What is the magic number ? Is there 1 set of formulae for an even set of numbers and a different set of formulae for when the there is an odd number ? Thanks. He did, however, discover magic squares using 36 triangular numbers from 0 to 630 (with a magic sum equal to 1295). " This 2 sided activity has one magic square on each side, for a total of 20 problems. How to solve 3x3 magic square simple solution in Tamil Use 1 to 9 number Should not repeat All row coloum and diagonal sum should be 15 First write one to nine three numbers in a line than make. Published February 2000,July 2007,August 2007,February 2011. A magic square is an arrangement /data/ak$. , 3×3, 5×5, 7×7. A magic square with magic total 34. Here's an example. Its the game where you have to fill the boxes with numbers from 1 to total number of boxes such that sum of any row or column must be equal to other. A square consisting of consecutive numbers starting with 1 is sometimes known as a “normal” magic square. Simplify the problem and call yourself again. Recently an algorithm was developed that allowed the automatic generation of any magic square of odd-numbered dimensions. Product-magic squares question. Question: Tag: python,algorithm,decorator,python-decorators,rate-limiting I found this rate-limiting python decorator based on redis classes. Since there is the same sum for the three rows, three columns and two diagonals, it is possible to write down eight simultaneous linear equations for the nine unknowns (one in each cell). For a magic square of order n, the magic sum is (n) = 1 n ∑n2 k=1 k which turns out to be (n) = n3 +n 2: Here is the beginning of a table of. If n x n is the size of the magic square, and if the numbers in the magic square start from 1 onwards, than the magic constant is given by (n(n 2 +1))/2. About the Sum of Things. The encoding process repeats the following: multiply the current total by 17 add a value (a = 1, b = 2, , z = 26) for the next letter to the total So at. Similarly for the columns. This sum is known as the magic sum or the magic constant of the magic square. The puzzle consists of a 3 × 3 grid whose squares have to be: filled with digits from 1 through 9. A Magic Square is: The square is itself having smaller squares (same as a matrix) each containing a number. All of the B squares and C1, C2, C5, C6, F1, F2, F17, and F18 have black borders. The smallest semi-magic squares of cubes currently known are 4×4 constructed in 2006 by Lee Morgenstern, an American mathematician. Order-7 with Square Inlays. 3x3 magic squares of squares! Best regards. A 3 x 3 magic square is a 3 x 3 grid filled with distinct numbers from 1 to 9 such that each row, column, and both diagonals all have the same sum. Updated: Feb 12, 2014. The normal variations of these puzzles (the 3x3 puzzles that contain only 1-9) will have a magic constant of 15. Show your work. How to solve 3x3 magic square simple solution in Tamil Use 1 to 9 number Should not repeat All row coloum and diagonal sum should be 15 First write one to nine three numbers in a line than make. After completing the Easy Kids Math Square Game, let's move on to a more challenging Math 3×3 Magic Square. The metal of Moon is silver. In fact, [2] gave a generalization of magic square of order 4, [3] develop an algorithm for all magic squares of order four and Dawood, et al. Using these numbers, 2 4/9, 2 5/9, 2 6/9, 2 8/9, 3, 3 1/9, 3 3/9, 3 4/9 & 3 5/9. Magic Squares (#124) A magic square of size N is a square with the numbers from 1 to N ** 2 arranged so that each row, column, and the two long diagonals have the same sum. and the square can be transposed to another by moving any column or row to the opposite. 3x3 Magic Square of Squares ($1000 prize) The basic idea of a magic square is that the rows, columns, and diagonals all add up to the same magic sum. This pdf has been removed. Let's define a magic square as a matrix whose sums of all the numbers on a line, a column and on both the main diagonal and the main anti-diagonal are the same. 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. A 4x4 Magic Square is the first magic square of even order as a 2x2 magic square is not possible. Create your own Decimal Magic Square for a classmate to solve. From the wikipedia entry on Magic Squares: a magic square is a square grid (equal number of rows and columns) filled with distinct numbers such that the numbers in each row, and in each column, as well as the numbers in the main and secondary diagonals, all add up to the same value, called the magic constant. The Sum of Magic Squares is a Magic Square and the product of a Magic Square M with a number a is again a Magic Square aM. Make A 4x4 Magic Square From Your Birthday! Year {{ column }} The sum of every row, column, diagonal, and most 2x2 blocks is Birthday Magic Squares Video on. My 6x6 magic square of squares is NOT using squared consecutive integers but it is interesting to see the used numbers:. The simplest magic square is the 1x1 magic square whose only entry is the number 1. Enter the size of the magical square and if you want a magic sum for the square. magic square (n = noun. 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: Each 2×2 subsquare, including wrap-round, sums to s / k , where s = n ( n 2 + 1)/2 is the magic sum. The general approach to writing a recursive function: Handle the simple cases. Ask your friends to arrange the numbers from 2 - 10 in the 9 cells of the matrix to get the sum of 18 in any direction. c) If x' = (x-1) mod 2 + 1, then: for all 7040 squares every row and every column sums up to 6. on your worksheet. In a magic square you have to add 3 numbers again and again. Magic squares are easy to construct, and one usually tries to impose additional restrictions. Simple method for 3 by 3 magic squares Solve the 3x3 magic squares in no time! This video show 2 ways on how to efficiently solve the 3x3 magic squares with 100% accuracy. The number of 5 is multiplied exponentially by 2. To me that's not a magic square, but then again maybe your book says it is. For the 6×6 case, there are estimated to be approximately 1. 