Try changing the bottom row above: use "5,4,3,2,1,0" instead, do you get the same result as "4,3,2,1,0,1"?

### 65 is the Magic Sum of a 5 x 5 Magic Square

You can also try experimenting by writing in your own numbers in the red squares. To see the totals, press The numbers at the top and the left are the sums for the diagonal rows - including the broken diagonals. Explanation: The numbers in the Red Squares form the 3x3 magic Square. The numbers beside the Red Squares show the totals for each row. The horizontal and vertical totals are to the right and below in green squares. The other, blue, squares show the diagonal totals - including all of the "broken diagonals".

You can make your own Magic Square in two ways. Try both methods:. Observe the numbers in the Magic Square. This reveals the underlying structure of a 5x5 Magic Square. One pattern represents the large numbers and the other the small ones.

All 5x5 Pan-Magic Squares have a similar underlying structure. By changing the order of the numbers in these two sets of numbers, distinct squares are possible. Reflecting, rotating, and translocating, each square multiplies this by to give a grand total of 28, different 5x5 pan-magic squares. This method always produces "Pan-magic" squares, i. The magic square below is the sum of the patterns that these numbers make.

Use them or enter new ones and then click To understand the structure, move the mouse over the blue arrows and wait. Look at the pattern of your numbers in the square below The Bottom Right number under the blue down arrow above is the first number in the sequence for the square.

By convention it is "1", but any number can be used. Use them or enter new ones and then click. To understand the structure, move the mouse over the blue arrows and wait. Look at the pattern of your numbers in the square below. The Bottom Right number under the blue down arrow above is the first number in the sequence for the square.Tool to generate magic squares.

Magic Square - dCode. A suggestion? Write to dCode! Thanks to your feedback and relevant comments, dCode has developped the best Magic Square tool, so feel free to write! Thank you! Set number 1 on the left of the median line, the other numbers are written following the rule: if the cell is empty, in the cell in the bottom right of the previous one, else directly to the left of the occupied cell. When the cell does not exist, go to the other side of the matrix. For a size 3x3, the minimum constant is 15, for 4x4 it is 34, for 5x5 it is 65, 6x6 it isthen, Any lower sum will force the use of either negative numbers or fractions not whole numbers to solve the magic square.

Kaldor's magic square is a square used in economics, which has nothing to do with digits or numbers of mathematics but rather with concepts from economic policy. To download the online Magic Square script for offline use on PC, iPhone or Android, ask for price quote on contact page!

Message for dCode's team: Thanks to your feedback and relevant comments, dCode has developped the best Magic Square tool, so feel free to write! Send this message. See also: Equation Solver — Number Partitions.

Franklin's square is a panmagic square with a magic constant of Improve the Magic Square page!

Write a message Thanks to your feedback and relevant comments, dCode has developped the best Magic Square tool, so feel free to write! What are the minimal possible sums magic values? What is the Franklin Square? What is the Lo-Shu Magic Square? What is the KaldorMagic Square?

## The Sum Trick and Magic Square

Using dCode, you accept cookies for statistic and advertising purposes.The constant sum in every row, column and diagonal is called the magic constant or magic sumM. In this post, we will discuss how programmatically we can generate a magic square of size n. Before we go further, consider the below examples:. Did you find any pattern in which the numbers are stored?

In any magic square, the first number i. Let this position be i,j. The position of next number is calculated by decrementing row number of previous number by 1, and incrementing the column number of previous number by 1. At any time, if the calculated row position becomes -1, it will wrap around to n Similarly, if the calculated column position becomes n, it will wrap around to 0.

If the magic square already contains a number at the calculated position, calculated column position will be decremented by 2, and calculated row position will be incremented by 1.

This article is compiled by Aashish Barnwal and reviewed by GeeksforGeeks team. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Writing code in comment? Please use ide. Python program to generate. Fill the magic square. Printing magic square. To display output. This code is contributed. WriteLine "The Magic Square for ". WriteLine "Sum of each row or column ". WriteLine. Improved By : Mithun Kumarrathbhupendra.Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page. A Magic Square is an arrangement of numbers in a square grid, where the numbers in each row, and in each column, and the numbers in the diagonals, all add up to the same number.

