General Solutions for Even Order Magic Squares by Ching Tseng Shen

Cover of: General Solutions for Even Order Magic Squares | Ching Tseng Shen

Published by Victory Pr .

Written in English

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  • Combinatorics,
  • Magic squares

Book details

The Physical Object
ID Numbers
Open LibraryOL11633170M
ISBN 100962076570
ISBN 109780962076572

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Additional General Solutions for Even Order Magic Squares book Format: Online version: Shen, Ching Tseng, Magic squares. Monterey, CA: Victory Press, © (OCoLC) Document Type. 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.

However. 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. 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.4/5. Magic square of order 2 cannot be constructed. Normal magic squares of all sizes can be constructed except 2×2 (that is, where order n = 2). Number of magic squares of a given order.

Excluding rotations and reflections, there is exactly one 3×3 magic square, exactly 4×4 magic squares, and exactly5×5 magic squares. The set of all magic squares of order may be88 represented by MS().

The set of all magic squares of order whose magic constant is will be denoted MS() (19, p. An arbitrary row of a magic square will be denoted by with a subscript, such as.

Similarly,VV3File Size: KB. A magic square is an NxN square matrix whose numbers consist of consecutive numbers arranged so that the sum of each row and column, and both diagonals are equal to the same sum (which is called the magic number or magic constant).

A magic square of singly even order has a size that is a multiple of 4, plus 2 (e.g. 6, 10, 14). This means that the subsquares have an odd size, which plays a. Singly even order Magic Squares are those which are divisible by 2 but not by 4. The earliest square would be 6x6 order square, then we have 10x10, 14x14, 18x18 etc.

SINGLY EVEN ORDER - 6X6 SQUARE%(7). For a 24 by 24 magic square, the magic number isand the opposite number isFor a by magic square, the magic number isand the opposite number isand; For a by magic square, the magic number isand the opposite number is Well, that's all for this even order magic square recipe.

It turns out that 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 2 3 80 4 5 0 0 6 16 96 This accounts for all of.

2 2. Basic facts and definitions A primitive magic square (referred to as a magic square in what follows) of order n is a square consisting of the n2 distinct numbers 1, 2, 3,n2 in n2 subsquares such that the sum of each row, column and main diagonals adds up to the same total, n(n2 + 1)/2.

A double even order magic square is one whose order is divisible by : Abdullahi Umar. the history of magic squares. “Odd order” magic squares. Before I describe the “Gamma plus two” method of generating “odd order” magic squares, it helps if we realize that magic squares are actually a two dimensional representation of the surface of a doughnut; making the upper edge continuous with theFile Size: KB.

To commemorate the year Prime magic square A 67 13 Plus prime magic square BFile Size: 2MB. On these pages we will consider only even order Quadrant Magic Squares (QMS). Conditions for QMS Harvey May 22/ Only squares of orders 4x General Solutions for Even Order Magic Squares book be quadrant magic.

Orders 2, 6, 10, etc. have quadrants that are an odd order and so cannot contain the proper patterns. Even order squares divided in.

Hey guys I am trying to implement a method for solving singly even magic square, but it seems to generating the wrong results. Result generated by the following code Enter in size of square: Behforooz, Hossein: On Constructing 4 by 4 Magic Squares with Pre-assigned Magic Sum, J.

of Mathematical Spectrum; Vol. 40, No. 3, /, pp. Make magic squares using the following sets of nine numbers. 4, 4, 4, 13, 13, 13, 22, 22, 22 b. 27, 27, 27, 43, 43, 43, 59, 59, Make three different 3-by-3 magic squares that have a magic number of Find the magic number for each square and then complete the.

Solving Magic Squares: Generic Solutions to Solving Magic Squares [Simpson, Donald C.] on *FREE* shipping on qualifying offers. Solving Magic Squares: Generic Solutions to Solving Magic Squares Free day shipping within the U.S. when you order $ of eligible items sold or fulfilled by Amazon.

Or get business-day 1/5(1). Now, while this Magic Squares book may be a bit advanced for your toddler right now, it's never too young to start, because using the right approach and tools, it's perfectly feasible to teach your baby math and reading skills, even at the tender age of six months - then you can buy him my book.

Now generate the magic square of order $2m+1$ using the Siamese method centered on the array of letters (starting in the center square of the top row), but fill each set of four squares surrounding a letter sequentially, according to the order prescribed by the letter.

That order is illustrated on the left side of the figure below, and the. Magic squares of odd order You are encouraged to solve this task according to the task description, using any language you may know.

A magic square is an NxN square matrix whose numbers (usually integers) consist of consecutive numbers arranged so that the sum of each row and column, and both long (main) diagonals are equal to the same sum. This illustrated treatise on Magic Squares covers the history of Magic Squares, information about the general classes of Magic Squares, various formulae for creating Magic Squares, detailed analyses of 3 x 3, 4 x 4 and 5 x 5 Magic Squares, variations on Magic Squares, Magic Square routines, puzzles and presentations, including 'one novel contribution by the author which combines /5(4).

An enumeration of magic squares of order 5 is possible with existing personal computers, if you use a compiled language and a reduced program. In SeptemberI 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 MHz, under Turbo Pascal.