8 per 100,000. justify that15 is the sum of eachrow of a 3X3 magic square using the number 0-9. -----Prize puzzle. The Magic Sum of the 9x9 square is 3,285 being the number of days in a 9 year period. What I have so far is a matrix with letters as entries. This magic square is only comprised of Prime Numbers less than 100, with no repeated numbers. Interesting, because most of the 3x3 squares with 7 correct sums come from the Lucas family, in which the magic sum is a square. We define a magic square to be an matrix of distinct positive integers from 1 to n 2 where the sum of any row, column, or diagonal (of length n) is always equal to the same number (i. The magic constant for a order-3 normal magic square (a 3x3 magic square) will always be 15. Self-complementary magic square when it is a magic square which when complemented (i. Published February 2000,July 2007,August 2007,February 2011. If the Lo Shu is considered a matrix and is muliplied by itself three times, a new magic square is formed. If the sum of a second column = 9, the sum of the last column will be 36. File Square. The normal variations of these puzzles (the 3x3 puzzles that contain only 1-9) will have a magic constant of 15. How would I generalized the set of all 3 x 3 magic squares? I don't know what to do this at all for this. Minimal Sum Value (by default) See also: Sudoku Solver — Matrix Calculator. Show that d/s is an integer. Materials: Decimal Magic Squares 1. If you haven’t heard about it before, the 3x3 magic square is a matrix where the sum of every number in an edge or a diagonal equals to 15 (the magic number). John Hewson had a thorough analysis of the 18 combinations of three values:. A 4x4 Magic Square is the first magic square of even order as a 2x2 magic square is not possible. Solving 3 x 3 Magic Squares. Also includes Benjamin Franklin magic square for kids. The magic constant of a normal magic square depends only on n and has the following value: M = n(n^2+1)/2. Improve your odds for winning Bingo, contests, etc. You may like to try this with other sets of three consecutive numbers (numbers which come one after the other). 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. 3x3 magic square for sum 30, 78, 90, 216, 237 & more worksheet with answers to practice & learn 4th grade math problems on patterns is available online for free in printable & downloadable (pdf & image) format. n = 3, 4, 5, …, the magic constants are: 15, 34, 65, 111, 175, 260, … We are given a square board of. See also Killer Sudoku – Wikipedia | Printable Sudoku Sum from Printable Sudoku Free Topic. This page has 3x3, 4x4 and 5x5 magic square worksheets that will get you ready for other challenges like the printable sudoku puzzles and more!. It is the only Magic Square solution if we require the center number to be 5. An order-7 magic square uses the 16 primes between 1 and 49 to form the number '19'. 7 10 8 6 3) The sum is 27. Make A 4x4 Magic Square From Your Birthday! Year {{ column }} The sum of every row, column, diagonal, and most 2x2 blocks is Birthday Magic Squares Video on. The 3x3 magic square was used as part of rituals in India from vedic times, and continues to be used till date. Fill 3x3 magic square with distinct numbers 1. A 3 x 3 magic square is a 3 x 3 grid filled with distinct numbers from 1 to 9 such that each row, column, and both diagonals all have the same sum. Task: Arrange digits, in a 3x3 square to make magic squares. Magic Square Matrix Date: 03/24/2003 at 10:47:27 From: John Subject: Magic squares Let M be an integer-valued 3x3 matrix whose entries form a magic square. Below is a 3 x 3 example. Magic square problem: 1. Sun Kamea in Astrology The Sun represents the conscious ego, the self and its expression, personal power, pride and authority, leadership qualities and the principles of creativity, spontaneity, health and vitality, the sum of which is named the “life force”. More formally, the sum of the entries yields what is refered to as the Magic Constant: The smallest Magic Square is a 1 x 1 square with entry '1': The next simplest Magic Square is a 3 x 3. A "magic square" is magic in both rows and columns. In recreational mathematics, a magic square is an arrangement of distinct numbers, usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the forward and backward main diagonals, all add up to the same number. A perfect magic square is a n n square in which each of the entries 1;:::;n2 is used exactly once, and one in which the sum of. There are certain rules for 3 × 3 as well as 4 × 4 magic square. as was done in the original method. Benjamin Franklin found himself charmed by these properties, and would often strive to produce magic squares of his own. ( NOTE: This sum must be n*(n 2 +1)/2). 1 To construct a (3 x 3) magic square. Given an grid of integers, how many 3 x 数据结构与算法. First off, we need to assign the order 4 to the magic square and set a number as the value of the smallest element of the magic square. You could also add the same number to each of the nine numbers in a magic square, and the result would clearly be a new magic square. This magic square uses a 4x4 matrix with 16 cells. The sum of the numbers in every row, column and diagonal must equal 27. 8x8 magic square of order 8 and astrological planet Mercury with magic constant 260. For an example, see the picture below. Properties of magic squares. This is a natural extension to the problem. The magic square given above is of order 5X5 and it's sum is 65. The oldest magic square of order four was found inscribed in Khajuraho, India dating to the eleventh or twelfth century. If the Lo Shu is considered a matrix and is muliplied by itself three times, a new magic square is formed. Magic Square is invented puzzles in the magic is an arrangement of numbers, Magic Square Serves Online Sudoku Games,Online Puzzle Games,Free Online Games,Maths Game,Brain Games,Puzzle Games. The general approach to writing a recursive function: Handle the simple cases. All the rows contain all nine x as do the the three triads. It is known as the Chautisa Yantra since its magic sum is 34. Before going further, stop and think about how many 3x3 magic square solutions might exist. This magic square can be made simply by flipping both the diagonals. The magic constant is 369, formed by 3x1, 3x2, 3x3. 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. 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. Instructions to Students: On an exam’s matching portion, if using a 3x3 magic square, you would have 9 items. Minimality of K = 216 for 3x3 mulgic square, Proof sketch:. Algorithms that create magic squares are even cooler. Python recursive function not recursing. The total possible magic squares that can be created from the numbers 1, 4, 9, 16, and 25 are 1, 0, 1, 880, and 275,305,224, respectively. 3 X 3 magic square recursively c++,algorithm,math,recursion I'm trying to find all possible solutions to the 3X3 magic square. Also at Level 4, Fractional Magic Squares. Shaded 3x3 squares are magic squares. // Determines if a 3x3 grid of numbers is a magic square. 