square. Fun: Difficulty: Puzzle ID: #21793 Submitted By: Jacoby. Deb Russell is a school principal and teacher with over 25 years of experience teaching mathematics at all levels. -The number being repeated the most should be in the middle. The simplest magic square is the 1x1 magic square whose only entry is the number 1. Now the 5X5 magic square is filled, and you can create another magic square with an odd number of cells on each side by the same method. (This number is well known since 1973, found by R. A square of size nxn will by filled by numbers from 1 to n 2. A magic square of order n is an arrangement of n × n 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 (see Wikipedia:Magic Square). With this square we have a lot more magic than in foregoing 12×12 square: 16 semi-magic 4×4 units more! Relative to the well-known Morris 12×12 and the HSA 12×12, this abundance of panmagic and semi-magic subsquares is quite an extra panmagic quality; on the other hand, the square lacks the constant sum of franklin-diagonals*. that is: 1) The dimensions of s is nxn 2) Every integer in [1,2,,n*n] appears in s, exactly once. By the way, the old Chinese way of representing numbers was with knots on a string. Play this puzzle with friends or students. The famous Loh-Shu (scroll of the river Loh) from 2800 BC is the oldest magic square. In a first level it must find the solution that should be equal to 15 in 3 columns 3 rows and the two diagonals the sum automatically makes the number blocked to use another time if the solution is to find the user passed to another level more difficult. Each row and column of the magic square contains three numbers. Similarly, a 4x4 magic square with 16 cells contains only the values 1 through 16, and a 5x5 magic square only contians the values 1 through 25. Pythagoras is a Greek mathematician and philosopher who lived in the 6 th century B. Place the number 1 in the center box on the top row. Take away one piece of the puzzle and turn over the other 4 puzzle pieces. Every 2 x 2 block of cells (including wrap-around) sum to 2T (where T= n 2 + 1) (i. Up to a rotation and re ection of the gure, there is one answer: 4 3 8 9 5 1 2 7 6 There are a few more magic characteristics of this array. However, the numbers are not {1, 2, …, 64}, so it is of. The most common one is a 3x3 square using the integers 1 through 9 in which the sum of each row, column and diagonal totals 15. The code for testing the diagonal values and for testing that the square contains all of the numbers 1 through n is trickier (n is size * size). 3x3 Magic Square: In the strict definition of a magic square, a 3x3 square must add to 15 (see the formula at the end of first para) A general recipe to construct a 3x3 number square is as follows ( I call it number square as the sum is not equal to 15 and numbers can be in any range and not necessarily from 1 to 9 as per definition of a magic. Here are a few manual games involving magic squares. We can convert any digit, a, to any other digit, b, in the range [1, 9] at cost |a - b|. Find 14 different ways of making 34 will earn you a level 1 trophy. 880 magic squares of size 4× 4. The guidelines are the same, except that you must use the numbers from 1-16 to make all the rows, columns, and both diagonals add to the same number. 5x5 magic square with sum 65 of planet mars - download this royalty free Vector in seconds. See Figure 1. Choose a square and draw it in your notebook, or on a sheet of paper. The android Magic Square puzzle game app is shaped like a Square (3 * 3 matrix) user must enter a decimal number. It is said that Albrecht Dürer a German painter, engraver, mathematician, and theorist from Nuremberg had made one such Magic Square in 1514. Looks like it might be difficult, but if you know the secret, you can make and solve any 3 x 3 magic square. Advanced Problem Solving II Jenya Soprunova KSU, Fall 2017 Solutions 4 Magic Squares A Magic Square is an n n table of numbers from 1 to n2 such that the sum of the entries in every row, every column, and the two diagonals is the same. Any given square will have 7 other similar squares found by rotating and flipping. Create a two-dimensional array of size n. Write a Python program to calculate magic square. I have an array of 25 non-consecutive integers, and I have to arrange them in 5x5 2D array so that this array forms a magic square. These two magic squares have some relationship regarding placement of numbers. how to fill a square of 5x5 cells using numbers 1 to 25 at once so that sum of each row and column and diagonal being equal. In 1514, the Dutch artist, Albrecht Dürer, incorporated a magic square of the fourth order into his etching, "Melencolia. The sum is called the magic constant or magic sum of the magic square. In a 4 x 4 square, you will use. You can also vary the length of the Knight's Move. The principle of magic squares can be extrapolated from two dimensions to any number of higher dimensions, including magic cubes and magic tesseracts, whose cross-sections consist of magic cubes, and so forth. Magic Squares. The way you calculate the MUST center of any magic square with odd numbers (e. So I need to reduce the sum of the first diagonal by 1 and increase the sum of the second by 1. The magic square has served as a talisman for good luck, a key to make gold, an aid to childbirth,. It is known as the Chautisa Yantra since its magic sum is 34. " One method of finding a solution to a puzzle in which the digits one to nine have to be arranged in a particular formation is by trying every different. In magic square theory, all of these are generally deemed equivalent and the eight such squares are said to make up a single equivalence class. In magic squares of odd numbers, 3X3, 5X5, 7X7, etc. If outside boundary fill end of row or column. 