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# 3x3 magic square all solutions ### 3x3 Magic Square - DadsWorksheets

1. 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. The normal variations of these puzzles (the 3x3 puzzles that contain only 1-9) will have a magic constant of 15. This should make solving the early puzzle worksheets pretty easy
2. imize S, then A, then B. If it's not possible, show why. A through I, arranged in increasing order, do not form an arithmetic series. (In an arithmetic series, the difference between successive terms is always the.
3. A magic square is an arrangement of distinct numbers (i.e. 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. Here's one sample solution: 8 1 6 3 5 7 4 9
4. imum constant is 15, for 4x4 it is 34, for 5x5 it is 65, 6x6 it is 111, then 175, 260,... Any lower sum will force the use of either negative numbers or fractions (not whole numbers) to solve the magic square. What is the Franklin Square
5. I'm trying to find all possible solutions to the 3X3 magic square. There should be exactly 8 solutions. My code gets them all but there are a lot of repeats. I'm having a hard time tracking the recursive steps to see why I'm getting all the repeats
6. Everything you'd ever want to know about 3x3 magic squares was figured out long ago; there is even a formula to find all of them. So this brute force method is, well, very brutish. Nevertheless, this was a very fun little project and there are many ways this code could be extended to do something more interesting

### Properties of 3x3 Magic Squares - Duisenber

Hence, the magic constant for a 3×3 square is 15. All rows, columns, and diagonals must add up to this number. 2 Place the number 1 in the center box on the top row and 4 are broken diagonals, consisting of each corner square and the two opposite middle edge squares, just mentioned above. If all 9 numbers form a single arithmetic progression, then the magic square can be derived from the basic 816-357-492 square by a linear transformation: A * x + B, where A and B are constants, and x is value in a square The Magic 3x3 Square top You have 1+2+3+4+5+6+7+8+9=45. In a magic square you have to add 3 numbers again and again. Therefore the average sum of three numbers is 45:3=15 computer. 3x3 magic squares answers is handy in our digital library Page 2/8. Bookmark File PDF 3x3 Magic Squares Answers an online entry to it is set as public for that reason you can download it instantly. Our digital library saves in combination countries, allowing you to get the most less latency era to download any of our books subsequent to this one. Merely said, the 3x3 magic squares.

$\begingroup$ @Arthur what's hard is to show that the set spans the space of all 3x3 magic squares. $\endgroup$ - TommyX Feb 9 '17 at 20:43 $\begingroup$ You could come up with a matrix representing the system of equations you want - that all rows, columns and diagonals have the same sum, and then show that it has a 3 dimensional solution Read 3X3 MAGIC SQUARE SOLUTION PDF direct on your iPhone, iPad, android, or PC. PDF File: 3x3 Magic Square Solution - PDF-3MSS8-1 Download full version PDF for 3x3 Magic Square Solution using the link below: € Download: 3X3 MAGIC SQUARE SOLUTION PDF The writers of 3x3 Magic Square Solution have made all reasonable attempts to offer latest and precise information and facts for the readers of. A magic square has every row, column, and diagonal sum to the same number. How many magic squares are there using the numbers 1 to 9?This video shows you all.. That solution consists of sixteen 3×3 Magic Squares that use all the numbers from 1 to 144. The one in the corner is the most familiar one. The other ones are just that familiar Magic Square plus 9, 18, 27 and a few other multiples of 9. I used the 4×4 Magic Square below as a guide as I placed the sixteen 3×3 Magic Squares on the excel file I made, 12 factors 864-874. make science GIFs like. In the 3x3 square, it is impossible to make all of the diagonals magic. The Main Diagonals are Magic when you put the middle value (the 3 and the 1) in the center location in their sequences in the top array. If you put these middle numbers in other positions, then one of the broken diagonals becomes magic instead