42/3 = 14 is the middle no. Sum of all the rows,columns,pillars and files is 514. We fill the squares in the grid with the numbers from 1 to 9, without repeating the same number twice. A magic square is a n n grid of numbers such that the sum of each row is equal, and equal to the sum of each column. Magic squares are squares that contain particular numbers arranged in equal rows and columns such that the sum of each row and column (and sometimes diagonal) are the same. Magic squares exist for all values of n, with only one exception - it is impossible to construct a magic square of order 2. Magic square sum 15. If the Lo Shu is considered a matrix and is muliplied by itself three times, a new magic square is formed. Let M be the common sum along any row, column or diagonal of the square. The colours are opposite Sun colours: yellow for numbers and purple or magenta for the background. This is a 3x3 magic square which uses the numbers 1 to 9: 276 951 438 In this article we will use. The ORDINAL Greek value of "Jesus Christ" = 205 and the 205th Semiprime = 685. This sum is known as the magic sum or the magic constant of the magic square. have left me a bit stumped I am afraid. The magic square given above is of order 5X5 and it's sum is 65. Consider normal magic. Here is a magic square. Here are the rules to construct a magic square:. So, for example, in a 3x3 magic square, n = 3. Fill each square so that the sum of each row is the same as the sum of each column. The number 15 is called the magic number of the 3x3 square. The odd numbers never appear in the corners of a 3x3 magic square Using only the digits 1 to 16 complete the magic square s0 that the sum of each row, column or diagonal is 34. Example 1:. 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. Bottom right = 0. The square of Varahamihira as given above has sum of 18. 8 1 6 3 5 7 4 9 2 Is a magic square. Albrecht Dürer introduced the Magic Square in 1514 in one of his paintings "Melancolia I". Go through right corner. Find the sume of all the numbers. Magic Square of Jupiter – Hermetic Baphomet, Eliphas Levi “In the Western Occult Tradition, each planet has traditionally been associated with a series of numbers, and in particular, the organizations of those numbers. The lowest possible value in the center cell for a 3x3 Magic Square is 5. By learning magic square the students may commemorate Birthday of Ramanujan, falls on 22nd December 1887. We also know 5×5 and 6×6 squares, then 8×8 and 9×9, but not yet 7×7. Use your calculator to figure out which number is incorrect in the following magic squares. Create all the eight 3x3 magic squares. The sum of all the numbers of the square is 3321. The typical (or normal) magic square consists of consecutive integers (starting with 1 and ending with n²) placed into 'n' rows by 'n' columns so that all rows, all columns and both diagonals sum to the same total. This means 45 = 3M so 15 = M. The ORDINAL Greek value of "Jesus Christ" = 205 and the 205th Semiprime = 685. python,recursion. Add this game to your site Newsletter. How can you determine the sum by using a key number in the magic square? 54. Is an arrangement of 9 distinct integers, in a square, such that the numbers in all rows, all columns, and both diagonals sum to the same constant 8-bit Pixel Art Magic Square with Numbers 1-9. The conjecture is that it would work for squares of any order, but that may not have been proven yet. Little Magic Squares and A Square of Circles , Level 2, Big Magic Squares Level 3. To my surprise it worked. For normal magic squares of order. 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. Below i have a check for 15 vert hor and diag. The magic square corresponding to wp ( 7,11,13,14), below the dual matrix There are 24*9=216 Walsh permutations that correspond to magic squares of order 4. 3x3 magic square of order 3 assigned to astrological planet Saturn with magic constant 15. 3x3 Magic Square of Squares ($1000 prize) The basic idea of a magic square is that the rows, columns, and diagonals all add up to the same magic sum. The top and bottom half of each row and column sum to 130. It has been shown that "the question of whether there is a 3x3 magic square of squares is equivalent to the question of whether there. Complete this 3 x 3. The sum of 1-9 = 45. 1 The next simplest is the 3x3 magic square where the sum is 15. You can click on the numbers to select them. This information is useful in many situations. We define a magic square to be an matrix of distinct positive integers from 1 to n 2 where the sum of any row, column, or diagonal (of length n) is always equal to the same number (i. A simplified idea is introduced to check when it is possible to obtain minimum perfect square sums. 2 where the sum of any row, column or diagonal is always equal to same number. MAGIC SQUARE WORKSHEET 2. A magic square is an nxn (i. I have a taller and more magical order, however, demanding similarly that the two diagonals sum to 33, and also for each of the four 2 x 2 blocks (an exercise shows that then also the central 2 x 2 block, in the middle of the 4 x 4 square, must have sum 33). 1729 = 10 3 + 9 3 = 12 3 + 1 3. Mercury Magic Square. Enter the size of the magical square and if you want a magic sum for the square. Magic Square (Python) The sum is called the magic constant or magic. I was told by others that the matrix is 8x11. Improve your luck in all aspects of life. In any 3x3 Magic Square this "Magic Sum" will be 3 times whatever the value is in the center cell. A simplified idea is introduced to check when it is possible to obtain minimum perfect square sums. Unlike most magic squares they have seen in the past, this magic square is unique. they share a square in common. Hence, Total Sum = 4 * (Magic Sum - Middle Number) + Middle Number. program to find the magic square using array. The Jaina Square. On the other hand, if we sum up all 9 elements, we must have the sum of the numbers 1 to 9. ===> Square of Jupiter A talisman made using this square gives power and prestige to the bearer. centre square = 2. You will know you have solved the magic square when the sum of each row, column, and diagonal totals 65. ) You can use this method to check if the square has been tampered with. Use a pantriagonal 4x4x4 magic cube and a panmagic 7x7 square to construct a pantriagonal 28x28x28 magic cube, consisting of 343 proportional pantriagonal 4x4x4 magic cubes. do they know any. Magic square problem: 1. Minimal Sum Value (by default) See also: Sudoku Solver — Matrix Calculator. ) In a general magic square of order n, the magic sum S to which the numbers in any. 1234 567 8 9 Player 1: 3. VSR explains how to create magic squares in few seconds using Vedic Mathematics. 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:. The sum is referred to as the magic constant. In addition, bent diagonals (such as 52-3-5-54-10-57-63-16) also total 260 (Madachy 1979, p. The oldest and most common magic square known is the one with integers from 1 to 15 with a. For the answer key, please click here. The simplest magic square is the 1x1 magic square whose only entry is the number 1. They have a long history, appearing in both ancient Chinese scriptures and Dark Ages Christian sculptures. ROSS ECKLER. In this puzzle the sum in every row, column and diagonal is 15. 