# Magic Square 6x6

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Since the highest/lowest numbers used in our 6x6 were +/- 17 1/2, the numbers we will use are +/- 18 1/2 through +/- 31 1/2. The numbers in the Red Squares form the 3x3 magic Square. However, note that the two bottom quadrants are magic order-3 squares. is magic, since every row, column, and diagonal adds up to 4035. Item may leave raw edge and may have 1-2cm deviation exist. The other, blue, squares show the diagonal totals - including all of the "broken diagonals". In September 1997, I drove such an enumeration in 6 hours and half with a reduced program (group G of order 32 and permutation "complement to 26") on a K6 of AMD, running at 200 MHz, under Turbo Pascal. through magic square in the class room at high school level to know better, one of the contributions of Ramanujan. MoFang JiaoShi MeiLong 6x6. A magic square contains the integers from 1 to n^2. The number 666 is most famously noted in St. The constant sum in every row, column and diagonal is called the magic constant or magic sum, M. How would I calculate it. By learning magic square the students may commemorate Birthday of Ramanujan, falls on 22nd December 1887. The YuXin Little Magic 6x6 is a the newest 6x6 speed cube from YuXin. It is unknown if regular magic squares of cubes are possible for orders 4-8 (order-3 has been proved impossible). Inspiration was due to three young master-class students in Nijmegen, the Netherlands, who in March 2007 reached world news because they had constructed a spectacular 12×12 panmagic square (). the diagonals that wrap round at the edges of the square, also add up to the magic constant. Recently Viewed Products. Your starting number always goes in the center of the top row. These 6x6 magic squares, even in their normal forms, are quite challenging and good brian teasers for middle school math wizards or even for math saavy adults. Infinite 3x3 Magic Square, Amitai's Solution. The are other methods, but as we will see they are not as straightforward as the methods we showed for odd ordered magic squares and doubly-even ordered magic squares. The order n must be a scalar greater than or equal to 3. dadsworksheets. It holds true to the Little Magic name with its light and airy feel. A magic square contains the integers from 1 to n^2. The constant sum in every row, column and diagonal is called the magic constant or magic sum, M. So for the example below, 15 is the magic number. The reason being called a Magic Square is the sum of any row or column or diagona. 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. MAGIC WORD SQUARES LEONARD GORDON Tucson, Arizona This article shows how to construct a 6x6 magic word square using the method described in my Eulerian Magic Word Squares" (November, 1996). To the right is a 6x6 magic square of cubes constructed in 2008 by Lee Morgenstern. Almost the only thing that carried over from one nation to another was the notion that a magic square was a. Several 4x4 and 5x5 magic squares of squares are published in the M. To the authors' knowledge, these are the only known doubly pandiagonal magic squares. 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. The total number of rectangles in a square of nxn squares is equal to the sum of the 1 square wide rectangles for each rectangle from the 2x2 up to and including the nxn one being considered. nita-kaumudi of 1356,7 has fewer garbled squares, but the text is somewhat difficult. Candy found 640,120,320 irregular ones. The constant values $ M $ of the sums of the magic squares have a minimum value (for non-zero integer positive values). There is only one distinct Magic Square of order N=3. This 4x4 square we will place as 2x2 squares in the 4 corners in the left hand side 6x6 square. For example: Here the sum of all rows, columns and main diagonals is equal to 15. 6 x 6 and. e 4X4, 6X6…) Luckily, smart people noticed that there is some kind of a pattern for filling the correct numbers in the correct cells in order to get a magic square, as well as they also observed that odd magic squares follow a different pattern than the even ones. Can you show me? Is there a method? Is there different ways to do it using a sequential set of numbers and non-sequential? I am not really a Mathematician, but know a bit. This is one reason why 666 was demonized,. and planet Jupiter Jupiter seal derivation 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 Magic square of order three. "Even" Magic Squares may be further divided into two sub-categories: "singly even" Magic Squares, which means that the number of cells on each side of the Magic Square is evenly divisible by two, but not by four (e. boolean checkmagic() Returns true if the matrix is a magic square. For more details see: Ultramagic Squares of Order 7: D7 (November 2001) was a big surprise. Calculating Magic Square In Any Order Using Standard Template Library (STL) Download demo project - 26. is magic, since every row, column, and diagonal adds up to 4035. Cosmic Little Magic 6x6. Magic Squares: History I There is a legend that the (semi-mythical) emperor Yu, c. They include 2, 6, 10, 14, 18, 22, and so on. Recently an algorithm was developed that allowed the automatic generation of any magic square of odd-numbered dimensions. 275,305,224 5×5 magic squares of size 5 × 5. For example, a 3 x 3 Magic Square. Thse worksheets start with normal 6x6 magic squares having numbers from 1-36, but the non-normal versions of the 6x6 puzzles are tremdously difficult to solve and will likely require your calculator and some time. (The format will be N (X) , where "N" is the number of times that the number "X" appears in your birth date. The 6 x 6 Magic Square of the Sun contains the first 36 integers arranged in such a fashion so that each line of numbers, whether added horizontally, vertically or diagonally from corner to corner, will yield the "solar number" 111. Applications of AI for Magic Squares Jared Weed Department of Mathematical Sciences Worcester Polytechnic Institute Worcester, Massachusetts 01609-2280 Email: [email protected] "Even" Magic Squares may be further divided into two sub-categories: "singly even" Magic Squares, which means that the number of cells on each side of the Magic Square is evenly divisible by two, but not by four (e. This programming exercise is concerned with creating odd sized magic squares (i. The are other methods, but as we will see they are not as straightforward as the methods we showed for odd ordered magic squares and doubly-even ordered magic squares. Maths By Amiya : Magic Box Concept Odd By Odd 3x3 , 4x4 and 6x6 and others Magic Squares 6x6 and 5x5. Magic Squares are square grids with a special arrangement of numbers in them. Magic Squares of Order 4n Here we will generalize the method used to generate fourth-order magic squares to generate squares of order 4n. The magic square, given as a charm of easing childbirth in the Jabirean corpus, is thought to be of Chinese origin. "Even" Magic Squares, which means that there is an even number of cells on each side of the Magic Square. There are 8 ways to make a 3×3 magic square. The following is a 6x6 magic square. Choose a matrix size (i. The same Pyramid method can be used for any odd order magic square as shown below for the 5x5 square in Figure 2. Therefore it does not fulfill the requirements of the task, because it will incorrectly identify almost 100% of all magic squares as not. The total areas are therefore 7776 (6 5). A magic square is a series of numbers on a square grid, placed so that any row, column or diagonal line always adds up to the same number. 