A booklet consisting of various magic square puzzles with solutions. 9 different 3x3 6 different 4x4 6 different 5x5 2 different 6x6 Original puzzle resource credi my 3x3 semi-magic square of squares having a magic sum which is three times This is the only known solution. For his other 19 solutions, the magic sum was three times a square different from any of the entries. Their sums (< 3 x 5000²) are 3 x 1225², 1275² If you have a solution for a 3x3 Magic Square and the center cell has some value N, you can always generate a solution for a center value of N + 1 by simply adding 1 to the value in all 9 cells. For that matter, you can always add any arbitrary constant to all 9 cells and get a solution with larger values

### Prolog: Finding all 3x3 magic squares without using clp(FD

• As for 2x2 - the smallest magic square is 3x3 and 2x2 is impossible. If you remove both the diagonal constraints and the unique constraint then 2x2 works and you'll get solutions with a distinct number on each diagonal, or all four entries the same. $\endgroup$ - flinty Jun 17 '20 at 20:0
• The table below shows all the 3x3 magic squares. Have a careful look, and you'll see that each of the 3 by 3 magic squares in the grid above can be changed into its neighbors by flipping it, as if through a mirror. Another way to change a 3x3 magic square into another is by subtracting all the numbers from 10
• g a Magic Square problem solution YASH PAL March 26, 2021. In this HackerRank For

The Magic Square Order of 3x3 is one of the odd and prime magic square which consists of three rows and columns. The puzzle requires 9 different numbers to solve the puzzle which should give the same magic constant with the addition of numbers horizontally, vertically and diagonally. The first Magic Square Puzzle found has numbers from 1 to 9 which gives a Magic Constant of 15. The examples of. A 3x3 magic square is an arrangement of the numbers from 1 to 9 in a 3 by 3 grid, with each number occurring exactly once, and such that the sum of the entries of any row, any column, or any main diagonal is the same. Backtracking Algorithm A backtracking algorithm is a recursive algorithm that attempts to solve a given problem by testing all possible paths towards a solution until a solution. Play Magic Square Online - Solve our magic square puzzles to experience the best brain exercise. The great 3X3 Magic Square. 3X3 4X4 5X5 6X6 7X7 8X8 9X9 10X10. 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. Each cell in a nXn grid has a different number. 4x4 Magic Square - How to Solve the 4x4 Magic Square - How to Fill the 4x4 Magic Square The sum is referred to as the magic constant. 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

### Magic Square Generator/Solver 3x3, 4x4, 5x5 Online Calculato

• imum cost. * Remember that Google is your friend: the quickest way to find all the 8 magic squares is through a web search :) * In this way, we hard-code the 8 magic squares into the solution. *
• All Topics Topic Science Mathematics » magic square 3x3 solution? jade_louise09 Posts: 1, Reputation: 1. New Member : Nov 28, 2011, 05:16 PM magic square 3x3 solution? How to solve decimal magic square? Unknown008 Posts: 8,076, Reputation: 723. Uber Member : Nov 28, 2011, 10:22 PM.
• ing all permutations of integers 1, 2, 3,., 9 and for each one, check if it forms a magic square if the permutation is inserted into the square starting from the upper left hand corner

### c++ - 3 X 3 magic square recursively - Stack Overflo

3x3 Magic Square. Problem. A $3 \times 3$ magic square is a square grid containing the numbers 1 to 9 in such a way that the sum of each row, column, and diagonal has the same magic total. By considering rotations and reflections to be equivalent, prove that this $3 \times 3$ magic square is the only solution. Solution. We shall begin by assigning letters to each of the cells in the \$3. Algebra -> Test -> SOLUTION: Create a 3x3 magic square using the number 3,5,7,9,11,13,15,17,and 19 Log On Test Calculators and Practice Test. Answers archive Answers. Word Problems Word. Lessons Lessons : Click here to see ALL problems on test; Question 171313: Create a 3x3 magic square using the number 3,5,7,9,11,13,15,17,and 19 Found 2 solutions by solver91311, Edwin McCravy: Answer by. Actually, all 3x3 Magic Squares have an identical structure. And, if the same numbers are used, e.g., 1 to 9, the same square always results; it may be reflected, rotated, or both, but it is always the same square. In the 3x3 square, it is impossible to make all of the diagonals magic. The. In January 2013, Lee Morgenstern computed that there is no 3x3 semi-magic square of distinct positive cubes with all entries under (10 6) 3. And that there is no 3x3 semi-magic square using a list of all primitive taxicab(2) solutions with entries under (10 6) 3 that are twice-scaled up to entries under (10 24) 3. See details on his searches So I can make that into a magic square with the integers from 20 through 28 just by adding 20 to each number: 1+20=21 8+20=28 3+20=23 6+20=26 4+20=24 2+20=22 5+20=25 0+20=20 7+20=27 which is this magic square 21 28 23 26 24 22 25 20 27 All the rows, columns and diagonals add up to 72. ----- Or I could have made that into a magic square with the integers from 21 through 29 by adding 21 to each.