1,2,3,… ,n2, With in this formula we find that the magic sum of the square in Figure 10, which may be verified by direct addition, is There is a method of constructing an odd-order magic square which is attributed. Let's define a magic square as a matrix whose sums of all the numbers on a line, a column and on both the main diagonal and the main anti-diagonal are the same. Could you work this out just from knowing that the square uses. There is another method where you can generate the first 4 sets of 3x3 magic square and then derive the remaining 4 by subtracting 10 from each element. This is the only 3 x 3 magic square that can be made excluding reflections and rotations. 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. 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. 17 = 2 3 + 3 2 This is the only number of the form x + p q + q p. The problem of Magic Squares is to generate a square (2x2, 3x3,. This magic square can be made simply by flipping both the diagonals. Example 1: Input: [[4,3,8,4], [9,5,1,9], [2,7,6,2]] Output: 1 Explanation: The following subgrid is a 3 x 3 magic square: 438 951 276 while. Magic Squares Task 2. 3x3 magic squares, but only one will give you the right message, so do the experiments carefully! Remember that each row, column, and diagonal in your square must add up to the same number. FindCreate all the eight 3x3 magic squares. It is impossible to construct a 2 by 2 magic square (n = 2) and so the first. Tes Classic Free Licence. 3x3 magic square for sum 30, 78, 90, 216, 237 & more worksheet with answers to practice & learn 4th grade math problems on patterns is available online for free in printable & downloadable (pdf & image) format. Boyer proved that magic squares of triangular numbers are impossible for orders 3, 4, and 5. The sum of two magic squares is a magic square ; The scalar multiple of a magic square is a magic square. 3x3 Magic Square of Squares ($1000 prize) The basic idea of a magic square is that the rows, columns, and diagonals all add up to the same magic sum. My assignment is to make a magic square based on an odd integer entered by the user. A magic square has the same sum in each row, column, and diagonal. The oldest and most common magic square known is the one with integers from 1 to 15 with a. the same sum. The 9 numbers that will go inside of the squares can be multiples of numbers, consecutive numbers, odd/even consecutive numbers, etc. Derive the remaining magic squares by reflections and rotations (based on Presh Talwalkar's blog). 65 is also the sum of two squares two different ways: 8² + 1² = 65; 7² + 4² = 65. For example, 36 is: a perfect square, 6^2 and the sum of the integers 1 to 8 (1+2+3+4+5+6+7+8 = 36) so let us call a "magic square" any number that is both a perfect square AND equal to the sum of consecutive integers beginning with 1. 17 = 3 4 - 4 3 Is this the only number of the form x + p q - q p? JRM 30:3, page 234. 82 ( 6) 7 Gan356R 3x3 Magic Cube Educational Toys for Brain Training - Colorful US$ 14. Write a number in each circle so that the number in each square equals the sum of the two numbers on either side of it. have the same sum—the magic sum. A 1 by 1 magic square contains just the number 1 and is so simplistic, it is not worth discussing. Being pan-diagonal, the broken diagonals also sum to the magic constant. Figure 1:. all the cells), and all 3x3 and 4x4 squares sum to 34 (the magic constant). The idea of nested magic squares is well known in the literature, generally known by bordered magic squares. Good luck! 16 3 2 13 5 10 11 8. Sum of each row and column should be equal. A magic square is an arrangement of numbers in a square in such a way that the sum of each row, column, and diagonal is one constant number, the so-called "magic constant. The numbers 1 to 9 are placed in the small squares in such a way that no number is repeated and the sum of the three digits column-wise, row-wise and diagonally is equal to 15. to turn your ‘semi-magic’ square into a ‘magic’ square. A magic square is a square matrix in which the sum of every row, every column, and both diagonals is the same. 16 corners of 3 x 3 squares; 16 corners of 4 x 4 squares. Play this puzzle with friends or students. This magic square is only comprised of Prime Numbers less than 100, with no repeated numbers. Dürer's magic square has the additional property that the sums in any of the four quadrants, as well as the sum of the middle four numbers, are all 34 (Hunter and Madachy 1975, p. The number 15 is called the magic number of the 3x3 square. It is impossible to construct a 2 by 2 magic square (n = 2) and so the first. The only way to get 7. For any Magic Square of the order 3 x 3; the first term of the progression will be F = S/ 3 - 4D Here S denotes the Magic Sum, F the first number of the sequence used for filling and D the common difference between the numbers in the sequence. 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 to the sum for each line and both diagonal lines. Magic Squares of Order 3 At the beginning, we saw the 3 3 lo-shu magic square. By early April, St. A "magic square" is magic in both rows and columns. VSR explains how to create magic squares in few seconds using Vedic Mathematics. htm Miscellaneous Patterns added July 2007. The Siamese method, or De la Loubère method, is a simple method to construct any size of n-odd magic squares (i. Magic Squares One are of such problems is permutations, i. This problem is part of a series exploring magic squares. I sorted the deck into single colors, and then started constructing a square. A normal 3x3 magic square has a sum of 15. Bimagic square. These are often referred to as doubly-even magic squares. The magic constant of a normal magic square depends only on. While we have only looked at three cell magic squares so far, you might have noticed a couple of things that turn out to be fundamental to all odd cell magic squares. A 3x3 magic square is a 3x3 grid containing the numbers 1-9 once each, and in which every row, column, and diagonal sums to 15: 294 753 618 And I presume we all know the rules to Sudoku. 