188710 24 89 16 BE A PROUD19 86 23 11 INDIAN. Published February 2000,July 2007,August 2007,February 2011. The number 666 is most famously noted in St. column and 3x3 square contains these letters exactly once and the 6x6 Hidden Word Sudoku puzzle was based on the letters in WATERS. Thse worksheets start with normal 6x6 magic squares having numbers from 1-36, but the non-normal versions of the 6x6 puzzles are tremdously difficult to solve and will likely require your calculator and some time. To the authors' knowledge, these are the only known doubly pandiagonal magic squares. 6x6 pandiagonal additive magic squares (using consecutive integers) are impossible. The constant that is the sum of every row, column and diagonal is called. Play Magic Square Game. Please practice hand-washing and social distancing, and check out our resources for adapting to these times. Let us add 10 to all numbers of any 4x4 square to get a 4x4 square with a total of 74. However for even magic squares the problem becomes more complex. If x and y have different parities (i. May be you see it in some magazines or your teacher might have introduced it in a class. Markus has also produced this Power Point presentation to summarise what he knew about Coloured Squares at the time. That is, squares for which the number of cells on a side is a multiple of 4. The constant sum in every row, column and diagonal is called the magic constant or magic sum, M. It is thus a gnomon magic square. Save that for the magic square that you make for your guests. The 6x6 Magic Square was found in the palace foundation of Mongolian Prince Anxi to ward off the evil spirits. There are 8 ways to make a 3×3 magic square. Source(s): https://shrink. Magic Squares of Order 4n Here we will generalize the method used to generate fourth-order magic squares to generate squares of order 4n. Put the pieces together so that the rows and columns add to 30. There is only one distinct Magic Square of order N=3. The constant that is the sum of every row, column and diagonal is called. Both squares have been constructed in April 2007 by Willem Barink, author of the puzzle-game Medjig (strongly magic square related). First, I define a helper function that always returns a positive value for the expression mod(a,q), because the MOD function in SAS can sometimes return a negative value. e 3X3, 5X5, 7X7…) and Even(i. Calculate the magic constant. MAGIC SQUARE OF 6x6 - Magic Sums of 111 and Solar Symbol. A magic square consists of the distinct positive integers 1, 2, , such that the sum of the n numbers in any horizontal, vertical, or main diagonal line is always the same number, known as the magic constant. M = 3×3 8 1 6 3 5 7 4 9 2. One of the puzzles involves creating a 6 x 6 Magic Square using 18 dominoes from a double-six set. 22 12 18 8788 17 9 25 Yes. Here's the secret to solving any 3 x 3 magic square. Supernova Little Magic M 6x6. Thse worksheets start with normal 6x6 magic squares having numbers from 1-36, but the non-normal versions of the 6x6 puzzles are tremdously difficult to solve and will likely require your calculator and some time. For a size 3x3, the minimum constant is 15, for 4x4 it is 34, for 5x5 it is 65, 6x6 it is 111, then 175, 260,. Hackerrank: Forming a magic Square. Semimagic square - rows and columns add up to the same magic constant 3. New!! Even if Pentium4 machine working at 3GHz is used, it is thought that it will take 220,500 years or more by the time. That is, squares for which the number of cells on a side is a multiple of 4. Composite Magic Squares Construction. In the present talk, the history of magic squares will be discussed in. magic square is used on a shuffleboard court on cruise ships as an aid in keeping scores (2, p. 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. So for the example below, 15 is the magic number. and planet Jupiter Jupiter seal derivation 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 Magic square of order three. 2225*10^54 9x9 7. 7x7 Magic Squares. Magic Square Solver. Magic Word Square Word Sudoku Puzzles and variations--9x9, 12x12, hidden word, diagonal, classic, etc. Magic Squares of Order 4n Here we will generalize the method used to generate fourth-order magic squares to generate squares of order 4n. MoYu AoShi GTS M 6x6. The 6x6 Magic Squares History Around 1789, Euler formulated his "conjecture" that there were no Graeco-Latin squares of orders 2, 6, 10, 14, etc. They include 2, 6, 10, 14, 18, 22, and so on. Let us add 10 to all numbers of any 4x4 square to get a 4x4 square with a total of 74. The Yuan rulers were enamoured with Chinese culture and sought to both adopt and preserve it. In each case these are written again. 2200-2100 BCE, copied a magic square o the back of a giant turtle in the Luo, a tributary of the Huang He (Yellow River). Magic Squares Magic Square. For example, a 3 by 3 magic square has three rows and three columns, so its order is 3. AKA: YLM 6x6, YLM 6x6x6. Each digit must be found once and only once per line, per column and per region. an ODD Integer greater than one). Burbank, California: Hahne Publications. and 4 are "broken diagonals", consisting of each corner square and the two opposite middle edge squares, just mentioned above. while we have found last March two of them…Excellent news!…. 7x7 Magic Square With Sum 175 Of Planet Venus Stock Vector - Illustration of planet, grid: 88349897. But with the flawed definition of semi-magic-squares the whole problem becomes tirival, since we can find exactly 1 solution for each possible combination of (n-1)² fields each having values in [1,t] you can just calculate the number of possible flawed squares as (t-1)^((n-1)^2) \$\endgroup\$ - Falco Jul 7 '14 at 14:38. The term "doubly even" isn't very descriptive and all it means is a multiple of four. YuXin £ 25. 36-16=20/2=10. YuXin Little Magic Magnetic Square-1 Black. Singly even magic squares are only divisible by 2 and not 4. 