65 – 56 = 9, a square number and 65+56 = 121, another square number. Compare each sum to see if. There are 880 different magic squares of order 4. 9 12 15 27 4) The sum is 60. Generally a 3 x 3 Magic square is filled with numbers 1 to 9 ( 9 = 3 x 3), a 4 x 4 magic square with 1 to 16 ( 16 = 4 x 4 ) and a 5 x 5 magic square with 1 to 25 etc. n(n2+ 1)/2. let's take an example to check, whether the square matrix is magic square or not. 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 main diagonal is constant. Determining the number of diﬀerent magic squares of order 6 or larger is an unsolved mathematical problem. The dimension of the square matrix is an (odd integer x odd integer) e. The math behind the Siamese method of generating magic squares. , each number is used once), usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the main and secondary diagonals, all add up to the same number, called the "magic constant. for a 5 by 5 square, the magic number is 65. A double even order magic square is one whose order is divisible by 4. Similarly, the products of the numbers in the three columns are 72, 105 and 48; their sum is again the number 225. [2] The constant that is the sum of every row, column and diagonal is called the magic constant or magic sum, M. and top right from 19 to 27, bottom left with 28 to 36 and bottom right with 10 to 18. Step 2: Combinations that sum to 15. In the tenth century, a famous magic square, called Chautisa Yantra, appeared in India. These numbers are special because every row, column and diagonal adds up to the same number. A domino magic square is deﬁned using a set of dominoes to form a magic square, each domino supplying two numbers. The fact that there are nine ( a square number) prime numbers in the 5x5 magic square that sum to another square number (100) and that the sum of the prime numbers in just the cruciform portion of the magic square is 61 (part of the 11-60-61 Pythagorean triplet) is cause to take a closer look at the 5x5 magic square. The most basic magic square of order n, that is, n rows and n columns, or an n x n array, uses the consecutive integers from 1 to n^2. The magic constant of a normal magic square depends. Variations on the 3x3 magic square can be found by rotating the entries around the center box. (This number is well known since 1973, found by R. Place the number 1 in the center box on the top row. The goal is to arrange the numbers from 1 to N^2 within a NxN grid in such a way that the sum of all rows, the sum of all columns and the sums of both diagonals become equal, i. I have changed different indices values and the program returns false. As a reminder, a magic square is a matrix N * N whose numbers are distinct and between 1 and (N * N) where the sum of a line, a column or a diagonal is always equal to the same number. There are two notes in the Quandaries and Queries database about 3-by3 magic squares. A magic square is a grid of numbers where the values in each of the rows, columns and diagonals adds up to the same sum, known as the "magic number. A most-perfect magic square of doubly even order n = 4k is a pan-diagonal magic square containing the numbers 1 to n 2 with three additional properties:. The magic square of order 3 is. This number 34 is the "magic number" of the magic square. I know that the so called magic constant has to be 15, so 5 have to be placed in the middle, which reduces the combinations to 8! = 40. The revised code prints each of these solutions. The magic square is a square matrix, whose order is odd and where the sum of the elements for each row or each column or each diagonal is same. The way you calculate the MUST center of any magic square with odd numbers (e. If the matrix in the file is not a magic square, your program should print out the same output, except it should state that the matrix "is not a magic square. The simplest magic square is the 1×1 magic square whose only entry is the number 1. Each of these 3x3 magic square puzzles is solved by determining the values that make the sums all rows, columns and diagonals equal to the same value. The other pages in this section allow you to experiment and enter your own values - select 3x3, 4x4 or 5x5 above. Create a two-dimensional array of size n. Magic square 2: 1. Sum is the term we use for the answer of an addition problem. 1 The next simplest is the 3x3 magic square where the sum is 15. N must be odd. Isolated black and white illustration. In a magic square, the numbers in the rows, columns, and diagonals all have the same sum. We can also build a magic square and subtract. 