Manuals/calci/MAGICSQUARE

MAGICSQUARE (Size,FirstNumber,GammaIncrement,Plus2Increment)

$Size$ is the size of the magic square.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle FirstNumber} is the value of the first number.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle GammaIncrement} is the value of the gamma increment.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Plus2Increment} is the value of the plus2 increment.

Description

This function gives the table values of a magic square.
A magic square contains set of numbers that is arranged in same number of rows and columns such that the sum of each row,column and the front and back main diagonals are the same value.
There are many ways to find the magic square values.
Also all the values are existing for magic square other than the 2x2 matrix.
Because it is impossible to construct the magic square of size 2.
Let the order of the magic square is n.
According to that the magic square is of three main types:

  1. Odd number. 
  2. Singly even 
  3. Doubly even.

Let the magic square of order n.
Odd number: It means that the magic square with the order of odd numbers.
To determine the sum of any normal magic square we use the formula: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{n*(n^2+1)}{2}} .
Singly even : It means the number which is divisible by 2 but not by 4.
There is no magic square constructed by 2x2 square matrix , so singly even magic square is constructed for 6,10,14 and so on.
So the formula for generating the singly even numbers is:Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (n*4)+2} .
The formula for magic sum for the singly even magic square is:Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{n*(n^2+1)}{2}} .
Doubly even: It means the number which is divisible by 4.
So doubly even square is constructed for 4,8,12 and so on.
The formula for magic sum for the doubly even magic square is:Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{n*(n^2+1)}{2}} .
In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle MAGICSQUARE (Size,FirstNumber,GammaIncrement,Plus2Increment)} , is the size of the magic square.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle FirstNumber} is the starting number which is indicating the numbers have to start from.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle GammaIncrement} is the gamma increment and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Plus2Increment} is the plus 2 increment.
The formulas for the magic square is:
Let square size = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M} ,First number = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F} ,Gamma increment = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle GI} ,and Plus two increment = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle PI} .

*Pure Sum=(1/2)(M)(M^2+1).
*First number total=M(F-1). 
*CT=1+2+..M.
*Gamma increment total(GIT)=(CT-M){M(GI-1)}.
*PIT(Plus2 Increment Total )=(CT-M)(PI-1).                    
*SET(singly even total)=(M*M/2)(PI-GI) for singly even, 0 otherwise. 
*Calculated Magic Sum = PS + FT + GIT + PIT + SET

Instead of MAGICSQUARE we can write as "MS".

Examples

1.MAGICSQUARE(3)

2	7	6
9	5	1
4	3	8

2.MAGICSQUARE(4,7,2,4)

7	41	39	13
33	19	21	27
23	29	31	17
37	11	9	43

3.MAGICSQUARE(6,4,2,3)

69	18	15	48	60	57
22	76	4	64	55	46
74	8	20	53	50	62
6	81	78	27	39	36
85	13	67	43	34	25
11	71	83	32	29	41

4.MS(3,3,2,3)

5	17	14
21	12	3
10	7	19

References

Magic Square

Manuals/calci/MAGICSQUARE

Contents

Description

Examples

Related Videos

See Also

References

69	18	15	48	60	57
22	76	4	64	55	46
74	8	20	53	50	62
6	81	78	27	39	36
85	13	67	43	34	25
11	71	83	32	29	41

69	18	15	48	60	57
22	76	4	64	55	46
74	8	20	53	50	62
6	81	78	27	39	36
85	13	67	43	34	25
11	71	83	32	29	41

69	18	15	48	60	57
22	76	4	64	55	46
74	8	20	53	50	62
6	81	78	27	39	36
85	13	67	43	34	25
11	71	83	32	29	41