10x10 Math magic square Posted by Mahmood ul Haq at 2:50 PM. The Mamluks ruled Egypt from 1250 to 1517. Enter the title of your math square puzzle. Every other pattern is a rotation or reflection. 77 × 10 19 squares. YJ YuShi V2 M 6x6. MATLAB Has A Built-in Function _magic(n) That Returns An N Times N Magic Square. 6x6 square will have numbers from 1 to 36, while 4x4 square had numbers from 1 to 16. 6x6 pandiagonal additive magic squares (using consecutive integers) are impossible. The classic sudoku is a 9×9 square puzzle made of 9 lines (L1 to L9), 9 columns (C1 to C9) et nine "regions" (R1 to R9). The order n must be a scalar greater than or equal to 3. 6) Your 6 x 6 magic square is ready. Supernova Shadow M 6x6. Each digit must be found once and only once per line, per column and per region. No, square numbers are numbers which have a whole square root. The 6x6 Magic Squares History Around 1789, Euler formulated his "conjecture" that there were no Graeco-Latin squares of orders 2, 6, 10, 14, etc. Beginning of the article " Some notes on the magic squares of squares problem " published in , Springer, New-York; Supplement to the article, and first 6x6 and 7x7 magic squares of squares constructed after the article and after the supplement; Open problems from the article (your solutions or partial results are welcome, I offer a €100 prize + a bottle of champagne!). 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; It is impossible to have exactly 2 odd integers. In order to construct these magic squares we applied the previous known magic squares of orders 3 to 14, except order 12. In the case of a 6x6 square, we'll have 4 3x3 squares in a grid. New!! Even if Pentium4 machine working at 3GHz is used, it is thought that it will take 220,500 years or more by the time the above program is finished. Given , convert it into a magic square at minimal cost by changing zero or more of its digits. Our first sample consists of 12 0, 12 ro, 6 ri, and 6 i figures The. The 8x8 "Knight's move" Magic Square. 5x5 Magic Squares. There are formula for 4x4 and 6x6, even 8x8 and larger, but the algorithms don't work from one to the next. Gaston Tarry proved in 1901 that there were no Graeco-Latin square of order 6, which supported Euler's conjecture. Both squares have been constructed in April 2007 by Willem Barink, author of the puzzle-game Medjig (strongly magic square related). If you relax that condition and allow for larger, negative, or repeating numbers you have however this answer which shows magic squares form at least a three dimensional subspace of $\Bbb R^{3\times 3}$, and for any given middle number there are infinitely many magic squares with that as the middle number. This 4x4 square we will place as 2x2 squares in the 4 corners in the left hand side 6x6 square. Magic Squares of Order 4n Here we will generalize the method used to generate fourth-order magic squares to generate squares of order 4n. It uses all the integers from -18 to 18 (except 0). Use the same method as you would with odd magic squares: the magic constant = [n * (n^2 + 1)] / 2, where n = the number of boxes per side. By the 19th century 100x100 magic squares, with 10,000 individual cells, were being produced. 3x3 magic squares of squares! Best regards. The era brought rapid change in science and architecture, but continued the development of the arts from the Song Dynasty with little interruption. Inspiration was due to three young master-class students in Nijmegen, the Netherlands, who in March 2007 reached world news because they had constructed a spectacular 12×12 panmagic square (). It contains n² order m magic squares using the numbers 1 to (mn)² The smallest are order-9 from order-3 and order-3. 7x7 Magic Square With Sum 175 Of Planet Venus Stock Vector - Illustration of planet, grid: 88349897. is magic, since every row, column, and diagonal adds up to 4035. So, in the example of a 6x6 square:. 6 x 6 and. the diagonals that wrap round at the edges of the square, also add up to the magic constant. A new set of puzzles in a few hours. Mamluk A dynasty of rulers succeeding the Ayyubid as governors of Egypt and Syria. These numbers are special because every row, column and diagonal adds up to the same number. A magic square of order n is an arrangement of n^2 numbers (usually 1, 2, 3) such that the sum of the numbers in all the rows, columns and big diagonals is a constant. 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. A 3 x 3 grid (3 squares across, 3 squares down) means you use the numbers 1, 2, and 3. A pandiagonal magic square or panmagic square (also diabolic square, diabolical square or diabolical magic square) is a magic square with the additional property that the broken diagonals, i. -----6x6 If I am right, 6x6 magic squares of squares using squared consecutive integers (0² to 35², or 1² to 36²) are impossible. Mamluk A dynasty of rulers succeeding the Ayyubid as governors of Egypt and Syria. Supernova Shadow M 6x6. A 6x6 magic magic square (N=1, n=6) can be made by additional exchanging 3 pairs of corresponding numbers. This magic square has rank 3, with singular values 34,8 √ 5,2 √ 5,0. The dimensions must equal. The sum of each row or each column or each diagonal can be found using this formula. Magic squares with cells 4x4 or 6x6 or 7x7 were particularly popular, with 10x10 squares being produced by the 13th century. It should be pointed out that there are many other versions of such 6 x 6 magic squares. Refer to your quilt pattern for the triangle square size and number of units required. The magic of magic squares 1. are studies. 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. May be you see it in some magazines or your teacher might have introduced it in a class. We will examine the way this particular 6 6 magic square was generated. But because multiply magic squares cannot use consecutive integers, 6x6 pandiagonal multiplicative magic squares are possible!. Complete the magic square using the following integers: -13, -10, -7, -4, 2, 5, 8, 11. Both squares have been constructed in April 2007 by Willem Barink, author of the puzzle-game Medjig (strongly magic square related). 74 When "show" or "quick" is activated, a backtracking algorithm will continue the search for a solution; interruption can be caused by clicking the option "mouse". A Magic Square is combination of numbers where the numbers in all rows, all columns, and both diagonals sum to the same constant. Order 6 multiply magic squares. "Even" Magic Squares may be further divided into two sub-categories: "singly even" Magic Squares, which means that the number of cells on each side of the Magic Square is evenly divisible by two, but not by four (e. Unfortunately to late to be published in the M. 