10 5 4 15 Figure 1. M is one more than Q and one less. Go through right corner. The 4 x 4 Magic Square to the left is the "basic" 4 x 4 Magic Square. The more numbers to make magic squares from, the more difficult they become to complete. Sudoku is a particular type of magic square involving a 9 x 9 grid with nine 3 x 3 sub-grids, which first appeared in newspapers in the late 19 th century. We hope that you find exactly what you need for your home or classroom!. This is a buttery feeling square-1 that turns well right out of the box. For example, in the magic square below, the sum of each row is 18, the sum of each column is 18, and the sum of each diagonal. In this puzzle the sum in every row, column and diagonal is 15. Exapmple of it's history and other information is, for example, in the first attached wiki article. Another fact is the magic constants for magic squares of order n = 3, 4, 5 and 6 are 15, 34, 65 and 111 respectively. Similarly for 5 *5 Magic square also. Prime lattices 754. Below is a 3x3 magic square C code for odd numbers 3 to 15 and displaying the magic sum total number 15 for rows, columns, and diagonals for odd number 3 in Example1 Output. Or put more generally, adding a number Y to every square will make the sum 30 + Y * 4. Magic Squares of Order 3 At the beginning, we saw the 3 3 lo-shu magic square. The Magic Square and Pythagoras. In this paper, we will use the integers from 0 to 15 and so our 4 ด 4 magic squares will all have their magic sum equal to 30 (see Exercise 1. Associative magic square when it is a magic square with a further property that every number added to the number equidistant, in a straight line, from. The products of the numbers in the three rows are 96, 45 and 84; added together, they give 225 which is the square of 15, the sum of each row. 2 A method of constructing a magic square of doubly even order 2. A Magic Square 4 x 4 can he considered as the King of all the Magic Squares, for its an array of 16 numbers which can be added in 84 ways to get the same Magic Sum. It is the only Magic Square solution if we require the center number to be 5. The five numbers in each row across, each column down, and each of the two diagonals add up to 65. Notice that the set of nine numbers 1, 1, 1, 5, 5, 5, 8, 8, 8 cannot be arranged to make a 3-by-3 magic square. Save that for the magic square that you make for your guests. Write the number of the problem corresponding to the letter in each box of the magic square. e, square) matrix of numbers containing all numbers from 1 to n2 such that all the numbers in any given row, column, or main diagonal sum to the same number. In the magic square trick, an audience names any two digit number between 22 and 99 and after you fill in the 16 boxes there will be 28 possible combinations where the boxes will add up to the given number. You know that each magic square appears 8 times in this set (rotated and flipped); this means there are 880 unique 4x4 magic squares. But if all integers are raised to the second power, all rows, columns and diagonals have still a constant sum result. The square contains nine numbers total, ranging from 1 to 9. The lowest. How does the average of these numbers compare with the. Magic squares have been studied in an attempt to create them and better understand their properties. In squares of order 4 where the numbers run sequentially from 1-16 the magic constant (the sum of a single line, row or diagonal) is 34, but Subirachs' square does not contain the numbers 12 or 16 (see image, above). Code Review Stack Exchange is a question and answer site for peer programmer code reviews. Of course, you can't use this approach for 5x5 magic squares (which have 1. Advanced Problem Solving II Jenya Soprunova KSU, Fall 2015 Homework 8 Magic Squares A Magic Square is an n n table of numbers from 1 to n2 such that the sum of the entries in every row, every column, and the two diagonals is the same. By examining the array, I see that I can exchange the 10 and 7 from the second column with the 11 and 6 in the first: And the result is a 4x4 magic square:. Notice that a semimagic square with this property is magic. The other pages in this section allow you to experiment and enter your own values - select 3x3, 4x4 or 5x5 above. Similarly, a 4x4 magic square with 16 cells contains only the values 1 through 16, and a 5x5 magic square only contians the values 1 through 25. A version of the order 4 magic square with the numbers 15 and 14 in adjacent middle columns in the bottom row is called Dürer's Magic Square. Magic Squares are great and can be used in applications for every grade level. So instead of each number is replaced by two power of this number. )” A proof is furnished for the. Can you fill in the missing numbers in these magic squares? 1) The sum is 15. Consider a 4 × 4 magic square with elements 0, 1, , 15. A Magic Square 4 x 4 can he considered as the King of all the Magic Squares, for its an array of 16 numbers which can be added in 84 ways to get the same Magic Sum. Insert the remaining numbers in the grid to produce a magic square so that the sum of the numbers in any of the horizontal rows. Mainly, I have to "check" it. There are 36 ‘essentially different’ order-5 pandiagonal magic squares that can each be transformed into 3 other magic squares. 