4 9 2 3 5 7 8 1 6 Some de nitions also require the sum along the main diagonals to add to the same total. Using these numbers, 2 4/9, 2 5/9, 2 6/9, 2 8/9, 3, 3 1/9, 3 3/9, 3 4/9 & 3 5/9. A 3x3 pattern of magic square, known as the 'Lo-Shu' in Chinese, was the base of the Tibetan calendar and astrology. "An alpha-magic square is a math puzzle in which the numbers of letters needed to spell the numbers also form a magic square … so that the array above adds to a constant sum of 216 on any row, column, or diagonal AND the numbers of Cyrillic letters needed to spell the Russian names of the numbers in this array, or precisely 15, 9, 12 / 9, 12, 15 / 12, 15, 9, also adds to a constant sum (36. The key to a magic square is that all the rows of triads ( or three elements ) and columns of triads must add up to the same number, lut us say T. For example, 4 + 3 + 8 = 15. If you make a mistake you can click on a number to deselect it. The one in the corner is the most familiar one. A magic square of singly even order has a size that is a multiple of 4, plus 2 (e. 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. A most-perfect magic square of order n is a magic square containing the numbers 1 to n2 with two additional properties:. asked by Mark on April 22, 2010. Complete figure 1 by putting numbers in the blank squares so that the sum for each row, column, and diagonal is 27. The magic constant of a normal magic square depends. For a function that returns true/false, there will be 3 conditions: you know the answer is true, you know the answer is false, or the problem is still too complicated. 1 Answer to Arrays (25 points) A magic square is an n × n grid of numbers with the following properties: 1. Add the numbers 24 and 26 to the empty two internal cells. 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. A 3 x 3 magic square is a 3 x 3 grid filled with distinct numbers from 1 to 9 such that each row, column, and both diagonals all have the same sum. centre square = 9/6: This means that the sum of the magic square has to be 27/6. 4 9 2 3 5 7 8 1 6 All other normal 3x3 magic squares are rotations and/or reflections of the Lo Shu square. well after making a couple of squares of order 3, 5 ands 7, i see a pattern as to how one can choose the magic sum to one's liking for a specific odd order. Magic Square (5x5) 27 Feb 2020. ) Different algorithm, but it's also workable in this type of formula. so hard (in PROLOG) Magic Squares. Materials: Decimal Magic Squares 1. The Magic Sum of the whole 27x27 square is 9,855 being the number of days in a 27 year period. The idea of bordered magic squares is well known in the literature. 3×3 Square Puzzle, let's continue the challenge with this 3×3 Square. Also at Level 4, Fractional Magic Squares. Select a Magic Square. Some numbers are already filled-in in a 3x3 square. "Mercury Magic Square: the magic constant is 260, the sum of all the numbers of the square is 2080. It is also an instance of most perfect magic square. Magic Squares (#124) A magic square of size N is a square with the numbers from 1 to N ** 2 arranged so that each row, column, and the two long diagonals have the same sum. then, magic square with sum = 42 is. Here's a summary: In recreational mathematics and combinatorial design, a magic square is a square grid filled with distinct positive integers in the range such that each cell contains a different integer and the sum of the integers in each row, column and diagonal is equal. A magic square is an nxn (i. It consists of two sets of the natural numbers 1–8, and its constant sum (p) is 18. Magic square 2: 1. A checker - returns the common sum if the square is magic, or undef if it's not. The only way to get 7. 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:. 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. let us state the order as x. on your worksheet. A magic square of order n is an arrangement of n 2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. 42/3 = 14 is the middle no. Let us see if we can try to create one on our own. Magic Square (5x5) 27 Feb 2020. Each cell in a nXn grid has a different number and the numbers range from 1 to n 2. "An alpha-magic square is a math puzzle in which the numbers of letters needed to spell the numbers also form a magic square … so that the array above adds to a constant sum of 216 on any row, column, or diagonal AND the numbers of Cyrillic letters needed to spell the Russian names of the numbers in this array, or precisely 15, 9, 12 / 9, 12, 15 / 12, 15, 9, also adds to a constant sum (36. a 3x3 square grid) has 9 elements such that the SUM of the 3 numbers in all 8 main directions (three rows, three columns, and both diagonals) is the same. 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. Magic Square We've all seen examples of magic squares. You find more on my page Magic Square. ROSS ECKLER. “Moon Magic Square: the magic costant is 369, formed by 3x1, 3x2, 3x3. Courtesy Fortean Picture Library. An order 7 magic square would total 175, while an order 10 magic square would equal 505. All answer keys are included for easing. 4 magic squares that use catchup for the main diagonals in two of their base squares combine to make two Catchup2 groups. An algorithm which works for odd order squares will not work for even order squares without the further addition of another algorithm. The sum of each row, column and main diagonal must be equal. The magic constant = n[(n^2+1)/2]. How to check for multiple attributes in a list. The Magic Sum of the inner and central 3x3 square is 1,095 being the number of days in a 3 year period. As the common difference is 1, we get the first 6 natural numbers for filling. Complete the 5x5 magic square. If n x n is the size of the magic square, and if the numbers in the magic square start from 1 onwards, than the magic constant is given by (n(n 2 +1))/2. Explain 5 (a) If x is an integer, explain, in terms of x, why the magic sum of an altered Lo-Shu magic square could never be 22, 38 or -2. 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 this work, bordered magic squares are constructed in such a way that the final magic sum of each bordered magic square is 2020. Your task is to write a program that reads the order of a magic square, and then reads n2 additional. This means 45 = 3M so 15 = M. Plated in 14-karat gold, the Magic Square can be worn or carried. Slide 7: The Magic Formula To find out what the magic total is, we can use a formula, which will tell us the total of the rows, columns, diagonals etc. Magic Square Solver. Therefore there is only one magic 3x3Therefore there is only one magic 3x3 square. 