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. If you relax that condition and allow for larger, negative, or repeating numbers you have however this answer which shows magic squares form at least a three dimensional subspace of $\Bbb R^{3\times 3}$, and for any given middle number there are infinitely many magic squares with that as the middle number. 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. M = 3×3 8 1 6 3 5 7 4 9 2. 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. The Magic Square above illustrates the properties of a Magic Square. The numbers beside the Red Squares show the totals for each row. This paper brings block-wise construction of magic squares of order 39 to 45. There should be an algorithm for magic square with an even number of rows/columns somewhere. However for even magic squares the problem becomes more complex. In a more serious vein, magic squares (or latin squares in general, which are defined below) "are an essential feature in statistical investigations of many kinds" (11, p. The FINAL FORMAT OF 6 X 6 IS GIVEN ABOVE. The above magic squares of orders 3 to 9 are taken from Yang Hui's treatise, in which the Luo Shu principle is clearly evident. A magic square is a square matrix in which the sum of every row, every column, and both diagonals is the same. 79809*10^34 8x8 5. square would not be constant unless the original additive magic square was constant. Put the pieces together so that the rows and columns add to 30. Magic Squares have been the subject of interest among mathematicians for several centuries because of its magical properties. "Even" Magic Squares may be further divided into two sub-categories: "singly even" Magic Squares, which means that the number of cells on each side of the Magic Square is evenly divisible by two, but not by four (e. The puzzle contains digit from 1 to 9 and empty squares. Semimagic square - rows and columns add up to the same magic constant 3. YuXin Little Magic 6x6. Almost the only thing that carried over from one nation to another was the notion that a magic square was a. At 14/05/99 Wilfred Whiteside informed that he has calculated all the solutions for the 5x5 case and found that there are 253,688 different matrixes. The Magic square is…. The following is a 6x6 magic square. What Are Magic Squares? 3. e 3X3, 5X5, 7X7…) and Even(i. 9 different 3x3 6 different 4x4 6 different 5x5 2 different 6x6 Original puzzle resour. The problem is to find a 3 by 3 magic square all of whose entries are distinct perfect squares, or prove that such a square cannot exist. the program starts with the first possible 6x6 magic square (in lexicographical order). Singly even magic squares are only divisible by 2 and not 4. Indeed, if x and y have the same parity, all the terms have the parity of m. “Even” Magic Squares, which means that there is an even number of cells on each side of the Magic Square. Candy found 640,120,320 irregular ones. Lab 6j: Magic Squares One interesting application of two-dimensional arrays is magic squares. The 8x8 "Knight's move" Magic Square. Previous work related to fourth order normal squares has shown that symmetries such as the dihedral group exist and that (under certain conditions) normal magic squares can be categorized. The number 15 is called the magic number of the 3x3 square. It was given after the Great Deluge to the Mythical Emperor Lo Shu by a Magical Turtle. A 5x5 grid requires you use the numbers 1 to 5, and so on. Feb 12, 2018 - 6x6 Magic Square Normal Set 1 Worksheet #Magic #Square #Worksheet Stay safe and healthy. An Upside Down Magic Square The MAGIC OF MATHS book tells you all about magic squares, and How to Make 4x4 Magic Squares which will produce any number. On this page, I show how to take two small magic squares to make a much bigger magic square. Mesosyn method for constructing a 6x6 magic square. In creating an 8x8 magic square we need a total of 28 more numbers to fill in the outer edge of our 6x6, making it an 8x8. In the present talk, the history of magic squares will be discussed in. Can you make a 6x6 Graeco-Latin made up of six regiments of six officers each of. Semimagic square - rows and columns add up to the same magic constant 3. you have a few. Login to reply the answers Post; How do you think about the answers? You can sign in to vote. 6x6 magic square of squares. But with the flawed definition of semi-magic-squares the whole problem becomes tirival, since we can find exactly 1 solution for each possible combination of (n-1)² fields each having values in [1,t] you can just calculate the number of possible flawed squares as (t-1)^((n-1)^2) \$\endgroup\$ - Falco Jul 7 '14 at 14:38. The total areas are therefore 7776 (6 5). "Even" Magic Squares, which means that there is an even number of cells on each side of the Magic Square. For example, a 3 by 3 magic square has three rows and three columns, so its order is 3. Burbank, California: Hahne Publications. Magic Squares Lia Malato Leite Victoria Jacquemin Noemie Boillot Experimental Mathematics University of Luxembourg Faculty of Sciences, Tecnology and Communication 2nd Semester 2015/2016. Magic square of order 1 is trivial The 1 Bordered magic square when it is a magic square and it remains magic when the rows and columns at the outer edge is removed. The "magic square" grid on the right will then be highlighted with the counts for each of the numbers appearing in your name. Due to differences in computer monitors, actual colors may vary slightly from those shown. Computers , Magic Squares 6x6 magic squares , Cliff Pickover , King Fahd , Magic Squares , singly even magic squares. Please practice hand-washing and social distancing, and check out our resources for adapting to these times. AKA: YLM 6x6, YLM 6x6x6. From what I have been able to find there appears to be no truly random method for constructing singly even squares such as 6×6 as there was for 5×5, 7×7, and other odd-ordered magic squares. UNDER CONSTRUCTION Numerology. Let us add 10 to all numbers of any 4x4 square to get a 4x4 square with a total of 74. The Lo Shu Square, as the magic square on the turtle shell is called, is the unique normal magic square of order three in which 1 is at the bottom and 2 is in the upper right corner. Feb 12, 2018 - 6x6 Magic Square Normal Set 1 Worksheet #Magic #Square #Worksheet Stay safe and healthy. So the presence of an operation does not render Amitai's entries in each magic square cell from being numbers. x even and y odd), 3 terms are odd and the 6 other ones are even (and. From E7 can be created nearly 1000 million more. But because multiply magic squares cannot use consecutive integers, 6x6 pandiagonal multiplicative magic squares are possible!. Thse worksheets start with normal 6x6 magic squares having numbers from 1-36, but the non-normal versions of the 6x6 puzzles are tremdously difficult to solve and will likely require your calculator and some time. In September 1997, I