5x5 Magic Square Help!? I have to do a work sheet and it has clues to complete this magic square. Could you work this out just from knowing that the square uses. Note that if you add both rows and both columns together, you should get a sum of $15+15+15+15=60$, but this counts the numbers in the yellow squares twice. Place the number 1 in the center box on the top row. Thanks for contributing an answer to. Square is divided into equal number of rows and columns. A Magic Square is a matrix with the same number of rows and columns; where rows, columns and diagonals all sum up to the same number called the Magic Number. It is said that Albrecht Dürer a German painter, engraver, mathematician, and theorist from Nuremberg had made one such Magic Square in 1514. Remarkably, someone has found a magic cube containing Dürer’s square as a subplane. " Saturday, February 17, 2018. Illustration about planet, grid, background, mythology, sigil, square, vector, magic, isolated, kamea, science, column - 88349897 from magic square of order four 5x5 magic square with sum 65 of planet Mars 6x6 magic square with sum 111 of the Sun 8x8 magic square with sum 260 of planet Merxury. The constant sum in every row, column and diagonal is called the magic constant or magic sum, M. This magic square uses a 4x4 matrix with 16 cells. " Saturday, February 17, 2018. The puzzle also exists in other sizes, particularly the smaller 8-puzzle. I particularly like the version for a 5x5 magic square because the method couldn't be any simpler and a 5x5 magic square could be performed as a second phase - a further complication - in a magic square routine. A magic square adds up the values in each vertical, horizontal, and diagonal row to the same value. This is the very famous maths puzzle ,you may have come across this puzzle, you have to fill the nine boxes such that on addition from horizontally, vertically and diagonally its sum should be 15. An order-7 magic square uses the 16 primes between 1 and 49 to form the number '19'. Sum is the term we use for the answer of an addition problem. Magic square in China was known about 2 000 BC, so they have been known during 4000 years. Lo Shu is part of the legacy of the most ancient Chinese mathematical and divinatory (Yi Jing) traditions, and is an important emblem in Feng Shui (translate as 'wind-water'), the art of geomancy concerned with the placement of objects in relation. The resulting magic square (Fig. Magic square 2: 1. For example, build a magic square and add or build a magic square and add , etc. By the way, if your kids manage to solve the 3x3 Magic Square, they can try the 4x4 Magic Square. Magic Square. The first square, as in the odd-ordered square, consists of the numbers 1 to 6. This number is. Determining the number of diﬀerent magic squares of order 6 or larger is an unsolved mathematical problem. The sum of each row, column and main diagonal must be equal. The 3 numbers above the square moves down in the square and fills the open spaces, The same for the other numbers outside the square, then use left, right and up. If N is the order, then N x N different numbers are used to. The magic number for each of the magic squares above is 15. A non-normal square does not use minimal numbers in its cells, so the sums of the rows, columns and diagonals may be larger. The sum of the integers from 1 to N is given by the well-known formula N(N+1)/2. In this magic square, the sum of the rows, sum of the columns, and sum of the diagonals have to equal 15, and each number 1-9 can only occur once in the square. You may try to make magic square of order 5x5 for 25. for a 4 by 4 square, the magic number is 34. [2] The constant that is the sum of every row, column and diagonal is called the magic constant or magic sum, M. There is a simple algorithm for creating magic squares with odd values of N, like the example one above. Self-complementary magic square when it is a magic square which when complemented (i. Submit to see the results which display all the numbers in the grid organized so that the sum of numbers in every row, column and. The sum of numbers in any row, column, or diagonal is always sixty-five. If one squares all entries in in the square, the square remains magic: all row,column and diagonal sums are equal to 3263025. sum(M) = 15 15 15 as are the sums of the elements in each row, obtained by transposing: sum(M') = 15 15 15 See Also. * matrix is a magic square if it is square in shape (same number of rows as * columns, and every row the same length), and all of its row, column, and * diagonal sums are equal. It creates. This pattern was known in China more than 2000 years ago. Mainly, I have to "check" it. A square made from numbers is a magic square if the sum of each row, column, and diagonal is the same. Write a C Program to Check whether entered matrix is magic square or not. 65 – 56 = 9, a square number and 65+56 = 121, another square number. A most-perfect magic square of doubly even order n = 4k is a pan-diagonal magic square containing the numbers 1 to n 2 with three additional properties:. The Four Corner Magic and semi pandiagonal Squares S. I've tried multiple ways with no solution! Frustration!. I just find many sumbmission ignoring this condition. 