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MAGIC SQUARES

A magic square is a square array of numbers where consecutive numbers where ordered into a pattern of square  in such a manner that the numbers in each column, each row, and both diagonals of the square would sum up to the same numeric value.   The minimum size of a magic square is 3x3.  The 3x3 Magic Square has the form:

 

8

1

6

3

5

7

4

9

2

This square contains consecutive numbers from 1 to 9. In addition to this, each numbers in all columns, all rows, and both diagonals sums up to 15.  Magic Square has been documented in China as early as two thousand years ago. It comes in a form of a puzzle that is both a numerical and positional problem, where all the rows, columns and both diagonal of the square grid must add up to the same number.  Based on ancient Chinese records, the solution for the 3x3 magic square is called the Lo Shu diagram and has appeared as early as the first century AD.

A 4x4 Magic Square has the form

 

1

15

14

4

12

6

7

9

8

10

11

5

13

3

2

16

The square consists of consecutive numbers from 1 to 16.  All the rows, column, and the two diagonals have sum equal to 34.

 

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