drove such an enumeration in 6 hours and half with a reduced program (group G of order 32 and permutation "complement to 26") on a K6 of AMD, running at 200 MHz, under Turbo Pascal. Published February 2000,July 2007,August 2007,February 2011. The other, blue, squares show the diagonal totals - including all of the "broken diagonals". From what I have been able to find there appears to be no truly random method for constructing singly even squares such as 6×6 as there was for 5×5, 7×7, and other odd-ordered magic squares. The YuXin Little Magic 6x6 is a the newest 6x6 speed cube from YuXin. Adding the numbers in each of the columns in the square will sum 111, with all six rows summing to the beastly number 666. Use the same method as you would with odd magic squares: the magic constant = [n * (n^2 + 1)] / 2, where n = the number of boxes per side. However, the pattern of exchanging seems to be quite arbitrary and non-symmetrical. " These magic square puzzles have been arranged in a way that they strengthen students' problem-solving skills as well as basic math abilities. Composite Magic Squares Construction. 6x6 pandiagonal additive magic squares (using consecutive integers) are impossible. Every normal magic square of order three is obtained from the Lo Shu by rotation or reflection. 7x7 Magic Squares. AKA: YLM 6x6, YLM 6x6x6. A 5x5 grid requires you use the numbers 1 to 5, and so on. Magic Squares of Order 4n Here we will generalize the method used to generate fourth-order magic squares to generate squares of order 4n. 6 x 6 and. The 6x6 Magic Squares History Around 1789, Euler formulated his "conjecture" that there were no Graeco-Latin squares of orders 2, 6, 10, 14, etc. the set 1 to 16 if the numbers 1, 6, 11, 16 lie thus on a diagonal curve. YuXin Little Magic 6x6. The sum of the elements in each column and the sum of. The "magic square" grid on the right will then be highlighted with the counts for each of the numbers appearing in your name. Hackerrank: Forming a magic Square. You might have heard of palindromic sentences. Source(s): https://shrink. 6x6 square will have numbers from 1 to 36, while 4x4 square had numbers from 1 to 16. The magic constant of a normal magic square depends. A 10x10 magic square (N=2,n=10) can therefore be made by additional exchanging 15 pairs of corresponding numbers (in yellow color). The idea of magic rectangles is used to bring pan magic squares of orders 15, 21, 27 and 33, where 3 × 3 blocks are with equal sums entries and are semi-magic squares of order 3 (in rows and. View MATLAB Command. Although the principal characteristics of a magic square are the equality of its row, column, and main diagonal sums, magic squares with additional special properties have. So, each order n square makes a total of n 2 squares in this way. Calculate the magic constant. For my first ever even ordered magic squares, I for some reason chose the most difficult squares to construct, and these are squares of singly even order. The idea of nested magic squares is well known in the literature, generally known by bordered magic squares. 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. We will examine the way this particular 6 6 magic square was generated. Magic squares with cells 4x4 or 6x6 or 7x7 were particularly popular, with 10x10 squares being produced by the 13th century. Enter the title of your math square puzzle. 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". Question: The Magic Square Is An Arrangement Of Numbers In A Square Grid In Such A Way That The Sum Of The Numbers In Each Row, And In Each Column, And In Each Diagonal Is The Same. For example, the number twelve can be expressed as 10 + 2 and as 20 - 8. RAMANUJAN'S MAGIC SQUARE It is 22nd Dec 1887. By the 19th century 100x100 magic squares, with 10,000 individual cells, were being produced. Magic: The Gathering World Championship The Magic The Gathering World Championships (Worlds) have been held annually between 1994 and 2011 It was the most important tournament in the game of Magic The Gathering, offering cash prizes of up to $45,000 to the winners Besides the main event Worlds were always a huge gathering of Magic players, who come to watch the pros and compete in. A new set of puzzles in a few hours. The same Pyramid method can be used for any odd order magic square as shown below for the 5x5 square in Figure 2. It should be pointed out that there are many other versions of such 6 x 6 magic squares. Anyway, before rambling on lets get to the actual problem. But with the flawed definition of semi-magic-squares the whole problem becomes tirival, since we can find exactly 1 solution for each possible combination of (n-1)² fields each having values in [1,t] you can just calculate the number of possible flawed squares as (t-1)^((n-1)^2) \$\endgroup\$ - Falco Jul 7 '14 at 14:38. The 6 x 6 Magic Square of the Sun contains the first 36 integers arranged in such a fashion so that each line of numbers, whether added horizontally, vertically or diagonally from corner to corner, will yield the "solar number" 111. Size: 6 x 6 x 2 Verified Purchase I will never use a "square pan" without these sharp edges ever again. 42 PM on Wed. Size: 6 x 6 inches (15cmx15cm ) each sheet Series floral dot stripe cotton fabric bundle patchwork fabric bundle Quilted bundle doll's clothes fabric quarter Note: All fabrics are cut by hand. Students must complete the grids so that each column, row and diagonal add up to the given magic sum. square would not be constant unless the original additive magic square was constant. You will be given a matrix of integers in the inclusive range. Singly even magic squares are only divisible by 2 and not 4. In a magic square you have to add 3 numbers again and again. The total of 6x6 magic square is not decided although a report is told that there is near 1,800 trillion order. For more details see: Ultramagic Squares of Order 7: D7 (November 2001) was a big surprise. A magic square contains the integers from 1 to n^2. These numbers are special because every row, column and diagonal adds up to the same number. We can use almost the same process as we used to generate a fourth-order magic square to create any 4n 4n magic square. how do I solve 6x6 magic square with 111 as the sum? Source(s): solve 6x6 magic square 111 sum: https://biturl. At 14/05/99 Wilfred Whiteside informed that he has calculated all the solutions for the 5x5 case and found that there are 253,688 different matrixes. 