4x4 Magic Squares Inventory with Colors. Normal magic square - rows, columns and diagonals add up to the same number, or magic constant 2. Magic Squares To create a “Magic Square” you must begin by choosing 9 numbers to put in your 3x3 matrix. Magic squares such as the Loubère have a center cell which must always contain the middle number of a series of consecutive numbers, i. If a magic square exists, then each row, column and diagonal has to be 15. Therefore the affine magic squares coincide with the algebraic magic squares. Within the engraving, Durer included a magic square. 3) The sum of all rows in s is the same as the sum of all columns in s, is the same as the sum of the diagonal elements in s. Each 2×2 subsquare, including wrap-round, sums to s/k, where s = n(n 2 + 1)/2 is the magic sum. 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. Get My Books!. These are: 1+5+9, 1+6+8, 2+4+9, 2+5+8, 2+6+7, 3+4+8, 3+5+7, 4+5+6. A magic square is an arrangement of numbers in a square array such that the numbers in every row and every column have the same total. By the way, the old Chinese way of representing numbers was with knots on a string. Merriam-Webster’s Collegiate Dictionary defines a magic square as: “a square containing a number of integers arranged so that the sum of the numbers is the same in each row, column, and main diagonal and often in some or all of the other diagonals. , the size of the square can only be an odd number, 3x3, 5x5, 7x7, 9x9, and so on). The famous Loh-Shu (scroll of the river Loh) from 2800 BC is the oldest magic square. Jun 3, 2016 - Free printable magic squares worksheets for math class, containing 3x3 and 4x4 magic square puzzles. magic square (remember the row size has to be odd number) For 3x3 you had the row sum as 15. The numbers of the central 3x3 grid in the above 21x21 magic square can be reduced to their Pythagorean root numbers to generate the classic 3x3 Luo Shu magic square. In one sense this is true, in another it is not. Given an grid of integers, how many 3 x 3 “magic square” subgrids are there? (Each subgrid is contiguous). Mission: Solve 5x5, 6x6 etc magic squares methodically. Find 21 different ways to earn a level 2 trophy. 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). • Next integer should be placed to upper right of the current integer. 5 Sum = 15 There are 9 distinct magic square for this case (with a total of 41 if reﬂected squares are counted as diﬀerent). The revised code prints each of these solutions. These numbers are special because every row, column and diagonal adds up to the same number. The Determinants of 4x4 Magic Squares Up to sign, there are only 12 distinct determinants for 4x4 magic squares (using the elements 0 to 15). Create a two-dimensional array of size n. He is renowned for his works on subjects such as Multiplication Tables and the theorem bearing his name, Pythagoras' theorem, which still forms part of the foundations of today's Mathematical Sciences. 24 Sep 2007 4 160. The 3 Most Significant Digits of the numbers in this square gives us another magic square with a sum of 1632. Arrange the numbers, -1,0,1,2,3,4,5,6,and 7 into a magic square. By Michael Hartley. for a 7 by 7 square, the magic number is 175. A magic square are a group of numbers arranged in a square layout in such a way that the sum of the numbers in any row, in any column, and on either diagonal are always the same. M = magic(3) M = 8 1 6 3 5 7 4 9 2 This is called a magic square because the sum of the elements in each column is the same. Sum of the 3 numbers in each row, column and diagonal should be 15. If the Lo Shu is considered a matrix and is muliplied by itself three times, a new magic square is formed. This is a buttery feeling square-1 that turns well right out of the box. Also 5 x 5 magic square using the integers from -9 to +15. , each number is used once), usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the main and secondary diagonals, all add up to the same number, called the "magic constant. a c c u s e p r o p e l h a n d e d i n v a d e d i e t e r s a y e r s. Decimal Magic Squares WorksheetWorks. A 'perfect' magic cube of order m > 1 is a m×m×m-array of the numbers from 1 to m 3, where the sum of m numbers along any straight line equals the magic constant S = m·(m 3 +1)/2. How to solve a 3x3 magic square equal to 27? using the numbers 5,6,7,8,9,10,11,12 and 13. And the sum of the exponent is here and so all the products are here. The first square, as in the odd-ordered square, consists of the numbers 1 to 6. The magic square with A through I all odd integers and S minimum, is defined by m=9: 3 13 11 17 9 1 7 5 15. On the other hand, if you count all the squares individually you get $1+2+\cdots+9=45$. for a 7 by 7 square, the magic number is 175. The resulting magic square (Fig. 16 3 2 13 And what is the magic? It is the number 34!5 10 11 89 6 7 12 This number is the sum of the various fields within the magic4 15 14 1 square. Notice that the set of nine numbers 1, 1, 1, 5, 5, 5, 8, 8, 8 cannot be arranged to make a 3-by-3 magic square. three numbers in All Rows, All Columns and. Inspired by the ancient Egypt of the Pharaohs, Pythagoras is the one. For a 3x3 magic square, there is actually only one normal solution and all of the puzzles are derived from rotations or reflections of that puzzle. a more challenging Math 3×3 Magic Square. Square is divided into equal number of rows and columns. I will place the numbers from 1 to 9 in the square and the sum of each row, column and diagonal will be 15. The sum of each row, column and main diagonal