The constant values $ M $ of the sums of the magic squares have a minimum value (for non-zero integer positive values). $$ M = n (n ^ 2 + 1) / 2 $$ For a size 3x3, the minimum constant is 15, for 4x4 it is 34, for 5x5 it is 65, 6x6 it is , then , A 6 6 magic square is then the first to have order 4n + 2. The following is a 6x6 magic square. We will examine the way this particular 6 6 magic square was generated. 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. Murphy (Random House, , $, ISBN ). Although this book is intended for younger readers, it is a great way to introduce the magic square. It tells of Ben Franklin’s many inventions including the story of how he created the magic square. To order, call Visit this site to play magic squares games. Magic Squares of Order 4n Here we will generalize the method used to generate fourth-order magic squares to generate squares of order 4n. That is, squares for which the number of cells on a side is a multiple of 4. We can use almost the same process as we used to generate a fourth-order magic square to create any 4n 4n magic square.

34 The IUP Journal of Computational Mathematics, Vol. III, No. 3, Magic Square Construction Algorithms and Their Applications Krishnappa H K*, N K Srinath** and Ramakanth Kumar P*** In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the sum of n numbers in all rows, all columns and both diagonals is . Magic Squares in the Tenth Century: Two Arabic Treatises by Anṭākī and Būzjānī In order to navigate out of this carousel please use your heading shortcut key to navigate to the next or previous heading. Back. Harry Potter and the Sorcerer's Stone, Book 1 J.K. : Hardcover. Some squares are irregular and have magic properties which are not retained during this breakdown process, e.g., some magic squares of order 6 and some pan-magic squares of order 7. For Pan-Magic Squares of order 4 and order 5, there are no surprises - all the squares are regular. Conclusion. The spreadsheet program offers a simple, widely. This page was last edited on 17 August , at Files are available under licenses specified on their description page. All structured data from the file and property namespaces is available under the Creative Commons CC0 License; all unstructured text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply.

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”. The ‘order’ is the number of rows and columns, so a magic square of order 4 means it has 4 rows and 4 columns. If N is the order, then N x N different numbers are used to. Universal Magic and Bimagic Squares of Orders 3 to 32 Using 2 and 5. This work brings, magic squares of order 3 to 32 just with two digits in such a way that the magic squares [ ] June 9, 0 Universal Magic and Bimagic Squares of Orders 3 to 32 Using 1 and 8. The basis for construction is the concept of base lines. For the purposes of this discussion a base line for the order-4 magic square is a 4-bit code containing equal numbers of 0's and 1's. The Order-4 Base Square Generator contains two base lines, one for the rows and the other for the columns. These are combined to make a base square. Media in category "Associative magic squares of order 4" The following 48 files are in this category, out of 48 total. Associative magic square 4x4 × ; 17 KB.