Magic Square
Magic Square Puzzle
Hello and welcome to the largest and the most difficult mathematical puzzle game in the world. It is one of the oldest and mysterious game. It gave rise to several mathematical puzzle games which are renowned in the world. It is the mother of Sudoku puzzle game. Magic Square is a game which is very difficult to solve and several scientists gave different theories to solve and it remained a mystery to solve complex and large magic square puzzles.
Here, you will learn the game, it's rules and regulations, history, theories, tips & tricks to play the game and some secrets to solve the game. You can also make some money solving some complex magic square puzzles which I will show you where.
What is Magic Square?
In simple terms, Magic Square is an arrangement of numbers in a square table where each numbers present in the cells are different and the addition of numbers present in the cells give an equal sum called Magic Constant or Magic Number vertically, horizontally and diagonally. Magic Square orders are generally of two types either Even Magic Square Order (Such as 4x4, 6x6, 8x8 etc.) or Odd Magic Square Order (Such as 3x3, 5x5, 7x7 etc.). I will be explaining about Odd Magic Square mostly. Here is one example of Magic Square solved for the order of 3x3 which gives a Magic Constant of 15:
Magic Square Types
There are several magic square types and different scientist and researchers have given different names to their findings. However, in my opinion, I can categorise Magic Square into 3 types. These three types can be explained as follows:
1) Primary Magic Square
Primary Magic Square is the first and the most important magic square type. It is the key to solve magic square puzzles. It is an unique solution to a particular order of magic squares and helps in solving the other magic constant of a particular order. It is the first and minimal solution to a particular magic square order and contains the natural numbers in the cells starting with 1 and uses consecutive natural numbers to solve the minimal magic constant or magic number. Every Magic Square order has an unique Primary Magic Number which give birth to two other magic square types. It can be illustrated as follows:
2) Standard Magic Square
Standard Magic Square is the Secondary Magic Square which is obtained by the addition of same number to the Primary Magic Square. It also has the consecutive natural numbers present in the cells which doesn't start with 1 but more than 1 to give equal Magic Constant or Magic Number. This can be illustrated with the figure below:
3) Derived Magic Square
Derived Magic Square is the Tertiary Magic Square which is obtained by the multiplication or addition with some numbers to Primary and Standard Magic Squares. It can also be obtained by the variation with different numbers in the cells. It doesn't have consecutive natural numbers present in the cells. However, it gives the equal some after addition and solves the Magic Constant or Magic Number. It can be illustrated with the figure below:
Difference between Primary and Standard Magic Square
All Primary Magic Squares are Standard Magic Squares but Standard Magic Squares are not Primary Magic Squares. There is only one Primary Magic Square in each order of Magic Squares. But, there are uncountable numbers of Standard Magic Squares present in each order of Magic Square. Standard Magic Squares are the derivatives of Primary Magic Squares obtained by the addition of equal number to each number present in Primary Magic Square. It can be describe with the figure below where Derived Magic Square is obtained by adding value 1 to each cells of Primary Magic Square.
Difference between Standard and Derived Magic Square
Standard Magic Squares are Derived Magic Squares from Primary Magic Squares. However, all Derived Magic Squares are not Standard Magic Squares. Derived Magic Squares can either be obtained from Primary or Standard Magic Squares by multiplication, addition or variation of different numbers present in the cells. This can be illustrated with figure below where both are Derived Magic Squares with one solution to Magic Constant but Derived Magic Square is not Standard Magic Square because it doesn't have consecutive natural numbers and derived by multiplication with value 2 to the solution of 18 Magic Constant of Standard Magic Square as shown in figure above.