must be equal. The lowest. Number Puzzle with Digits 1-9 in a 3 by 3 Grid Date: 10/09/2006 at 19:50:55 From: Mike Subject: Math Puzzle In a 3 cell by 3 cell grid, use the digits 1 through 9 to fill in the cells so each horizontal, vertical, and diagonal row of three has a sum of 15. Math Math brain teasers require computations to solve. Though there is only one magic square of order 3 apart from trivial rotations and reﬂ ections of Equa-tion (1), the number of squares per order quickly skyrockets. By the way, if your kids manage to solve the 3x3 Magic Square, they can try the 4x4 Magic Square. Interactive 5x5 magic square generator using backtracking algorithm. A set of six stamps and a souvenir sheet from Macau feature magic squares. No membership needed. The rows and the columns of this magic square have a sum of 36. This is always where you begin when your magic square has odd-numbered sides, regardless of how large or small that number is. 5 x 10 25 possible solutions). The magic square is a square matrix, whose order is odd and where the sum of the elements for each row or each column or each diagonal is same. let us state the order as x. In a 4 x 4 square, you will use. A bimagic square is first of all a normal magic square, in which the rows, columns and diagonals give a constant sum. This sum is called the magic sum associated to M and is denoted by S M. A magic square is an arrangement of numbers in a square array such that the numbers in every row and every column have the same total. There are 880 distinct order-4 squares, and 275 305 224 distinct order-5 magic squares. A magic square is an n n array whose entries are the integers 1;2;:::;n2 where the sum of each row, column and the 2 main diagonals equals the same sum. The first square, as in the odd-ordered square, consists of the numbers 1 to 6. By perfect square sum magic square, we understand that the total sum of entries of a magic square is a perfect square. Each row, column, and diagonal in a Magic Square will sum to the same result (in this case “15”). So, for normal magic squares of order n = 3, 4, 5, …, the magic constants are: 15, 34, 65, …. We give you two text files: Mercury. Check out his. Students can gain much practice in multiplication by choosing a multiple of the original and forming their own magic squares. Place numbers in the grid such that every row, column and 3x3 box contain the numbers 1 to 9. A magic square is a square array of numbers consisting of the distinct positive integers 1, 2, , n 2 arranged such that the sum of the n numbers in any horizontal, vertical, or main diagonal line is always the same number. So I need to reduce the sum of the first diagonal by 1 and increase the sum of the second by 1. It is said that Albrecht Dürer a German painter, engraver, mathematician, and theorist from Nuremberg had made one such Magic Square in 1514. Check that the sum of each row, column, and diagonal is the same. A Magic Square is one where each cell in the square contains a unique integer, where the sum of each column, each row, and both diagonals are the same, and where the numbers used are from 1 to n squared, where n is the “length” of the square. We worked with magic squares of orders 3 to 25. 3 The medjig-method of constructing magic squares of even order n>4 2. Two order-4 magic squares, one the reverse of the other. The sum is called the magic constant or magic sum of the magic square. Odd Magic Square: 5 x 5 It's Magic Sum is: 65 17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9 Odd Magic Square: 7 x 7 It's Magic Sum is: 175 30 39 48 1 10 19 28 38 47 7 9 18 27 29 46 6 8 17 26 35 37 5 14 16 25 34 36 45 13 15 24 33 42 44 4 21 23 32 41 43 3 12 22 31 40 49 2 11 20. Choose a square and draw it in your notebook, or on a sheet of paper. These pages attempt to show the complete list of 4x4 magic squares. Magic Square (Python) The sum is called the magic constant or magic. Each 2×2 subsquare, including wrap-round, sums to s/k, where s = n(n 2 + 1)/2 is the magic sum. n(n2+ 1)/2. Therefore the average sum of three numbers is 45:3=15. Write an equation for each row, column and main diagonal. 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. The number 15 is known as the magic sum, and the size of the square (3 by 3) is known as the order. For the 6×6 case, there are estimated to be approximately 1. Scenario According to the U. Schroeppel). If one squares all entries in in the square, the square remains magic: all row,column and diagonal sums are equal to 3263025. The trick to drawing the magic square is to realize that the numbers in a 4 by 4 magic square are always fixed as shown. Sayles (The Monist, 1913) -- Reprinted as Magic Squares and Cubes. The lowest. Follow-up to Puzzle 756. This wouldn't be a proof in general, but it should help you understand what is happening in that sum-switching step of the proof, and that it works because the elements of a matrix product are sums and then we sum a row of sums, and the terms within these two sums can be conveniently rearranged. Once you have one, you can get all the others by. In 1514, the Dutch artist, Albrecht Dürer, incorporated a magic square of the fourth order into his etching, "Melencolia. 