6) Your 6 x 6 magic square is ready. The sum of each row, column and diagonal is 111, the magic number for a 6 × 6 magic square. Supernova Shadow 6x6. The constant values $ M $ of the sums of the magic squares have a minimum value (for non-zero integer positive values). However, the way the above square was generated is rather intriguing. The magic square of Venus can make you a millionaire with lotto and lotto UK49 I will give you an example worth a millions words Winning number drawn at 10. Viewed 45k times. Lab 6j: Magic Squares One interesting application of two-dimensional arrays is magic squares. Please write back if you have any further questions about any of this. I The turtle's magic square is called the Luo Shu and is 4 9 2 3 5 7 8 1 6 I This story originated no later than 200 BCE. A magic square is a series of numbers on a square grid, placed so that any row, column or diagonal line always adds up to the same number. Adding the numbers in each of the columns in the square will sum 111, with all six rows summing to the beastly number 666. You can also achieve 15, if you add the middle number 5 three times. Magic squares with cells 4x4 or 6x6 or 7x7 were particularly popular, with 10x10 squares being produced by the 13th century. 880 magic squares of size 4× 4. The constant sum in every row, column and diagonal is called the magic constant or magic sum, M. Source(s): https://shrink. 1x1=1 2x2=4 3x3=9 4x4=16 5x5=25 6x6=36 7x7=49 8x8=64 9x9=81 10x10=100 94 is a square number, although its square root wouldn't be a. It should be pointed out that there are many other versions of such 6 x 6 magic squares. Pandiagonal means that the broken diagonals also add up to the. The constant values $ M $ of the sums of the magic squares have a minimum value (for non-zero integer positive values). The era brought rapid change in science and architecture, but continued the development of the arts from the Song Dynasty with little interruption. Beginning of the article " Some notes on the magic squares of squares problem " published in , Springer, New-York; Supplement to the article, and first 6x6 and 7x7 magic squares of squares constructed after the article and after the supplement; Open problems from the article (your solutions or partial results are welcome, I offer a €100 prize + a bottle of champagne!). So, in the example of a 6x6 square:. Supernova Little Magic M 6x6. Alaa Hussein Lafta 2. and known as Lo Shu. Question: The Magic Square Is An Arrangement Of Numbers In A Square Grid In Such A Way That The Sum Of The Numbers In Each Row, And In Each Column, And In Each Diagonal Is The Same. The smallest possible singly even magic square is 6x6, since 2x2 magic squares can't be made. 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. Gaston Tarry proved in 1901 that there were no Graeco-Latin square of order 6, which supported Euler's conjecture. The "magic square" grid on the right will then be highlighted with the counts for each of the numbers appearing in your name. RAMANUJAN'S MAGIC SQUARE It is 22nd Dec 1887. 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,. 275,305,224 5×5 magic squares of size 5 × 5. $\endgroup$ - JMoravitz Dec 29 '16. how do I solve 6x6 magic square with 111 as the sum? Source(s): solve 6x6 magic square 111 sum: https://biturl. The horizontal and vertical totals are to the right and below in green squares. Magic Squares are square grids with a special arrangement of numbers in them. The numbers in the Red Squares form the 3x3 magic Square. 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. It is unknown if regular magic squares of cubes are possible for orders 4-8 (order-3 has been proved impossible). A 6x6 magic magic square (N=1, n=6) can be made by additional exchanging 3 pairs of corresponding numbers. Many variations exist that contain numerous other features. There are even algorithms for solving certain classes of even magic squares. 74 When "show" or "quick" is activated, a backtracking algorithm will continue the search for a solution; interruption can be caused by clicking the option "mouse". Do you mean a matrix equation with a 6x6 matrix? In general, the size doesn't matter, but of course the calculations are becoming a bit more tedious once you get higher dimensions. 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. I must admit that this problem actually took me a good while to solve. The total of 6x6 magic square is not decided although a report is told that there is near 1,800 trillion order. This book contains a number of puzzles and games for one person. 275,305,224 5×5 magic squares of size 5 × 5. 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,. They have a long history, appearing in both ancient Chinese scriptures and Dark Ages Christian sculptures. Almost the only thing that carried over from one nation to another was the notion that a magic square was a. The battle for the next Masterpiece Optimus Prime continues. Third-Order Magic Square. The order 22 is also used. An intriguing aspect of the 6x6 magic square on the right is that if one looks at adjacent numbers, one obtains a pattern of the sequence of numbers in the 2x2 squares: X X X. test the user made entries are tested; a passed test means no guaranty, that there exists a 6x6 magic square with these entries. -----6x6 If I am right, 6x6 magic squares of squares using squared consecutive integers (0² to 35², or 1² to 36²) are impossible. Question: The Magic Square Is An Arrangement Of Numbers In A Square Grid In Such A Way That The Sum Of The Numbers In Each Row, And In Each Column, And In Each Diagonal Is The Same. They are available here: See the first 6x6 and 7x7 magic squares of squares. Powered by vbulletin magic squares in Title/Summary. Play Magic Square Game. In the present talk, the history of magic squares will be discussed in. magic square is used on a shuffleboard court on cruise ships as an aid in keeping scores (2, p. There are four different sizes of grids (3x3, 4x4, 5x5, and 6x6) with two worksheets for each size of grid. Leonhard Euler, 1707-1783. com : 6x6 Magic Square Normal Set 3 Worksheet. A magic square of size 6 x 6 is to be constructed, (with additional properties: nine of the 2x2 subsquares have equal sums and the inner 4x4 subsquare is pandiagonal). Magic Word Square Word Sudoku Puzzles and variations--9x9, 12x12, hidden word, diagonal, classic, etc. Magic squares with cells 4x4 or 6x6 or 7x7 were particularly popular, with 10x10 squares being produced by the 13th century. Supposedly the order 3 magic square was invented in China between 650 and 400B. and 4 are "broken diagonals", consisting of each corner square and the two opposite middle edge squares, just mentioned above. and 4 are "broken diagonals", consisting of each corner square and the two opposite middle edge squares, just mentioned above. There should be an algorithm for magic square with an even number of rows/columns somewhere. It turns out that 4232 of those sets of five elements leads to one or more valid magic squares, as summarized in the table below: Sets of Five Number of Numbers Leading Distinct to k Valid Magic k Magic Squares Squares --- ----- ----- 1 2176 