Each solution has a complement, just like magic squares. Super-Magic Stars: Six is the only order that can have the sum of peaks also magic.

Cell pairs equaling 6 pairs of cells define a way to put the 80 solutions into three groups. Definitions: Review magic star definitions and. This paper presents improved even order magic square construction algorithms, including both single even order magic square and double even order magic square construction algorithms.

Further, in order to show how the algorithms work, two specific magic squares are constructed. Moreover, the analysis of the algorithms is : Zhenhua Duan, Jin Liu, Jie Li, Cong Tian.

A magic square with magic total Magic squares with a given total Many magicians, including the authors of this paper, create magic squares as parts of their shows. Typically, an audience member is asked for a number (say between 30 and ) and the magician quickly creates a magic square and shows off the many ways that their total is Size: KB.

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.

Magic squares A magic square of order n is an arrangement of the integers from 1 to n 2 in an n × n matrix, with each number occurring exactly once, so that each row, each column, and each main diagonal has the same sum.

Prove that if a magic square of order n exists, the sum in question must be equal to n(n 2 + 1)/ b. This is a book on general recreational mathematics, but it does include a section on Magic Squares. The book is quite detailed in nature, but is oriented towards a mathematical analysis of its contents rather than any magical presentations.

Lorayne, H. () The Magic Book. London: W. Allen. The magic squares of odd order generated by MATLAB show a pattern with increasing elements generally moving diagonally up and to the right.

Contents Three Cases Odd Order A New Algorithm Doubly Even Order Singly Even Order Further Reading Three Cases The algorithms used by MATLAB for generating magic squares of order n fall into three cases: odd, n is odd. doubly-even, n. The Mathemagic of Magic Squares Steven Klee Outline What is a Magic Square.

History of Magic Squares Mathematics and Magic Squares Constructing Magic Squares Magic Circles Warm-Up The 15 Game Players take turns choosing numbers between 1 and 9, without repeats. The rst player to choose 3 numbers that add up to 15 Size: 1MB. These magic squares fall into three categories: those of odd order, those of even order, and those of doubly even order.

A square is of “odd” order if its order is an odd number. It's of “even” order if its order is an even number. (So far, duh. But.) A square is of “doubly even” File Size: KB. Magic Squares and Modular Arithmetic Jim Carlson November 7, 1 Introduction Recall that a magic square is a square array of consecutive distinct numbers such that all row and column sums and are the same.

Here is an example, a magic square of order three: 8 1 6 3 5 7 4 9 2 Fig. 1 The common row (or column) sum is called the magic sum. In File Size: 94KB. Source: Method for constructing a magic square of odd order (e.g. 3, 5, 7, 9,). A method for constructing magic squares of odd order was published by the French diplomat de la Loubère in his book A new historical relation of the kingdom of Siam (Du Royaume de Siam, ), under the chapter entitled The problem of the magical square according to the Indians.

An Order-9 pandiagonal Magic Square. The general belief among magic square enthusiasts has been that it is impossible to construct a pandiagonal order-9 magic square. However, in Mr.

Gakuho Abe discovered a whole series of such squares. See Dr. Alan Grogono's site at Magic Squares by "Grog" for more information.

For order 4, there are 3 orthogonal squares, which are squares are obtained with the 3 first basis; the 3 last basis give the same squares (see Appendix 3, § 5).

As a matter of fact, if you have one magic square which is solution. Many order-4 and higher antimagic squares, with all sums in consecutive order, were found by Lindon.

Charles W. Trigg, writing on "The Sums of Third Order Anti-Magic Squares," J ournal of Recreational Mathematics 2 (): —, showed that the eight sums of an order-3 antimagic square cannot be in any arithmetic progression,File Size: 1MB.

Solving 3 x 3 Magic Squares. Looks like it might be difficult, but if you know the secret, you can make and solve any 3 x 3 magic square. Here's the secret to solving any 3 x 3 magic square. Michelle J.

Linder's wonderful way with squares yields dozens of variations that even the newest quilter can make to create hundreds of beautiful blocks. See how one little square can be made into 12 different units that are mixed and matched to create Ni.

Doubly even order Squares. Doubly even Magic Squares: We have already formed the 8x8 square. The method used there can be always applied to form squares of ‘n’th order where ‘n’ is a multiple of 4.

This common value is called the “magic sum.” The order of a magic square is simply the number of rows (and columns) in the square. The magic square of Figure 10 is an order 3 magic square. By using the formula for the sum of the first n terms of an arithmetic sequence, it can be shown that if a magic square of order n has entries then theFile Size: KB.

Note: For singly-even n, it generate weak magic squares only. Singly-even magic squares Construction of magic square using basic Latin square is expressed in the following steps: Step First arrange the consecutive numbers 1 to n2 or () in basic Latin square format.

Find T.In the article Magic Squares we saw how to construct at least one magic square of any order. We can use some properties of magic squares to transform our manufactured square into many different magic squares. Some of the properties of magic squares are: A magic square will remain magic if any number is added to every number of a magic square.A magic square is an n × n array of numbers whose rows, columns, and the two diagonals sum to μ.A regular magic square satisfies the condition that the entries symmetrically placed with respect to the center sum to 2 μ circulant matrices we describe a construction of regular classical magic squares that are nonsingular for all odd by: 2.

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