### A very simple brute force approach to finding all 3x3

1. Magic Squares are not solved. They are filled out. There are proven methods in completing magic squares of any sizes. Follow the guidelines below and you should be on your way to completing any magic squares: 3 x 3 Square * Start with 1 in the top..
2. The proof are in the rules (or conditions) about how a magic square is built... In this case a 3x3 grid, you need a sequence of nine integer and positive numbers to make a magic square. You must order that numbers by size... the number that goes in the center of the grid is always the middle number of that group you ordered
3. I nearly gave up when I saw all the 2's on the diagonal, but then I spotted that 2 plus 2 plus 2 also adds to 6. Kim from Bottisham Village College and Natasha and Nathaniel both from Moorfield Junior School sent in a different solution again
4. g a Magic Square Problem in C++. Magic Square is the matrix of n*n having distinct positive integer in the range [1,n^2]. Such that sum of all the rows, columns, and diagonals are equal. If you want to know something more about Magic Square. For example, we start with the following matrix. 5 3 4 1 5 8 6 4
5. We consider 3X3 magic squares, allowing for arbitrary entries, and with sums of rows, columns and diagonals equal to the magic number m. The following questions are addressed (i) find a formula.

The square of Varahamihira as given above has sum of 18. Here the numbers 1 to 8 appear twice in the square. It is a pan-diagonal magic square.It is also an instance of most perfect magic square.Four different magic squares can be obtained by adding 8 to one of the two sets of 1 to 8 sequence Unlike 3x3 magic squares where there is only one basic solution to the puzzle, a 4x4 magic square has exactly 880 distinct normal solutions. The puzzles here are derived from rotations or reflections of these puzzles

To know about this interesting puzzle, Magic Square on Wikipedia Now, let's take a look at the code. PROGRAM: Python program for magic square operation #Function def generateSquare(n): # 2-D array with all # slots set to 0 magicSquare = [[0 for x in range(n)] for y in range(n)] # initialize position of 1 i = n / 2 j = n - 1 # Fill the square by placing values num = 1 while num <= (n * n): if. Magic squares of odd order magic constant for 5x5 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 magic constant for 3x3 is 15 8 1 6 3 5 7 4 9 2 verify 8 1 6 : 15 row 1 3 5 7 : 15 row 2 4 9 2 : 15 row 3 8 3 4 : 15 column 1 1 5 9 : 15 column 2 6 7 2 : 15 column 3 8 5 2 : 15 diagonal top left to bottom right 4 5 6 : 15 diagonal bottom left to top right magic constant. Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. Two solutions are considered to be the same if, as in the example shown, they contain the same six triples For a 3x3, 4x4, 5x5, 6x6, 7x7, 8x8, 9 x 9, and 10 x 10 magic squares the sum of the integers in any row, column, or diagonal will be 15, 34, 65,111, 175, 260, 369, and 505, respectively. Consider first a 3x3 magic square which we represent by the square matrix- G H I D E F A B C It has a total of nine unknowns but only eight equations defining a magic square of this dimension. The eight. Solving Magic Squares by Generating Permutations. Just for the sake of comparison against backtracking, this section describes the implementation of the solution of magic squares by generating permutations of the numbers in the range of a magic square. All the code dealing with permutations is after function ReportTimes. The variables required.