2176 2 1656 3312 3 80 240 4 304 1216 5 0 0 6 16 96 ----- ----- 4232 7040 This accounts for all 7040 of. A 6x6 magic magic square (N=1, n=6) can be made by additional exchanging 3 pairs of corresponding numbers. "Even" Magic Squares, which means that there is an even number of cells on each side of the Magic Square. So, in the example of a 6x6 square:. Then print this cost on a new line. By the 19th century 100x100 magic squares, with 10,000 individual cells, were being produced. Of the nine entries, five (49, 169, 289, 1225, and 2401) are perfect squares. Could you work this out just from knowing that the square uses. My 6x6 magic square of squares is NOT using squared consecutive integers but it is interesting to see the used numbers:. In September 1997, I drove such an enumeration in 6 hours and half with a reduced program (group G of order 32 and permutation "complement to 26") on a K6 of AMD, running at 200 MHz, under Turbo Pascal. The Turtle is the Symbol of the Star System Orion. We can convert any digit to any other digit in the range at cost of. 22 12 18 8788 17 9 25 Yes. Magic square of order 1 is trivial The 1 Bordered magic square when it is a magic square and it remains magic when the rows and columns at the outer edge is removed. Now let's prove these are the only possibilities. Can you make a 6x6 Graeco-Latin made up of six regiments of six officers each of. It contains n² order m magic squares using the numbers 1 to (mn)² The smallest are order-9 from order-3 and order-3. 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; It is impossible to have exactly 2 odd integers. However for even magic squares the problem becomes more complex. The horizontal and vertical totals are to the right and below in green squares. Magic Squares Magic Square. Published February 2000,July 2007,August 2007,February 2011. Cosmic Little Magic M 6x6. The Mamluks ruled Egypt from 1250 to 1517. MATLAB Has A Built-in Function _magic(n) That Returns An N Times N Magic Square. Recently Viewed Products. Description. 36-16=20/2=10. It is unknown if regular magic squares of cubes are possible for orders 4-8 (order-3 has been proved impossible). com : 6x6 Magic Square Normal Set 3 Worksheet. 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. A magic square is a series of numbers on a square grid, placed so that any row, column or diagonal line always adds up to the same number. boolean checkmagic() Returns true if the matrix is a magic square. For this example, the numbers used are consecutive integers, but this does not have to hold true for all Magic Squares. The Lo Shu Square, as the magic square on the turtle shell is called, is the unique normal magic square of order three in which 1 is at the bottom and 2 is in the upper right corner. A 10x10 magic square (N=2,n=10) can therefore be made by additional exchanging 15 pairs of corresponding numbers (in yellow color). article, I constructed, in June 2005, the first 6x6 magic squares of squares. Saturn 3x3 magic square OGHAM "Satarn 3x3 draíocht Jupiter 4x4 magic square OGHAM "Lúpatar 4x4 draíoc Mars 5x5 magic square OGHAM "Mars 5x5 draíochta ce Sun 6x6 magic square OGHAM "ghrian 6x6 draíochta Venus 7x7 magic square OGHAM "Véineas 7x7 draíocht Mercury 8x8 Magic Square OGHAM "Mearcair 8x8 draío Moon 9x9 Magic. Solving 3 x 3 Magic Squares. The following is a 6x6 magic square. These 6x6 magic squares, even in their normal forms, are quite challenging and good brian teasers for middle school math wizards or even for math saavy adults. We define a magic square to be an matrix of distinct positive integers from to where the sum of any row, column, or diagonal of length is always equal to the same number: the magic constant. MAGIC SQUARE OF 6x6 - Magic Sums of 111 and Solar Symbol. Of the nine entries, five (49, 169, 289, 1225, and 2401) are perfect squares. A magic square contains the integers from 1 to n^2. YJ YuShi V2 M 6x6. "Even" Magic Squares, which means that there is an even number of cells on each side of the Magic Square. 6 x 6 and. Your concept incorrectly identifies almost every magic square that exists as being non-magic (except for the small subset that MATLAB can generate). The Magic square is…. One of the possible solutions. Both squares have been constructed in April 2007 by Willem Barink, author of the puzzle-game Medjig (strongly magic square related). It is thus a gnomon magic square. Ian Wakeling told me that this is an application of a. Magic squares have been known and studied for many centuries, but there are still surprisingly many unanswered questions about them. In order to construct these magic squares we applied the previous known magic squares of orders 3 to 14, except order 12. Gaston Tarry proved in 1901 that there were no Graeco-Latin square of order 6, which supported Euler's conjecture. The constant sum in every row, column and diagonal is called the magic constant or magic sum, M. The Magic Square of 6x6, having the sum of all its numbers (Sigma 36) adding to 666 has always been a Solar Glyph, a veritable and secret pin number or access code to enter another solar system or dimension or galaxy, via the Triplet 111 Harmonic. First, I define a helper function that always returns a positive value for the expression mod(a,q), because the MOD function in SAS can sometimes return a negative value. Doubly Even Magic Squares. 775399 *10^19 7x7 3. 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. From the upper left, the first square on the right is a reflection through the center (transposes columns 1 and 3), for example. However for even magic squares the problem becomes more complex. We present an exact method for counting semi-magic squares of order 6. 6x6 magic square of squares. The numbers you use in a KenKen puzzle depend on the size of the grid you choose. It holds true to the Little Magic name with its light and airy feel. com : 6x6 Magic Square Normal Set 3 Worksheet. YuXin £ 25. If the numbers from 1 to 16 are used then the sum for each row, column and diagonal should be 34. 