1, 3 In a “magic square”, the sum of the numbers in each row, in each column and along the diagonals is the same. In this paper a generic definition for Strongly Magic Squares is given. Submit to see the results which display all the numbers in the grid organized so that the sum of numbers in every row, column and. Is this a magic square? (Along the first row 4/11 + 9/11 + 2/11 = 15/11) 4/11 + 9/11 + 2/11= ((4 + 9 + 2))/11= 15/113/11 + 5/11 + 7/11= ((3 + 5 + 7))/11= 15/118/11 +. M is one more than Q and one less. d) discuss the problems of constructing Magic squares from the structured set of 16 elements (Sect. This square became known as the One can lo-shu magic square. Pythagoras is a Greek mathematician and philosopher who lived in the 6 th century B. There are 275,305,224 such 5x5 squares. Magic Square Cutup Cut out the digits at the bottom of the page and arrange them inside the magic square so that the sum of the three numbers in any direction (vertically, horizontally or diagonally) is 15. Pan-Anti-Magic Squares. So for the example below, 15 is the magic number. Here are a few of them. The numbers in each row, column, and diagonal all sum up to 15 (ex. A magic squares is an n-by-n * matrix of the integers 1 to n^2, such that all row, column, and * diagonal sums are equal. A Magic Square 4 x 4 can he considered as the King of all the Magic Squares, for its an array of 16 numbers which can be added in 84 ways to get the same Magic Sum. On the wall to theright hangs themagic square Dürercreated. We hope that you find exactly what you need for your home or classroom!. I will be showing you a 3x3 matrix. Your matrix can be 3x3; 4x4; 5x5; etc. A magic square is a grid of numbers where the values in each of the rows, columns and diagonals adds up to the same sum, known as the "magic number. The number 15 is the sum of numbers in each row, column, and diagonal of the Lo Shu magic square. The square’s magic sum of 15, which for the Chinese represented “human being perfected,” has been culturally transformed in the Islamic context to reflect the phrase “O man” or “O Perfect Man” referring to the Prophet Muhammad. Magic Square (thebrandywinebridge. Another approach is to consider the ways to obtain 15 as a sum of 3 different numbers in the range 1. Get Started Get mobile app. But if all integers are raised to the second power, all rows, columns and diagonals have still a constant sum result. stock vector 145342215 from Depositphotos collection of millions of premium high-resolution stock photos, vector images and illustrations. The sum of the numbers in each row, column and both diagonals total 45. 4 14 15 1 (5) 4 Counting Magic Squares There are 880 distinct 4 4 magic squares of the –rst 16 integers, and the 275;305;224 distinct 5 5 of the –rst 25 integers, the latter were –rst counted by computer in 1973 (Schroeppel). The example above uses a center value of "5". k=1 k=1 Multiplicative magic squares 3 Then clearly [m;; ] is an MMS. You can also achieve 15, if you add the middle number 5 three times. let us state the order as x. The author remarks that “raising any third-order magic square to any odd power seems to yield a magic square. The goal is to arrange the numbers from 1 to N^2 within a NxN grid in such a way that the sum of all rows, the sum of all columns and the sums of both diagonals become equal, i. Completed: Without looking at any internet reference, I managed to solve a 3x3 and a 4x4 magic square, as well as part of a 5 and damn near a 6. The 3x3 example above is considered Panmagic, Diabolical, Nasik, or Pandiagonal, while the 4x4 above is merely magic. compact) Any pair of integers distant ½n along a diagonal sum to T (i. Reflecting, rotating, and translocating, each square multiplies this by 200 to give a grand total of 28,800 different 5x5 pan-magic squares. Is there a better way to write this? The magic square only uses numbers 1-9 and is in 3x3 matrix. The Magic Square Calculator: This program demonstrates the use of Perl programming to manipulate data in arrays to solve the problem of the Magic Square. The operations in Matlab are designed to be as natural as possible. Tes Classic Free Licence. Bonus: "The Magic Diamond", two routines, one for 4x4 magic square and one for a 5x5 magic square by Werner Miller. Interactive 5x5 magic square generator using backtracking algorithm. In order to construct a square of non-consecutive cubes, we can use a method similar to Morgenstern's 6x6 method. A non-normal square does not use minimal numbers in its cells, so the sums of the rows, columns and diagonals may be larger. This is a magic square, if we see, the sum of each row, column and diagonals are 15. 