The numbers in the Red Squares form the 3x3 magic Square. The numbers beside the Red Squares show the totals for each row. The horizontal and vertical totals are to the right and below in green squares. The other, blue, squares show the diagonal totals - including all of the broken diagonals. You can make your own Magic Square in two ways. Try both methods: Enter your own numbers into the. 1 magic square of size 3 × 3 880 magic squares of size 4× 4 For the 6×6 case, there are estimated to be approximately 1.77 × 10 19 squares. Transum, Saturday, February 17, 2018 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.

### 3 Ways to Solve a Magic Square - wikiHo

• e my target sum. The sum of all the values 1 through 16 is 136. Dividing this result gives 34, which is my target sum for each row, column, and diagonal. I then make an array of the numbers 1 through 16: Exa
• The Magic 3x3 Square Magic sum. In a magic square of order n, you have to assemble the number 1 to n² in an n by n grid-like above image.You have to consider the magic rule that indicates the.
• As earlier, this is also an open question that has an infinite number of solutions. Such open questions can deepen students' understanding and are also useful for assessing understanding. The algebraic magic square that is the basis on the questions in Task 8 is a generalised form of a 3-by-3 magic square. Students may see that this magic square has been produced by adding z to the.

Level 1 Level 2 Level 3 Level 4 Level 5 Magic Square More Puzzles. Drag the numbers into the blue cells to make an unmagic square. The totals of each row, column and diagonal should all be different. Congratulations! Claim your trophy by clicking on the red button below. Are there any other ways to make an unmagic square using these numbers? Your answer is not correct. Not all of your totals. Therefore you have to place number 5 in the middle of the magic 3x3 square. The remaining odd numbers have to be in the middles of a side and the even numbers at the corners. Under these circumstances there are eight possibilities building a square: All the eight squares change into each other, if you reflect them at the axes of symmetry. You count symmetric squares only once. Therefore there. Amazing mathematical magic square trick 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. The trick to drawing the magic square is to realize that the numbers in a 4 by 4 magic square are. The distribution is done in such a way that the sum in any direction is the same magic number. Solution: 3. Divide 18 by 3. You get the quotient '6'. Put 6 in the central cell of the 3x3 matrix. 4. To get the numbers in the central row, i.e. to the right and the left of 6, add 2 to 6 and subtract 2 from 6 respectively. The result is represented in the picture. 5. The next step is to find the.

M = magic(n) returns an n-by-n matrix constructed from the integers 1 through n 2 with equal row and column sums.The order n must be a scalar greater than or equal to 3 in order to create a valid magic square These are all the magic squares of order three. The 5 is always in the center, the other odd numbers are always in the centers of the edges, and the even numbers are always in the corners. Melancholia I is a famous Renaissance engraving by the German artist and amateur mathematician Albrecht Durer.¨ It shows many mathematical objects, in- cluding a sphere, a truncated rhombohedron, and, in.

### Magic Square Solver - GottfriedVille

Shaded 3x3 squares are magic squares. The sum of the numbers in all rows, columns and two diagonals should be equal in a magic square. EXAMPLE: UNIQUE SOLUTION: Email This BlogThis! Share to Twitter Share to Facebook Share to Pinterest. Labels: Magic Square Sudoku, Rules. 1 comment: Rohan Rao said... A sudoku, based on the magic square puzzle... June 3, 2009 at 5:30 PM Post a Comment. Newer. Magic Triangle 2 sums help page Find all the different ways that 3 numbers from 1 to 6 can be added to get a total of 10. You cannot use the same number twice in any sum. The same 3 numbers can be used in different orders. EXAMPLE: 1 + 3 + 6 = 10 and 1 + 6 + 3 = 10 both work. starts with a 1!starts with a 2!starts with a The Lo Shu Magic Square is an arrangement of the digits 1 through 9 in a 3x3 grid such that: each digit is only used one time. the sum of the each row, column, and diagonal all add up to the same value. is a valid Lo Shu Magic Square because it uses all 9 digits one time, and all of the rows, columns, and diagonals add up to the same value (15) A magic square is a simple mathematical game developed during the 1500. Square is divided into equal number of rows and columns. 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. Fill each square so that the sum of each row is the same as the sum of each column. In the example shown here, the sum of each row is 15.