5x5 magic square with sum 65 of. If you want to build a magic square, check this article, the python code is at the bottom – How to build a magic square A magic square is an arrangement of the numbers from 1 to N^2 (N-squared) in an NxN matrix, 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. For 7x7 the row sum is 175 What is the row sum for 9x9? Here is the summary of the magic square rules. The idea of bordered magic squares is well known in the literature. Sum is the term we use for the answer of an addition problem. First, the sum squares of the numbers in the top and bottom row are equal. Magic Square Game In this magic square game you have to move the numbers on the right inside the squares, so that the sum of any three numbers vertically, horizontally, or diagonally equals to 15. Mathematics can be used to discover the general form of all 3 x 3 magic squares. Top right = 1. Describe or list every possible magic sum for a 3x3 magic square. While the LuoShu (3×3 magic square) is simple to memorize by itself, one visual trick to remember the layout of the nine numbers is the Taijitu (yin-yang symbol). 24 2 4 16 22 32 6 20 8 3) The sum is 340. By learning magic square the students may commemorate Birthday of Ramanujan, falls on 22nd December 1887. The conjecture is that it would work for squares of any order, but that may not have been proven yet. com) Interesting artwork containing a variety of Magic Squares even 6 x 6, 7 x 7, and 9. 27 ( 5) 4 Number Adjustment IPG GAN356 3x3x3 Magnetic Magic Cube Puzzle with Removable Magnets - Stickerless Version US$ 124. In a magic square, each row, column and diagonal add up to the same total. " 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. It's O(N) 'why to use DP of O(N2)' : You don't need to for this problem. Discrete Mathematics 47 (1983) 1-11 1 North-Holland NIULICATIVE MAGIC SQUARES D. Magic Square Puzzles Magic squares are one of the simplest forms of logic puzzles, and a great introduction to problem solving techniques beyond traditional arithmetic algorithms. , 1 to 9, the same square always results; it may be reflected, rotated, or both, but it is always the same square. The Lo Shu square is an ancient 3x3 magic square which features in Chinese divination. Explain Yang Hui’s method for constructing a 3x3 magic square? 4. This magic square adds up to 34. Boyer also found that there are magic squares of order 7, which use the first 49 triangular numbers, starting with 0. A magic hexagon of order n is an arrangement of numbers in a centered hexagonal pattern with n cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant M. For example, 4 + 3 + 8 = 15. The sum of the integers from 1 to N is given by the well-known formula N(N+1)/2. The 3x3 square on turtle is known in China as the lo shu. Minimal Sum Value (by default) See also: Sudoku Solver — Matrix Calculator. The only way to get 7. The normal variations of these puzzles (the 3x3 puzzles that contain only 1-9) will have a magic constant of 15. Thus, the magic square constant is the sum of the first 16 digits (= 136) divided by 4 (the order of the square). Magic Square is a square in which the rows, the columns and the diagonals all add up to the same number – the Magic Number. There are 3 different sizes of grids (3x3, 4x4 and 5x5) with 3 worksheets of each size. 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 Magic squares (3X3). A magic square with magic total 34. With that done you should be able to finish the rest of the square. Magic Square Examine the 3 by 3 magic squares and find the sum of the four corner entries of each magic square. However, the concept may be extended to multiply. The sum of numbers in any row 8x8 magic square with sum 260 of planet Merxury. “Mercury Magic Square: the magic constant is 260, the sum of all the numbers of the square is 2080. So ALL rows, columns and diagonals should add up to 3. The Lo Shu grid is a 3 X 3 magic square in which the sum of the three numbers add up to 15 - row wise, column wise and diagonally. Using isequal to compare against the MATLAB magic square of a given size will not work, because of how many magic squares there are: "Excluding rotations and reflections, there is exactly one 3×3 magic square, exactly 880 4×4 magic squares, and exactly 275,305,224 5×5 magic squares. Magic Squares By Leighton McIntyre Goal: To arrange numbers in 3x3 and 4x4, addition and product magic squares Magic Squares Given the integers 1 through 9, we know that 1 + 2+ 3 + …. This is a 3x3 magic square which uses the numbers 1 to 9: 276 951 438 In this article we will use. 17 = 3 4 – 4 3 Is this the only number of the form x + p q - q p? JRM 30:3, page 234. The Lo Shu Magic Square appeared a few years ago when I wanted to know more about Acupuncture. 4 9 2 3 5 7 8 1 6 Some de nitions also require the sum along the main diagonals to add to the same total. The magic square below is a normal 4x4 magic square. Magic squares can be classified into three types: odd, doubly even ( n divisible by four) and singly even ( n even, but not divisible by four). Make a 3x3 magic square whose sum is equal to 27 Get the answers you need, now!. This is the turn of a nice puzzle sent by Christian Boyer, even if this is not particularly related to primes: A 3x3 magic square of cubes is proved impossible. 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. A symmetric magic square is also called an associative magic square (11, p. The trick with making such a square is to place the number 1 in the first row and middle column. 3x3 magic squares, but only one will give you the right message, so do the experiments carefully! Remember that each row, column, and diagonal in your square must add up to the same number. What is the magic number ? Is there 1 set of formulae for an even set of numbers and a different set of formulae for when the there is an odd number ? Thanks. 10 in the magic square above) multiplied by 3 is the sum of the rows or columns or diagonals. These would have order 6, 10, 14,. Determining the number of different magic squares of order 6 or larger is an unsolved mathematical problem. The odd or evenness of a magic square is solely dependent on the value of n. Consider a 3 X 3 matrix, s, of integers in the inclusive range [1, 9]. ( NOTE: This sum must be n*(n 2 +1)/2). This means 45 = 3M so 15 = M. c) If x' = (x-1) mod 2 + 1, then: for all 7040 squares every row and every column sums up to 6. Consider normal magic. 17 = 2 3 + 3 2 This is the only number of the form x + p q + q p. It would be very interesting to find a parametric solution with a non-square magic sum, generating an infinite number of 3x3 squares. Thus each of first row, second row, and third row has a sum of M. Step 2 Here, a 3-by-3 magic square is to be prepared using the numbers 3, 6, 9, 12, 15, 18, 21, 24 and 27. The simplest magic square is the 1x1 magic square whose only entry is the number 1:. How to solve 3x3 magic square simple solution in Tamil Use 1 to 9 number Should not repeat All row coloum and diagonal sum should be 15 First write one to nine three numbers in a line than make. This problem has been tied to various domains including arithmetic progressions, rational right triangles, and elliptic curves (Robertson [2]). Can you fill in the missing numbers in these magic squares? 