2 A method of constructing a magic square of doubly even order 2. • If the upper right position (x-1,y+1) is outside the range, then change the out-of-range index to the corresponding index. As you can see numbers in first row add up to 15 (8 + 1 + 6), so do the numbers of 2nd row 3 + 5 + 7. magic_square_sum_15_v1. is a magic square. Sum of the 3 numbers in each row, column and diagonal should be 15. Write a program to enter an integer number ‘n’. Explore magic squares from an historical and mathematical perspective. A Magic Square is a n x n matrix of distinct element from 1 to n 2 where sum of any row, column or diagonal is always equal to same number. In this magic square, the sum of the rows, sum of the columns, and sum of the diagonals have to equal 15, and each number 1-9 can only occur once in the square. The numbers of squares having each of these determinants are listed below: exponents in number of number of factorization squares squares |det| 2 3 5 7 |det| -|det| ----- ----- ----- ----- 0 - 5120 1920 7 1 1 0 160 160 2880 6 2 1 0 64 64 3840 8 1 1 0 96. The sum of H and J equals D. A magic square is a square grid of numbers, in which each number appears once and the numbers in each row, column, and the two main diagonals sum to the same value. It is known as the Chautisa Yantra since its magic sum is 34. Magic Squares: Decimals Materials: Magic Squares: Decimals cards _____ 1. Magic squares have been studied in an attempt to create them and better understand their properties. It will have 'n' rows and 'n' columns and totally there are n 2 small squares. Is there a better way to write this? The magic square only uses numbers 1-9 and is in 3x3 matrix. PART 2: Patterns in all magic squares Use the magic square templates on page 11. The resulting 144 pandiagonal magic squares can each in turn be transformed cyclically to 24 other magic squares by successively moving a row or column from 1 side of the square to the other side. The work is divided in two parts, one on primitive triples and another on non primitive …. Make a completely new magic square. The four square by four square magic square found above the seated female with wings is said to be the first to turn up in European art. Instead, considering entries as consecutive numbers, we considered consecutive odd numbers entries. Source: Wikimedia. A magic square is an arrangement of numbers 1,2,3, n 2 where every row, column and diagonal add up to the same magic sum S and n is also the order of the square. ");}} // Checks if the square is a Magic Square. 223 to construct a magic square yourself. Magic Square (Python) The sum is called the magic constant or magic. The constant sum in every row, column and diagonal is called the magic constant or magic sum, M. 5'15'10 1 5. Interactive 5x5 magic square generator using backtracking algorithm. The number n is called the order of the magic square. magic sum= b*x+x( x^2 -1 /2) = x(b+(x^2-1)/2). 17 24 1 8 15. A closer look will easily reveal the fact that the gradually smaller Magic Squares are not Pure Magic Squares, but this does not loosen the grip of its "Magic Spell" the least!. Solution 1: Build a magic square and add. Add down and across. 3x3, 5x5, 7x7) = is to calculate the total sum of Magic Square. So i'm creating a magic square and here is my code def is_magic_square(s): ''' Return whether a two dimensional integer array s is magic, that is: 1) The dimensions of s is nxn 2). The constant values $ M $ of the sums of the magic squares have a minimum value (for non-zero integer positive values). The fact that there are nine ( a square number) prime numbers in the 5x5 magic square that sum to another square number (100) and that the sum of the prime numbers in just the cruciform portion of the magic square is 61 (part of the 11-60-61 Pythagorean triplet) is cause to take a closer look at the 5x5 magic square. hat contains each of the numbers 1, 2, 3, , n2 exactly once and has the sum of the numbers in each of its rows, columns and diagonals equal to the same thing. 1 Extra constraints. There exist 68820306 reduced 5x5 magic squares and 32x68826306 = 2202441792 magic squares of order 5. This wouldn't be a proof in general, but it should help you understand what is happening in that sum-switching step of the proof, and that it works because the elements of a matrix product are sums and then we sum a row of sums, and the terms within these two sums can be conveniently rearranged. Methods for building them can be found in a references of this wiki article. Here are the rules to construct a magic square:. Because 87 is an odd number, we had a remainder that we needed to use for the boxes with 13, 14, 15 and 16 in them. Note that if you add both rows and both columns together, you should get a sum of $15+15+15+15=60$, but this counts the numbers in the yellow squares twice. A magic squares is an n-by-n * matrix of the integers 1 to n^2, such that all row, column, and * diagonal sums are equal. Solve a 15 sum square magic game. is the magic square matrix. Magic? Presentation Suggestions:. Here it follows: Horizontally, Vertically you will get the same result, except Leading diagonals. 1234 567 8 9 Player 1: 3. Both Diagonals equals 51. 'a' always appears in the bottom row, 2 nd cell from the right. As a further restraint, these sums are also consecutive. Complete this magic square to make the sums of the rows, columns, and diagonals the same. Lo Shu Square or the Nine Halls Diagram, often in connection with the Ho Tu figure and 8 trigrams, is the unique normal magic square of order three. For example, in the magic square below, the sum of each row is 18, the sum of each column is 18, and the sum of each diagonal. 5 Sum = 15 There are 9 distinct magic square for this case (with a total of 41 if reﬂected squares are counted as diﬀerent). Use addition to complete the puzzle. The android Magic Square puzzle game app is shaped like a Square (3 * 3 matrix) user must enter a decimal number. Each 2×2 subsquare, including wrap-round, sums to s/k, where s = n(n 2 + 1)/2 is the magic sum.