### Magic Square - Mathematische Basteleie

89 votes, 218 comments. Description A 3x3 magic square is a 3x3 grid of the numbers 1-9 such that each row, column, and major diagonal adds up to Magic Square 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, HackerEarth is a global hub of 5M+ developers. We help companies accurately assess, interview, and hire top developers for a myriad of roles Magic squares are interesting objects in both mathematics proper and in recreational mathematics. The students may have already encountered magic squares as this problem is part of a series: Little Magic Squares and A Square of Circles , Level 2, Big Magic Squares Level 3. Fractional Magic Squares. Level 4

• In a typical magic square, you start with 1 and then go through the whole numbers one by one. For example, a magic square of order 3 contains all the numbers from 1 to 9, and a square of order 4 contains the numbers 1 to 16. Not surprisingly, magic squares made in this way are called normal magic squares
• g and going, up and down, and oft times even from an angle (diagonal)
• There is no magic square that can be constructed in a 2 by 2 square but singly even magic squares can be constructed for n=6, 10, 14 and so on. Singly even magic squares are the most difficult to construct and so let's start with the smallest possible one where n = 6. To get the sum, we'll use the formula that we previously used: So, the sum for n=6 is 111. The first step is to break the.
• For N ≥ 4 some of these tilings are not compatible with any Latin square; i.e. all Sudoku puzzles on such a tiling have no solution. Solutions. The answer to the question 'How many Sudoku grids are there?' depends on the definition of when similar solutions are considered different. Ordinary Sudoku All solutions. For the enumeration of all possible solutions, two solutions are considered.
• Following are sample solutions of orders 6, 7, and 8 PM Triangles. The reader is left with a challenge to find additional solutions. Or even, all the solutions for a given order. Perimeter magic triagonals are neither as complex, or mathematically challenging as magic squares or cubes
• Update: New and improved version. Faster, better, and supports more devices. Grubiks team is proud to present the best online Rubik's Cube Solver! Used my millions around the world - this rubik's cube solving website will show you how to solve any valid scramble with an easy to follow step-by-step solution
• x Magic Cube Black » Mega 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. * * One way to generate a magic square when n is odd is to assign * the integers 1 to n^2 in ascending order, starting at the * bottom, middle cell The magic_square_5 class solves the problem of 5x5 magic squares following the visiting order of the above figure. The class performs only basic tests, when a row, a cell or a primary diagonal is completed. In my machine it was able to find about one or two solutions every second. It is still very slow but I believe that with a few optimisations it could be tweaked to enumerate all magic.

### Showing a set of matrices is a basis of all 3x3 magic square

How do you solve 3x3 magic square numbers 1-9 each row and column totals a prime number? Asked by Wiki User. See Answer . Top Answer. Wiki User Answered 2012-10-10 12:41:24. Using the digits 1 to. Rubik's Cube (3x3) Online Solution The Rubik's Cube 2020 Solution Guide uses the layered method - TOP layer, MIDDLE layer, & BOTTOM layer. Watch all stages with these new animated video guides to help get you started. Whether you solve 1 layer or all 3, be sure to tell your teacher about this program so all your classmates can solve with you! Teachers from all over the country use our. Rubik's Cube (3x3) Online Solution The Rubik's Cube 2020 Solution Guide uses the layered method - TOP layer, MIDDLE layer, & BOTTOM layer. Whether you solve 1 layer or all 3, be sure to tell your teacher about this program so all your classmates can solve with you! Teachers from all over the country use our program, at no cost, to teach their classes not only to solve, but content area STEAM. A Magic Square contains a certain bunch of numbers, in this case, 1..9, each of which has to be filled once into the grid. The 'magic' property of a Magic Square is that the sum of the numbers in the rows and columns and diagonals should all be same, in this case, 15. Try making a 3x3 magic square yourself. It's not that easy. If i