Amazing mathematical magic square trick In the magic square trick, an audience names any two digit number between 22 and 99 and after you fill in the 16 boxes there will be 28 possible combinations where the boxes will add up to the given number. The trick to drawing the magic square is to realize that the numbers in a 4 by 4 magic square are always fixed as shown.

Look at the following video to see how to remember the numbers and their places in the square. Only the four numbers A, B, C, D are dependent on the number given by the audience. You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.During these challenging times, we guarantee we will work tirelessly to support you.

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We will get through this together. Updated: November 5, References. Magic squares have grown in popularity with the advent of mathematics-based games like Sudoku. 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.

Next, start your square by placing the number 1 in the center box of the top row. Then, arrange the rest of the numbers sequentially by moving up 1 row, then 1 column to the right. To learn more, including how to solve singly even magic squares and doubly even magic squares, read on. Did this summary help you? Yes No. Log in Facebook Loading Google Loading Civic Loading No account yet? Create an account.

**3x3 Magic Square**

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Article Edit. Learn why people trust wikiHow.A magic square whose rows and columns add up to a magic number but whose main diagonals do not, is known as a semimagic square. Composing functions cycleRows. Line is a user defined modulo function, and helps calculate the addends for the number that will go in the current position.

Generates an associative magic square. If the size is larger than 3, the square is also panmagic. The make-ms procedure allows to construct different magic squares for a same n, by modifying the grid filling moves. Defining the magic square as two applications of transpose.

Encoding the traditional 'Siamese' method. Finally, rotate each corresponding row and column of the table by the corresponding value in the list. See last column of version before moved to the top row. See here for the solution for all three cases.

This REXX version will also generate a square of an even order, but it'll not be a magic square. See here for all three cases. Create account Log in. Toggle navigation. Page Discussion Edit History.

Magic squares of odd order From Rosetta Code. Jump to: navigationsearch.

Works with : GNU bc. Works with : Fortran version 95 and later. Works with : Free Pascal version 1.The resulting pandiagonal magic squares can each in turn be transformed cyclically to 24 other magic squares by successively moving a row or column from 1 side of the square to the other side. Completing these transformations on all 36 essentially different magic squares will produce the complete set of pandiagonal magic squares of order Each of the 36 essentially different magic squares is transformed to 3 others as follows.

Square 1 - original square Square 2 - exchange rows and columns of original with diagonals Square 3 - row and column transformation of original by reassembling in order Square 4 - exchange rows and columns of square 3 above with diagonals 24 additional squares from each by cyclical transformations The total number of order-5 pandiagonal basic magic squares is 36 times 4 times 25 equals From above square to 4 1 9 12 20 23 15 18 21 4 7 24 2 10 13 16 8 11 19 22 5 17 25 3 6 14 To new rows diagonals to rows diagonals to rows.

Alan Grogono, in contrast, uses the mathematical approach and considers the total number of squares which includes rotations and reflections. When making the above transformations, the resulting magic square will not necessarily be normalized. That is, the second cell in the top row may not be smaller then the first cell in the second row. If required, this may simply be done by reflecting the square around the leading diagonal exchanging rows and columns.

No rotation will be required because the top left hand cell will always contain the number 1. It seems that if the original square is basic, about 4 of the 24 squares resulting from the cyclical transformation will be basic and the other 20 will require normalizing.

If the original square is not basic, none of the other 24 will be either. A comparison of the following derivatives from square 31 with those above from square 1 will show that different squares require normalization to produce a basic magic square.

Notice that the 36 essentially different squares I show on this page match the first of the squares shown by Grogono and Suzuki although all 3 sets are listed in different orders.

Because different lists of the fundamental magic squares may be compiled differently, lists by different persons will very likely not match. Regardless of which list of the fundamental squares is used, after the cyclical permutations are performed, and all resulting squares are normalized where requiredthe resulting list of sorted pandiagonal magic squares will be identical.

He uses the number series from 0 to 24 instead of 1 to 25 to simplify mathematical computing. His pages are now found in the MathForum.

The following 36 essentially different magic squares were compiled from tables in W. Benson and O. But it gets better! The fact that each letter appears once in each broken diagonal indicates that it is pandiagonal. The values for the capitol letters may be assigned the values 0, 5, 10, 15 and 20 in any order.

For the lower case letters, the values are 1, 2, 3, 4, 5, again in any order.

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