Question

Construct a 5x5 magic square from all even numbers from 1 to 50.

Answer 1

Hint: To solve the problems based on magic squares we will first find out the value of the magic sum which will then be used in the magic square, then we will form each row and column in such a way where all the even numbers from 1 to 50 is used so that the sum of each row and column and also the sum of diagonal is equal to the magic sum.

Complete step-by-step solution:
To calculate the magic sum we will first need to find out the number of even terms in 1 to 50 which we will get it as 26 and then we will multiply with the number of columns or rows mentioned in the question which is 5 and we will finally get it as:
\[\Rightarrow \text{magic sum = }26\times 5=130\]
Now we will put all the numbers in such a way such that each even number from 1 to 50 is used only once in the whole table and the sum of each row and column will be equivalent to the magic sum. We will also have to make sure that the sum of diagonal elements of the magic square will give us the sum equivalent to the magic sum which we have calculated before. Now we will be using the same principle as Sudoku, which is we will first fill up the first row with random variables of our choice and then according to it we will form the magic square in which the sum of each diagonal, row, column will be equivalent to the magic sum.
So when we finally make a 5x5 magic square it will look something like this:

34	48	2	16	30
46	10	14	28	32
8	12	26	40	44
20	24	38	42	6
22	36	50	4	18

So when we finally add the rows, columns or even the diagonals we will get it equal to magic sum which is 130.
Let us take example of diagonal from top left to bottom right we will get it as:
34+10+26+42+18 = 130

Note: In this type of question there is many hit and trials which will be taking place to form the required magic square, to make the a magic square at the first try not to use big numbers in the first row itself try to balance each row and column by using big and small numbers at the same time so we will be able to use every single number provided.