Never execute an upgrade without a valid licence code! Without a valid licence code you get only a demo version which expires after 30 days. A downgrade is not possible! To get a valid MagIC Net licence code, please contact your local Metrohm distributor.Please be aware that a new version of MagIC Net might require also an update of the instrument firmware (internal instrument software) to be able to operate the system afterwards successfully. For further information please contact your local Metrohm distributor.If you install the Chinese or traditional Chinese language update please make sure, that the respective character support is activated in the language settings of your personal computer.In order to install a language update, extract and execute the EXE file from the downloaded and compressed ZIP file. Installation will then be carried out automatically. MagIC Net 3.3.
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A 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, M. The magic constant of a normal magic square depends only on n and has the following value:M = n(n^2+1)/2 For normal magic squares of order n = 3, 4, 5.,the magic constants are: 15, 34, 65, 111, 175, 260.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.
Magic Square of size 3-2 7 69 5 14 3 8Sum in each row & each column = 3.(3^2+1)/2 = 15Magic Square of size 5-9 3 22 16 152 21 20 14 825 19 13 7 118 12 6 5 2411 10 4 23 17Sum in each row & each column = 5.(5^2+1)/2 = 65Magic Square of size 7-20 12 4 45 3 44 36 35 27 192 43 42 34 41 33 25 17 9 140 32 24 16 8 7 4831 23 15 14 6 47 3922 21 13 5 46 38 30Sum in each row & each column = 7.(7^2+1)/2 = 175Did you find any pattern in which the numbers are stored?In any magic square, the first number i.e. 1 is stored at position (n/2, n-1). Let this position be (i,j). The next number is stored at position (i-1, j+1) where we can consider each row & column as circular array i.e. They wrap around.Three conditions hold:1. 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-1.
Similarly, if the calculated column position becomes n, it will wrap around to 0.2. 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 1.3. If the calculated row position is -1 & calculated column position is n, the new position would be: (0, n-2).Example:Magic Square of size 3-2 7 69 5 14 3 8Steps:1. Position of number 1 = (3/2, 3-1) = (1, 2)2. Position of number 2 = (1-1, 2+1) = (0, 0)3. Position of number 3 = (0-1, 0+1) = (3-1, 1) = (2, 1)4.
Position of number 4 = (2-1, 1+1) = (1, 2)Since, at this position, 1 is there. So, apply condition 2.new position=(1+1,2-2)=(2,0)5.
Position of number 5=(2-1,0+1)=(1,1)6. Position of number 6=(1-1,1+1)=(0,2)7. Position of number 7 = (0-1, 2+1) = (-1,3) // this is tricky, see condition 3new position = (0, 3-2) = (0,1)8.
Position of number 8=(0-1,1+1)=(-1,2)=(2,2) //wrap around9. Position of number 9=(2-1,2+1)=(1,3)=(1,0) //wrap aroundBased on the above approach, following is the working code.