6 x 6 and 10 x 10. This magic square is closely related to one made famous by Albrecht Dürer in his 1514 engraving Melencholia I, differing only by the exchange of the middle columns to reveal that date. And on the island, as a vigilant statue vibrant with life, stands the old oak tree. Cosmic Little Magic 6x6. The method is based on starting with an Eulerian square, but since a 6x6 Eulerian square does not exist, I must modify the method to make it work. A magic square is a grid of numbers for which every line, column and diagonal adds up to the same number. Now the 6 x 6 magic square will be divided into four 3 x 3 Magic squares. Enter the size of your math square. They include 2, 6, 10, 14, 18, 22, and so on. The other two types are: • odd (where n=3, 5, 7, 9, 11. and 4 are "broken diagonals", consisting of each corner square and the two opposite middle edge squares, just mentioned above. (Look at the. The magic square, given as a charm of easing childbirth in the Jabirean corpus, is thought to be of Chinese origin. It is thus a gnomon magic square. But there is another word play that is even more impressive: a magic […]. Supernova Little Magic 6x6. By learning magic square the students may commemorate Birthday of Ramanujan, falls on 22nd December 1887. New!! Even if Pentium4 machine working at 3GHz is used, it is thought that it will take 220,500 years or more by the time the above program is finished. However, the way the above square was generated is rather intriguing. It turns out that 4232 of those sets of five elements leads to one or more valid magic squares, as summarized in the table below: Sets of Five Number of Numbers Leading Distinct to k Valid Magic k Magic Squares Squares --- ----- ----- 1 2176 2176 2 1656 3312 3 80 240 4 304 1216 5 0 0 6 16 96 ----- ----- 4232 7040 This accounts for all 7040 of. RAMANUJAN'S MAGIC SQUARE It is 22nd Dec 1887. The are other methods, but as we will see they are not as straightforward as the methods we showed for odd ordered magic squares and doubly-even ordered magic squares. In an effort to make progress on these unsolved problems, twelve prizes totalling €8,000 and twelve bottles of champagne have now been offered for the solutions to twelve magic square enigmas. One of the possible solutions. What Are Magic Squares? 3. and known as Lo Shu. UNDER CONSTRUCTION Numerology. So, each order n square makes a total of n 2 squares in this way. Published February 2000,July 2007,August 2007,February 2011. Here are how some bigger squares work. An intriguing aspect of the 6x6 magic square on the right is that if one looks at adjacent numbers, one obtains a pattern of the sequence of numbers in the 2x2 squares: X X X. Now let's prove these are the only possibilities. The set of higher order Magic Squares were a part of the cosmological system of the early Chinese. Choose a matrix size (i. If N is the number of rows in the square, and S is your starting number, then the sum of each row will be [(N squared+2S-1)/2] x N. Size: 6 x 6 inches (15cmx15cm ) each sheet Series floral dot stripe cotton fabric bundle patchwork fabric bundle Quilted bundle doll's clothes fabric quarter Note: All fabrics are cut by hand. Try reading these sentences backwards: Live not on evil. Magic squares have been studied for many years, and there are some particularly famous magic squares. AKA: YLM 6x6, YLM 6x6x6. Your starting number always goes in the center of the top row. is magic, since every row, column, and diagonal adds up to 4035. YuXin £ 13. This will be after exchanging numbers 8,5,4 and replacee them by 35,32,31 and vice versa. We can use almost the same process as we used to generate a fourth-order magic square to create any 4n 4n magic square. The classic sudoku is a 9×9 square puzzle made of 9 lines (L1 to L9), 9 columns (C1 to C9) et nine "regions" (R1 to R9). 4, the numbers 35,32,31 will be available in the down magic square in place of 8,5,4. Supernova Shadow 6x6. MAGIC SQUARE OF 6x6 - Magic Sums of 111 and Solar Symbol. You will be given a matrix of integers in the inclusive range. From what I have been able to find there appears to be no truly random method for constructing singly even squares such as 6×6 as there was for 5×5, 7×7, and other odd-ordered magic squares. Question 1: Are there any 2 2 magic squares? Why or why not? Question 2: How many 3 3 magic squares can you nd? Question 3: For a given n n magic square what is the magic constant (i. 6 x 6 and. First, I define a helper function that always returns a positive value for the expression mod(a,q), because the MOD function in SAS can sometimes return a negative value. On this page, I show how to take two small magic squares to make a much bigger magic square. The 6x6 Magic Square was found in the palace foundation of Mongolian Prince Anxi to ward off the evil spirits. If N is the order, then N x N different numbers are used to. Almost the only thing that carried over from one nation to another was the notion that a magic square was a. Size: 6 x 6 x 2 Verified Purchase I will never use a "square pan" without these sharp edges ever again. is magic, since every row, column, and diagonal adds up to 4035. Let us add 10 to all numbers of any 4x4 square to get a 4x4 square with a total of 74. Calculate the magic constant. Play Magic Square Game. Beginning of the article " Some notes on the magic squares of squares problem " published in , Springer, New-York; Supplement to the article, and first 6x6 and 7x7 magic squares of squares constructed after the article and after the supplement; Open problems from the article (your solutions or partial results are welcome, I offer a €100 prize + a bottle of champagne!). When Kathleen Ollerenshaw introduced most-perfect magic squares in 1986 [1], she was referring to additive magic squares. Use the same method as you would with odd magic squares: the magic constant = [n * (n^2 + 1)] / 2, where n = the number of boxes per side. and top right from 19 to 27, bottom left with 28 to 36 and bottom right with 10 to 18. edu Abstract—In recreational mathematics, a normal magic square is an n nsquare matrix whose entries are distinctly the integers 1:::n2, such that each row, column, and major. If this 6 x 6 square is split into two horizontal 3 x 6 rectangles, each rectangle is associated. -----6x6 If I am right, 6x6 magic squares of squares using squared consecutive integers (0² to 35², or 1² to 36²) are impossible. The following is a 6x6 magic square. We can convert any digit to any other digit in the range at cost of. For my first ever even ordered magic squares, I for some reason chose the most difficult squares to construct, and these are squares of singly even order. Step by solution to solve a 3 x 3 Magic Square: Magic Square is a group of cells arranged in a grid based on the given dimensions. In the present talk, the history of magic squares will be discussed in. how do I solve 6x6 magic square with 111 as the sum? Source(s): solve 6x6 magic square 111 sum: https://biturl. MAGIC SQUARE OF 6x6 - Magic Sums of 111 and Solar Symbol. It uses all the integers from -18 to 18 (except 0). Thus, the number of rectangles in a 5x5 square is the sum of the 1 square wide rectangles in the 1x1, 2x2, 3x3, 4x4, and 5x5 squares or 4 + 18 + 48 + 100. In September 1997, I drove such an enumeration in 6 hours and half with a reduced program (group G of order 32 and permutation "complement to 26") on a K6 of AMD, running at 200 MHz, under Turbo Pascal. 6) Your 6 x 6 magic square is ready. By simply swapping the two halves of the second row from the top, these top two quadrants also become order-3 magic.