### SOLVE The 3x3 Magic Square Completely - There Can Only Be

Can you get another antimagic solution of the same size (5x5) using a distinct magic (3x3) square? 2. Can you get an antimagic 5x5 containing an eccentric (non-centered) magic 3x3. 3. Can you get a larger example (i.e. an antimagic 6x6 containing a magic 4x4)? 4. Can you get the opposite concept: a magic square containing inside an antimagic square (*) _____ (*) It has been shown that no. The magic number, given as a quotient, must be an integer. You can show by a clever calculation that there is the only solution n=3. You recognize that H or 32H is only a whole number, if 5/(2n-1) is, too. n=3 is a solution that fits. The numbers n= -2, 1,0 don't fit. You can also find this solution by a computer

### 870 If You Can Solve a 3×3 and a 4×4 Magic Square, Then

Magic Square. Magic squares have been a fascinating topic in mathematics for centuries. They are formed by filling in all the squares with the numbers starting from one so that the sum of all row, columns, and diagonals is the same. If you know how to play, you can use the square below. Otherwise, read the instructions and fill in the form at the bottom to begin a new game. Numbers to use: 1. Checking all possibilities for forming a magic square. Back to the drawing board. I thought of checking all combinations but on the outset there was 9! = 362.880 possible solutions. What did I know about forming a 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! = 40.320 a lot better. That was when. The set of all such zerozero magic square magic squares of order is symbolized 0MS( ) (19, p. 109). Obviously a zero magic square cannot also88 be a normal magic square since it must contain negative entries. One such would be ÖÙ ÖÙ ÖÙ ÖÙ ÕØ 411-12 -5 2 10 -8 -6 1 3-9 -7 0 7 9-3 -1 6 8 -10-2 5 12 -11 -4, constructed using a modification of the Hindu method described later. A or is a.

### Make Your Own 3x3 Magic Square - Grogon

The 4 x 4 Magic Square to the left is the basic 4 x 4 Magic Square. It uses the numbers 1 to 16 inclusive, and its Magic Total is 34, as predicted by the formula shown on another page.There are exactly 880 4 x 4 Magic Squares that can be created.. However, Magic Squares can be created that add up to any Magic Total you like, provided that you know the right formula Fraction Magic Square Task 37 Years 4 - 10 Summary Students usually only experience Magic Squares using whole numbers. This task shows that can also be made using fractions and opens the door to (a) linking with the classic whole number case, and (b) realising that a magic square can be made to total any number at all HackerRank Forming a Magic Square python solution - forming_a_magic_square.py. Skip to content. All gists Back to GitHub Sign in Sign up Sign in Sign up {{ message }} Instantly share code, notes, and snippets. Eitol / forming_a_magic_square.py. Created Sep 7, 2017. Star 0 Fork 0; Star Code Revisions 1. Embed. What would you like to do? Embed Embed this gist in your website. Share Copy.  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. Here is an example of a magic square: If we sum up the numbers on each row, (2+7+6, 9+5+1 Python Math: Exercise-20 with Solution. Write a Python program to calculate magic square. A magic square is an arrangement of distinct numbers (i.e., 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 The following program creates and displays a magic square. # Create an N x N magic square. N must be odd. import numpy as np N = 5 magic_square = np . 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 Algebra Magic Square. 5. 0: 4. 0: 3. 0: 2. 0: 1. 0: 0. Rate this resource. Students are presented with a 3 by 3 grid and a series of cards each containing an algebraic statement. Students are required to place the cards on the grid in such a fashion that each row, each column and each diagonal add to give the magic 'number' of 12a + 15b. Students are then challenged to make up their own puzzle. Although this is technically a magic square, it is not a very interesting example since there is only one number to calculate. 3x3 Magic Squares In a normal 3x3 magic square, the grid will consist of 9 boxe Non-Normal Magic Squares A magic square of order n was said to be normal if it was magic and the numbers 1, 2, 3, , n 2 are used in the cells.. Other, non-normal magic squares can be easily constructed using the rules we have described in the other pages with the entries being elements of an arithmetic progression

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