1) The sum is 21. So, if every number was divided by 3, say, we would have a Fraction Magic Square, which is Task 37. The sum of two magic squares is a magic square ; The scalar multiple of a magic square is a magic square. Improve your odds for winning Bingo, contests, etc. Fill the empty spaces with decimal numbers so that the sum of the numbers on each row, column and main diagonal is equal to the given number. After completing the puzzle, check your work with your partner. My husband and I have spent hours trying to help our kids solve this but aren't getting anywhere!!!!. That led me to think about the minimum amount of information that we need to provide, in order to determine the magic square. The constant sum in every row, column and diagonal is called the magic constant or magic sum, M. A Magic Square is: The square is itself having smaller squares (same as a matrix) each containing a number. Fill in the number in the middle square (second row and second. 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. I found that the latter do indeed exist, and that although these appear to be similar to linear area magic squares, their construction is quite different for two reasons: Depending on the slopes (and lengths) of the slanting dissection lines of a perimeter. Once you have one, you can get all the others by. This is the smallest sum possible using the numbers 1 to 16. Magic squares are rather old. Pan-magic squares have also been called Pan-Diagonal and Nasik. This information is useful in many situations. In this work, bordered magic squares are constructed in such a way that the final magic sum of each bordered magic square is 2020. Properties of Magic Square: Sum of every row, column and diagonal are same. In one sense this is true, in another it is not. - #brainteasers #math #magicsquare - Correct Answers: 14. Magic Square We've all seen examples of magic squares. Find the sum of all of the rows, columns, and diagonals which involve x. Consider a 3 X 3 matrix, s, of integers in the inclusive range [1, 9]. According to legend the first known magic square was discovered by Emporor Yu in China about 2200 B. For the 6×6 case, there are estimated to be approximately 1. If the Lo Shu is considered a matrix and is muliplied by itself three times, a new magic square is formed. (NOTE: This sum must be n*(n 2 +1)/2) The simplest magic square is the 1x1 magic square whose only entry is the number 1:. asked by Hannah on February 24, 2011; math. Upon completing the 3 x 3 grid, every row, column, and diagonal will add up to equal the same value. 1,2,3,… ,n2, With in this formula we find that the magic sum of the square in Figure 10, which may be verified by direct addition, is There is a method of constructing an odd-order magic square which is attributed. Consider first a 3x3 magic square which we represent by the square matrix- G H I D E F A B C. Enter the size of the magical square and if you want a magic sum for the square. There are four pairs of opposite numbers, comprising eight of the numbers, each with the same sum, which is Magic Sum - Middle Number. ? If you know, it is worth a bet on Glamorgan winning their fourth championship. Thanks for contributing an answer to. It will enrich mathematics learning and ensure developing interest among students. Look at your first column, decide how to finish that to get a column sum of 15. ) Different algorithm, but it's also workable in this type of formula. Instructions to Students: On an exam’s matching portion, if using a 3x3 magic square, you would have 9 items. It is essentially the same as the Lo Shu Square, but with 19 added to each number, giving a magic constant of 72. It was inscribed on the wall of Parshvanath temple in Khajuraho India in the 12th Century. - #brainteasers #math #magicsquare - Correct Answers: 14. 8 per 100,000. Go to page 2 of the discussion for an updated version. 1 Answer to Arrays (25 points) A magic square is an n × n grid of numbers with the following properties: 1. I have changed different indices values and the program returns f. If n x n is the size of the magic square, and if the numbers in the magic square start from 1 onwards, than the magic constant is given by (n(n 2 +1))/2. 6 8 5 9 4 2) The sum is 18. A magic square is an arrangement of numbers in a square in such a way that the sum of each row, column, and diagonal is one constant number, the so-called "magic constant. Can you fill in the missing numbers in these magic squares? 1) The sum is 15. How to solve 3x3 magic square simple solution in Tamil Use 1 to 9 number Should not repeat All row coloum and diagonal sum should be 15 First write one to nine three numbers in a line than make. In a magic square, every row, column and each of the diagonals add up to the same total. A Magic Square is a grid of numbers (N by N) in which the rows, columns, and diagonals add up to the same number. 3 9 5 11 6 2) The sum is 30. Math, I am eager to know what was the largest magic square ever constructed and known in the world of mathematics. So each sum appears exactly once as a line in your square. It dates back to Chinese mythology, you can read the story here. However, Figure 12 shows a non-trivial 2 9 2 semi-magic. A product-magic square of order three has 9 elements such that the PRODUCT of the three numbers in all 8 directions (3 rows, 3. We start filing from V1 as shown in the figure along side. A heterosquare of order n is an arrangement of the integers 1 to n 2 in a square, such that the rows, columns, and diagonals all sum to different values. Your matrix can be 3x3; 4x4; 5x5; etc. See how to form a MS 3 X 3 with a magic sum of 132 and a sequence of common difference 5. This square is composed of the consecutive series of numbers from 1 to 81 and as is usual with pure magic squares, all rows, columns, and the two main diagonals sum to the constant 369. Some people claim that it may date to around 2800 BCE. In addition the partially bordered square may be everted to give an opposite square whose internal 3x3 square is the only magic square. ); M=2n+1 where n=0,1,2,3…These are referred to as "odd order" magic squares. Below i have a check for 15 vert hor and diag. Dürer's magic square has the additional property that the sums in any of the four quadrants, as well as the sum of the middle four numbers, are all 34 (Hunter and Madachy 1975, p. Benjamin Franklin found himself charmed by these properties, and would often strive to produce magic squares of his own. Look at your first column, decide how to finish that to get a column sum of 15. For the 6×6 case, there are estimated to be approximately 1. I have changed different indices values and the program returns f. There are routines for constructing magic squares of odd order: 3-by-3, 5-by-5, etc. Repeat with other magic squares from the pack. Select a Magic Square. When Kathleen Ollerenshaw introduced most-perfect magic squares in 1986 [1], she was referring to additive magic squares. Go ahead, try the two diagonals, you now. 25 1 49 -----It is not known whether such a magic square exists. Magic squares is n×n matrix with positive integer entries as well as the sum of rows, columns and mains diagonal have the same magic constant, one of the most oldest magic square was discovered. Calculate the magic constant. For example, in every 4x4 magic square, that sum, called the magic sum, is 34. VSR explains how to create magic squares in few seconds using Vedic Mathematics. do they know any. He utilized a modified magic square of order four in order to prescribe combinations and quantities of ingredients of perfume. Similarly for the columns. Keep this card and you’ll be able to perform this stunt any time you wish. How to solve a 3x3 magic square equal to 27? using the numbers 5,6,7,8,9,10,11,12 and 13. Unfortunately, the proof, which is based on the theory of eigenvalues, fails to bring out two important facts: 1. The normal variations of these puzzles (the 3x3 puzzles that contain only 1-9) will have a magic constant of 15. The sum of each row or each column or each diagonal can be found using this formula. Then just add 5 to each individual value in the square so that the sum comes out to 30 instead of 15. 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. 3 x 3 Magic Squares. Can you fill in the missing numbers in these magic squares? 1) The sum is 34. The general approach to writing a recursive function: Handle the simple cases. If you add up any row, column, or diagonal, it sums to the same number, 15. The metal of Mercury is mercury. There are four different sizes of grids (3x3, 4x4, 5x5, and 6x6) with two worksheets for each size of grid. However, the concept may be extended to multiply. Remarkably the two numbers will be equal for any magic square, and it is known as the “magic product”. Magic square. The 9 numbers that will go inside of the squares can be multiples of numbers, consecutive numbers, odd/even consecutive numbers, etc. GAN 356 X S. 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. For a magic square of order n, the magic sum is (n) = 1 n ∑n2 k=1 k which turns out to be (n) = n3 +n 2: Here is the beginning of a table of. Let us see if we can try to create one on our own. When two third-order magic squares are added term by term, a new magic square is formed. 04 Catchup2 magic squares and some T4. As a further restraint, these sums are also consecutive. 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. So, if every number was divided by 3, say, we would have a Fraction Magic Square, which is Task 37. A magic square (of order n) is an nxn array such that each number between 1 and n 2 occurs precisely once, and all row sums and column sums are equal. The square is already full. Rule 1: the central number (i. The magic constant of a normal magic square depends only on n and has the value For normal magic squares of order n = 3, 4, 5, 27 20 25 Arabia Magic squares were known to Arabian mathematicians, possibly as early as the 7th century, when the Arabs got into contact with Indian or South Asian culture, and The 3x3 magic square was used as. This reveals the underlying structure of a 3x3 Magic Square. Consider a 3 X 3 matrix, s, of integers in the inclusive range [1, 9]. Just click on one of the lines marked with the symbol to jump directly to the specified page. Here is the square: 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17 As explained by Franklin, each row and column of the square have the common sum 260. The Magic Constant is the value that you get for each row, column or diagonal sum in a magic square. Find the number of 3x3 Magic Squares in a given MxN matrix. In a letter to Peter Collinson he describes four properties of the 8 × 8 square F1 as follows: 1. If we draw a 3x3 grid (three squares per Row & three squares per Column), we will obtain a total of nine (9) squares overall in which we can arrange numbers in different combinations. 6, 10, 14). On the other hand, if we sum up all 9 elements, we must have the sum of the numbers 1 to 9. and the square can be transposed to another by moving any column or row to the opposite. magic sum= b*x+x( x^2 -1 /2) = x(b+(x^2-1)/2). We also know 5×5 and 6×6 squares, then 8×8 and 9×9, but not yet 7×7. There are no heterosquares of order 2, but heterosquares exist for any order n ≥ 3. So when using the numbers 3 to 11, the number 7 is in the middle, and the magic sum is 21. The sum of each row or each column or each diagonal can be found using this formula. In the 3x3 square, it is impossible to make all of the diagonals "magic". This method makes 3x3 magic squares with 5 or more perfect squares. I have been making it a 3 x 3 for checking as well but for. I have changed different indices values and the program returns f. The magic constant for a order-3 normal magic square (a 3x3 magic square) will always be 15. Magic Squares are square grids with a special arrangement of numbers in them. Odd Magic Squares. For the 6×6 case, there are estimated to be approximately 1. Not all combinations of four of these base squares will generate an orthodox magic square, but the agonals and main diagonals will always sum correctly. 3x3 Magical Square All Add Up To 27 - Displaying top 2 worksheets found for this concept. Preview and details. How to solve 3x3 magic square simple solution in Tamil Use 1 to 9 number Should not repeat All row coloum and diagonal sum should be 15 First write one to nine three numbers in a line than make. The well-known square F1, as well as the less familiar F2, were constructed by Benjamin Franklin. Here the numbers 1 to 8 appear twice in the square. It was inscribed on the wall of Parshvanath temple in Khajuraho India in the 12th Century. 3 9 5 11 6 2) The sum is 30. However, the concept may be extended to multiply. The constant sum in every row, column and diagonal is called the magic constant or magic sum, M. Returns the common sum of the rows, columns and. Examples are given for the magic squares of orders 3 to 25. Construct a 3 x 3 magic square with the magic sum of 2. 136 is the square sum of Jupiter, whose regent is Zachariel. Step 2: Combinations that sum to 15. 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:. Once you understand the multiplication method, your group should investigate the following questions, using examples of 3x3 magic squares. A problem due to Martin LaBar is to find a 3x3 magic square with 9 distinct perfect square entries or prove that such a magic square cannot exist (LaBar [1]). Files included (1) Magic Squares Worksheet.